mirror of
https://github.com/princeton-nlp/tree-of-thought-llm
synced 2025-06-26 18:26:00 +00:00
fixed parsing issue
This commit is contained in:
emilyworks
parent
e614118830
commit
1b780a1dd8
@ -1,330 +0,0 @@
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[
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{
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"steps": [
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{
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"step": 0,
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"x": "4 5 6 10",
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"ys": [
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""
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],
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"new_ys": [
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"4 + 5 = 9 (left: 6 9 10)\n"
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],
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"values": [
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1.0
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],
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"select_new_ys": [
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"4 + 5 = 9 (left: 6 9 10)\n"
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]
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},
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{
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"step": 1,
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"x": "4 5 6 10",
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"ys": [
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"4 + 5 = 9 (left: 6 9 10)\n"
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],
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"new_ys": [
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"4 + 5 = 9 (left: 6 9 10)\n6 + 9 = 15 (left: 10 15)\n"
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],
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"values": [
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0.001
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],
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"select_new_ys": [
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"4 + 5 = 9 (left: 6 9 10)\n6 + 9 = 15 (left: 10 15)\n"
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]
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},
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{
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"step": 2,
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"x": "4 5 6 10",
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"ys": [
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"4 + 5 = 9 (left: 6 9 10)\n6 + 9 = 15 (left: 10 15)\n"
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],
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"new_ys": [
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"4 + 5 = 9 (left: 6 9 10)\n6 + 9 = 15 (left: 10 15)\n10 + 15 = 25 (left: 25)\n"
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],
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"values": [
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0.001
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||||
],
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"select_new_ys": [
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"4 + 5 = 9 (left: 6 9 10)\n6 + 9 = 15 (left: 10 15)\n10 + 15 = 25 (left: 25)\n"
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]
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},
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{
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"step": 3,
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"x": "4 5 6 10",
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"ys": [
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"4 + 5 = 9 (left: 6 9 10)\n6 + 9 = 15 (left: 10 15)\n10 + 15 = 25 (left: 25)\n"
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],
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"new_ys": [
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"4 + 5 = 9 (left: 6 9 10)\n6 + 9 = 15 (left: 10 15)\n10 + 15 = 25 (left: 25)\n25 + 2 = 27 (left: 8 8 14 27)\n"
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],
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"values": [
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0
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||||
],
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"select_new_ys": [
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"4 + 5 = 9 (left: 6 9 10)\n6 + 9 = 15 (left: 10 15)\n10 + 15 = 25 (left: 25)\n25 + 2 = 27 (left: 8 8 14 27)\n"
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]
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}
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],
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"idx": 900,
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"ys": [
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"4 + 5 = 9 (left: 6 9 10)\n6 + 9 = 15 (left: 10 15)\n10 + 15 = 25 (left: 25)\n25 + 2 = 27 (left: 8 8 14 27)\n"
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],
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"infos": [
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{
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"r": 0
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}
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],
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"usage_so_far": {
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"prompt_tokens": 2228,
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"cost": 0.11214000000000002
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}
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},
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{
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"steps": [
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{
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"step": 0,
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"x": "1 2 4 7",
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"ys": [
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""
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],
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"new_ys": [
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"1 + 2 = 3 (left: 3 4 7)\n"
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],
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"values": [
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1.0
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],
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"select_new_ys": [
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"1 + 2 = 3 (left: 3 4 7)\n"
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]
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},
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{
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"step": 1,
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"x": "1 2 4 7",
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"ys": [
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"1 + 2 = 3 (left: 3 4 7)\n"
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],
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"new_ys": [
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"1 + 2 = 3 (left: 3 4 7)\n3 + 4 = 7 (left: 7 7)\n"
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],
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"values": [
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0.001
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],
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"select_new_ys": [
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"1 + 2 = 3 (left: 3 4 7)\n3 + 4 = 7 (left: 7 7)\n"
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]
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},
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{
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"step": 2,
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"x": "1 2 4 7",
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"ys": [
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"1 + 2 = 3 (left: 3 4 7)\n3 + 4 = 7 (left: 7 7)\n"
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],
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"new_ys": [
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"1 + 2 = 3 (left: 3 4 7)\n3 + 4 = 7 (left: 7 7)\n7 + 7 = 14 (left: 14)\n"
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],
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"values": [
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0.001
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],
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"select_new_ys": [
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"1 + 2 = 3 (left: 3 4 7)\n3 + 4 = 7 (left: 7 7)\n7 + 7 = 14 (left: 14)\n"
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]
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},
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{
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"step": 3,
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"x": "1 2 4 7",
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"ys": [
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"1 + 2 = 3 (left: 3 4 7)\n3 + 4 = 7 (left: 7 7)\n7 + 7 = 14 (left: 14)\n"
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],
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"new_ys": [
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"1 + 2 = 3 (left: 3 4 7)\n3 + 4 = 7 (left: 7 7)\n7 + 7 = 14 (left: 14)\n14 + 2 = 16 (left: 8 8 16)\n"
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],
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"values": [
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0
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||||
],
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"select_new_ys": [
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"1 + 2 = 3 (left: 3 4 7)\n3 + 4 = 7 (left: 7 7)\n7 + 7 = 14 (left: 14)\n14 + 2 = 16 (left: 8 8 16)\n"
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]
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}
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],
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"idx": 901,
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"ys": [
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"1 + 2 = 3 (left: 3 4 7)\n3 + 4 = 7 (left: 7 7)\n7 + 7 = 14 (left: 14)\n14 + 2 = 16 (left: 8 8 16)\n"
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],
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"infos": [
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{
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"r": 0
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}
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],
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"usage_so_far": {
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"completion_tokens": 1403,
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"prompt_tokens": 4454,
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"cost": 0.2178
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}
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},
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{
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"steps": [
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{
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"step": 0,
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"x": "2 5 8 11",
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"ys": [
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""
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],
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"new_ys": [
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"2 + 5 = 7 (left: 7 8 11)\n"
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],
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"values": [
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1.0
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],
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"select_new_ys": [
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"2 + 5 = 7 (left: 7 8 11)\n"
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]
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},
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{
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"step": 1,
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"x": "2 5 8 11",
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"ys": [
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"2 + 5 = 7 (left: 7 8 11)\n"
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],
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"new_ys": [
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"2 + 5 = 7 (left: 7 8 11)\n7 + 8 = 15 (left: 11 15)\n"
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],
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"values": [
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0.001
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],
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"select_new_ys": [
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"2 + 5 = 7 (left: 7 8 11)\n7 + 8 = 15 (left: 11 15)\n"
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]
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},
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{
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"step": 2,
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"x": "2 5 8 11",
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"ys": [
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"2 + 5 = 7 (left: 7 8 11)\n7 + 8 = 15 (left: 11 15)\n"
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],
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"new_ys": [
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"2 + 5 = 7 (left: 7 8 11)\n7 + 8 = 15 (left: 11 15)\n11 + 15 = 26 (left: 26)\n"
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],
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"values": [
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0.001
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],
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"select_new_ys": [
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"2 + 5 = 7 (left: 7 8 11)\n7 + 8 = 15 (left: 11 15)\n11 + 15 = 26 (left: 26)\n"
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]
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},
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{
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"step": 3,
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"x": "2 5 8 11",
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"ys": [
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"2 + 5 = 7 (left: 7 8 11)\n7 + 8 = 15 (left: 11 15)\n11 + 15 = 26 (left: 26)\n"
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],
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"new_ys": [
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"2 + 5 = 7 (left: 7 8 11)\n7 + 8 = 15 (left: 11 15)\n11 + 15 = 26 (left: 26)\n26 + 2 = 28 (left: 8 8 14 28)\n"
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],
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"values": [
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0
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],
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"select_new_ys": [
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"2 + 5 = 7 (left: 7 8 11)\n7 + 8 = 15 (left: 11 15)\n11 + 15 = 26 (left: 26)\n26 + 2 = 28 (left: 8 8 14 28)\n"
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]
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}
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],
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"idx": 902,
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"ys": [
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"2 + 5 = 7 (left: 7 8 11)\n7 + 8 = 15 (left: 11 15)\n11 + 15 = 26 (left: 26)\n26 + 2 = 28 (left: 8 8 14 28)\n"
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],
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"infos": [
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{
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"r": 0
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}
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],
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"usage_so_far": {
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"completion_tokens": 2166,
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"prompt_tokens": 6682,
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"cost": 0.33042
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}
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},
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{
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"steps": [
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{
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"step": 0,
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"x": "3 4 4 13",
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"ys": [
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""
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],
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"new_ys": [
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"3 + 4 = 7 (left: 4 7 13)\n"
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],
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"values": [
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20.0
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],
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"select_new_ys": [
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"3 + 4 = 7 (left: 4 7 13)\n"
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]
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},
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{
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"step": 1,
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"x": "3 4 4 13",
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"ys": [
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"3 + 4 = 7 (left: 4 7 13)\n"
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],
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"new_ys": [
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"3 + 4 = 7 (left: 4 7 13)\n4 + 7 = 11 (left: 11 13)\n"
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],
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"values": [
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20.0
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],
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"select_new_ys": [
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"3 + 4 = 7 (left: 4 7 13)\n4 + 7 = 11 (left: 11 13)\n"
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]
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},
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{
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"step": 2,
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"x": "3 4 4 13",
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"ys": [
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"3 + 4 = 7 (left: 4 7 13)\n4 + 7 = 11 (left: 11 13)\n"
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],
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"new_ys": [
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"3 + 4 = 7 (left: 4 7 13)\n4 + 7 = 11 (left: 11 13)\n11 + 13 = 24 (left: 24)\n"
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],
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"values": [
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0.0
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],
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"select_new_ys": [
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"3 + 4 = 7 (left: 4 7 13)\n4 + 7 = 11 (left: 11 13)\n11 + 13 = 24 (left: 24)\n"
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]
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},
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{
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"step": 3,
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"x": "3 4 4 13",
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"ys": [
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"3 + 4 = 7 (left: 4 7 13)\n4 + 7 = 11 (left: 11 13)\n11 + 13 = 24 (left: 24)\n"
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],
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"new_ys": [
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"3 + 4 = 7 (left: 4 7 13)\n4 + 7 = 11 (left: 11 13)\n11 + 13 = 24 (left: 24)\nAnswer: (3 + 4) + (4 + 7) = 24\n"
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],
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"values": [
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0.001
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],
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"select_new_ys": [
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"3 + 4 = 7 (left: 4 7 13)\n4 + 7 = 11 (left: 11 13)\n11 + 13 = 24 (left: 24)\nAnswer: (3 + 4) + (4 + 7) = 24\n"
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]
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}
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],
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"idx": 903,
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"ys": [
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"3 + 4 = 7 (left: 4 7 13)\n4 + 7 = 11 (left: 11 13)\n11 + 13 = 24 (left: 24)\nAnswer: (3 + 4) + (4 + 7) = 24\n"
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],
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"infos": [
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{
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"r": 0
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}
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],
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"usage_so_far": {
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"completion_tokens": 2531,
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"prompt_tokens": 9163,
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"cost": 0.42675
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}
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}
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]
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File diff suppressed because it is too large
Load Diff
File diff suppressed because it is too large
Load Diff
@ -1,412 +0,0 @@
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[
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{
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"steps": [
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{
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"step": 0,
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"x": "1 1 4 6",
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"ys": [
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""
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],
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"new_ys": [
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"To determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input `1 1 4 6`:\n"
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],
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"values": [
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0.0
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],
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"select_new_ys": [
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"To determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input `1 1 4 6`:\n"
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]
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},
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{
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"step": 1,
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"x": "1 1 4 6",
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"ys": [
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"To determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input `1 1 4 6`:\n"
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],
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"new_ys": [
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"To determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input `1 1 4 6`:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. Here are the possible next steps for the input list `2 8 8 14`:\n"
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],
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"values": [
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0.001
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],
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"select_new_ys": [
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"To determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input `1 1 4 6`:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. Here are the possible next steps for the input list `2 8 8 14`:\n"
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]
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},
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{
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"step": 2,
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"x": "1 1 4 6",
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"ys": [
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"To determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input `1 1 4 6`:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. Here are the possible next steps for the input list `2 8 8 14`:\n"
|
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],
|
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"new_ys": [
|
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"To determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input `1 1 4 6`:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. Here are the possible next steps for the input list `2 8 8 14`:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input list `2 8 8 14`:\n"
|
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],
|
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"values": [
|
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0.001
|
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],
|
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"select_new_ys": [
|
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"To determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input `1 1 4 6`:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. Here are the possible next steps for the input list `2 8 8 14`:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input list `2 8 8 14`:\n"
|
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]
|
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},
|
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{
|
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"step": 3,
|
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"x": "1 1 4 6",
|
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"ys": [
|
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"To determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input `1 1 4 6`:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. Here are the possible next steps for the input list `2 8 8 14`:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input list `2 8 8 14`:\n"
|
||||
],
|
||||
"new_ys": [
|
||||
"To determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input `1 1 4 6`:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. Here are the possible next steps for the input list `2 8 8 14`:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input list `2 8 8 14`:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input list `2 8 8 14`:\n"
|
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],
|
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"values": [
|
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0.001
|
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],
|
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"select_new_ys": [
|
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"To determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input `1 1 4 6`:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. Here are the possible next steps for the input list `2 8 8 14`:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input list `2 8 8 14`:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input list `2 8 8 14`:\n"
|
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]
|
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}
|
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],
|
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"idx": 0,
|
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"ys": [
|
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"To determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input `1 1 4 6`:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. Here are the possible next steps for the input list `2 8 8 14`:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input list `2 8 8 14`:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input list `2 8 8 14`:\n"
|
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],
|
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"infos": [
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{
|
||||
"r": 0
|
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}
|
||||
],
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"usage_so_far": {
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||||
"completion_tokens": 3135,
|
||||
"prompt_tokens": 1833,
|
||||
"cost": 0.24308999999999997
|
||||
}
|
||||
},
|
||||
{
|
||||
"steps": [
|
||||
{
|
||||
"step": 0,
|
||||
"x": "1 1 11 11",
|
||||
"ys": [
|
||||
""
|
||||
],
|
||||
"new_ys": [
|
||||
"To determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. After performing an operation, the two numbers are replaced by the result, and the list is updated. Here are the possible next steps for the input `1 1 11 11`:\n"
|
||||
],
|
||||
"values": [
|
||||
0.0
|
||||
],
|
||||
"select_new_ys": [
|
||||
"To determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. After performing an operation, the two numbers are replaced by the result, and the list is updated. Here are the possible next steps for the input `1 1 11 11`:\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"step": 1,
|
||||
"x": "1 1 11 11",
|
||||
"ys": [
|
||||
"To determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. After performing an operation, the two numbers are replaced by the result, and the list is updated. Here are the possible next steps for the input `1 1 11 11`:\n"
|
||||
],
|
||||
"new_ys": [
|
||||
"To determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. After performing an operation, the two numbers are replaced by the result, and the list is updated. Here are the possible next steps for the input `1 1 11 11`:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. Here are the possible next steps for the input list `2 8 8 14`:\n"
|
||||
],
|
||||
"values": [
|
||||
0.001
|
||||
],
|
||||
"select_new_ys": [
|
||||
"To determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. After performing an operation, the two numbers are replaced by the result, and the list is updated. Here are the possible next steps for the input `1 1 11 11`:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. Here are the possible next steps for the input list `2 8 8 14`:\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"step": 2,
|
||||
"x": "1 1 11 11",
|
||||
"ys": [
|
||||
"To determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. After performing an operation, the two numbers are replaced by the result, and the list is updated. Here are the possible next steps for the input `1 1 11 11`:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. Here are the possible next steps for the input list `2 8 8 14`:\n"
|
||||
],
|
||||
"new_ys": [
|
||||
"To determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. After performing an operation, the two numbers are replaced by the result, and the list is updated. Here are the possible next steps for the input `1 1 11 11`:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. Here are the possible next steps for the input list `2 8 8 14`:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input list 2, 8, 8, 14:\n"
|
||||
],
|
||||
"values": [
|
||||
0.001
|
||||
],
|
||||
"select_new_ys": [
|
||||
"To determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. After performing an operation, the two numbers are replaced by the result, and the list is updated. Here are the possible next steps for the input `1 1 11 11`:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. Here are the possible next steps for the input list `2 8 8 14`:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input list 2, 8, 8, 14:\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"step": 3,
|
||||
"x": "1 1 11 11",
|
||||
"ys": [
|
||||
"To determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. After performing an operation, the two numbers are replaced by the result, and the list is updated. Here are the possible next steps for the input `1 1 11 11`:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. Here are the possible next steps for the input list `2 8 8 14`:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input list 2, 8, 8, 14:\n"
|
||||
],
|
||||
"new_ys": [
|
||||
"To determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. After performing an operation, the two numbers are replaced by the result, and the list is updated. Here are the possible next steps for the input `1 1 11 11`:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. Here are the possible next steps for the input list `2 8 8 14`:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input list 2, 8, 8, 14:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. Here are the possible next steps for the input numbers 2, 8, 8, and 14:\n"
|
||||
],
|
||||
"values": [
|
||||
0
|
||||
],
|
||||
"select_new_ys": [
|
||||
"To determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. After performing an operation, the two numbers are replaced by the result, and the list is updated. Here are the possible next steps for the input `1 1 11 11`:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. Here are the possible next steps for the input list `2 8 8 14`:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input list 2, 8, 8, 14:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. Here are the possible next steps for the input numbers 2, 8, 8, and 14:\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"idx": 1,
|
||||
"ys": [
|
||||
"To determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. After performing an operation, the two numbers are replaced by the result, and the list is updated. Here are the possible next steps for the input `1 1 11 11`:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. Here are the possible next steps for the input list `2 8 8 14`:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input list 2, 8, 8, 14:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. Here are the possible next steps for the input numbers 2, 8, 8, and 14:\n"
|
||||
],
|
||||
"infos": [
|
||||
{
|
||||
"r": 0
|
||||
}
|
||||
],
|
||||
"usage_so_far": {
|
||||
"completion_tokens": 5678,
|
||||
"prompt_tokens": 4034,
|
||||
"cost": 0.4617
|
||||
}
|
||||
},
|
||||
{
|
||||
"steps": [
|
||||
{
|
||||
"step": 0,
|
||||
"x": "1 1 3 8",
|
||||
"ys": [
|
||||
""
|
||||
],
|
||||
"new_ys": [
|
||||
"To determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input `1 1 3 8`:\n"
|
||||
],
|
||||
"values": [
|
||||
0.0
|
||||
],
|
||||
"select_new_ys": [
|
||||
"To determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input `1 1 3 8`:\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"step": 1,
|
||||
"x": "1 1 3 8",
|
||||
"ys": [
|
||||
"To determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input `1 1 3 8`:\n"
|
||||
],
|
||||
"new_ys": [
|
||||
"To determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input `1 1 3 8`:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. Here are the possible next steps for the input numbers 2, 8, 8, and 14:\n"
|
||||
],
|
||||
"values": [
|
||||
0.001
|
||||
],
|
||||
"select_new_ys": [
|
||||
"To determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input `1 1 3 8`:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. Here are the possible next steps for the input numbers 2, 8, 8, and 14:\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"step": 2,
|
||||
"x": "1 1 3 8",
|
||||
"ys": [
|
||||
"To determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input `1 1 3 8`:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. Here are the possible next steps for the input numbers 2, 8, 8, and 14:\n"
|
||||
],
|
||||
"new_ys": [
|
||||
"To determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input `1 1 3 8`:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. Here are the possible next steps for the input numbers 2, 8, 8, and 14:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input list `2 8 8 14`:\n"
|
||||
],
|
||||
"values": [
|
||||
0.001
|
||||
],
|
||||
"select_new_ys": [
|
||||
"To determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input `1 1 3 8`:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. Here are the possible next steps for the input numbers 2, 8, 8, and 14:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input list `2 8 8 14`:\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"step": 3,
|
||||
"x": "1 1 3 8",
|
||||
"ys": [
|
||||
"To determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input `1 1 3 8`:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. Here are the possible next steps for the input numbers 2, 8, 8, and 14:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input list `2 8 8 14`:\n"
|
||||
],
|
||||
"new_ys": [
|
||||
"To determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input `1 1 3 8`:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. Here are the possible next steps for the input numbers 2, 8, 8, and 14:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input list `2 8 8 14`:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. Here are the possible next steps for the input list `2 8 8 14`:\n"
|
||||
],
|
||||
"values": [
|
||||
0
|
||||
],
|
||||
"select_new_ys": [
|
||||
"To determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input `1 1 3 8`:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. Here are the possible next steps for the input numbers 2, 8, 8, and 14:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input list `2 8 8 14`:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. Here are the possible next steps for the input list `2 8 8 14`:\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"idx": 2,
|
||||
"ys": [
|
||||
"To determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input `1 1 3 8`:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. Here are the possible next steps for the input numbers 2, 8, 8, and 14:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input list `2 8 8 14`:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. Here are the possible next steps for the input list `2 8 8 14`:\n"
|
||||
],
|
||||
"infos": [
|
||||
{
|
||||
"r": 0
|
||||
}
|
||||
],
|
||||
"usage_so_far": {
|
||||
"completion_tokens": 8876,
|
||||
"prompt_tokens": 6219,
|
||||
"cost": 0.7191299999999999
|
||||
}
|
||||
},
|
||||
{
|
||||
"steps": [
|
||||
{
|
||||
"step": 0,
|
||||
"x": "1 1 1 8",
|
||||
"ys": [
|
||||
""
|
||||
],
|
||||
"new_ys": [
|
||||
"To determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input `1 1 1 8`:\n"
|
||||
],
|
||||
"values": [
|
||||
0.0
|
||||
],
|
||||
"select_new_ys": [
|
||||
"To determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input `1 1 1 8`:\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"step": 1,
|
||||
"x": "1 1 1 8",
|
||||
"ys": [
|
||||
"To determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input `1 1 1 8`:\n"
|
||||
],
|
||||
"new_ys": [
|
||||
"To determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input `1 1 1 8`:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. Here are the possible next steps for the input \"2 8 8 14\":\n"
|
||||
],
|
||||
"values": [
|
||||
0.001
|
||||
],
|
||||
"select_new_ys": [
|
||||
"To determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input `1 1 1 8`:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. Here are the possible next steps for the input \"2 8 8 14\":\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"step": 2,
|
||||
"x": "1 1 1 8",
|
||||
"ys": [
|
||||
"To determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input `1 1 1 8`:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. Here are the possible next steps for the input \"2 8 8 14\":\n"
|
||||
],
|
||||
"new_ys": [
|
||||
"To determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input `1 1 1 8`:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. Here are the possible next steps for the input \"2 8 8 14\":\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. Here are the possible next steps for the input numbers 2, 8, 8, and 14:\n"
|
||||
],
|
||||
"values": [
|
||||
0.001
|
||||
],
|
||||
"select_new_ys": [
|
||||
"To determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input `1 1 1 8`:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. Here are the possible next steps for the input \"2 8 8 14\":\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. Here are the possible next steps for the input numbers 2, 8, 8, and 14:\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"step": 3,
|
||||
"x": "1 1 1 8",
|
||||
"ys": [
|
||||
"To determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input `1 1 1 8`:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. Here are the possible next steps for the input \"2 8 8 14\":\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. Here are the possible next steps for the input numbers 2, 8, 8, and 14:\n"
|
||||
],
|
||||
"new_ys": [
|
||||
"To determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input `1 1 1 8`:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. Here are the possible next steps for the input \"2 8 8 14\":\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. Here are the possible next steps for the input numbers 2, 8, 8, and 14:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. Here are the possible next steps for the input list `2 8 8 14`:\n"
|
||||
],
|
||||
"values": [
|
||||
0
|
||||
],
|
||||
"select_new_ys": [
|
||||
"To determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input `1 1 1 8`:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. Here are the possible next steps for the input \"2 8 8 14\":\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. Here are the possible next steps for the input numbers 2, 8, 8, and 14:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. Here are the possible next steps for the input list `2 8 8 14`:\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"idx": 3,
|
||||
"ys": [
|
||||
"To determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list and replace them with the result. Here are the possible next steps for the input `1 1 1 8`:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. Here are the possible next steps for the input \"2 8 8 14\":\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. Here are the possible next steps for the input numbers 2, 8, 8, and 14:\nTo determine the possible next steps, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers from the list. Here are the possible next steps for the input list `2 8 8 14`:\n"
|
||||
],
|
||||
"infos": [
|
||||
{
|
||||
"r": 0
|
||||
}
|
||||
],
|
||||
"usage_so_far": {
|
||||
"completion_tokens": 11846,
|
||||
"prompt_tokens": 8396,
|
||||
"cost": 0.9626399999999999
|
||||
}
|
||||
},
|
||||
{
|
||||
"steps": [
|
||||
{
|
||||
"step": 0,
|
||||
"x": "6 6 6 6",
|
||||
"ys": [
|
||||
""
|
||||
],
|
||||
"new_ys": [
|
||||
"To determine the possible next steps, we can apply basic arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers in the list. Here are the possible next steps for the input `6 6 6 6`:\n"
|
||||
],
|
||||
"values": [
|
||||
0.0
|
||||
],
|
||||
"select_new_ys": [
|
||||
"To determine the possible next steps, we can apply basic arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers in the list. Here are the possible next steps for the input `6 6 6 6`:\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"step": 1,
|
||||
"x": "6 6 6 6",
|
||||
"ys": [
|
||||
"To determine the possible next steps, we can apply basic arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers in the list. Here are the possible next steps for the input `6 6 6 6`:\n"
|
||||
],
|
||||
"new_ys": [
|
||||
"To determine the possible next steps, we can apply basic arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers in the list. Here are the possible next steps for the input `6 6 6 6`:\nTo determine the possible next steps, we can apply basic arithmetic operations (addition, subtraction, multiplication, and division) to any pair of numbers from the list. Here are the possible next steps for the input list `2 8 8 14`:\n"
|
||||
],
|
||||
"values": [
|
||||
0.0
|
||||
],
|
||||
"select_new_ys": [
|
||||
"To determine the possible next steps, we can apply basic arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers in the list. Here are the possible next steps for the input `6 6 6 6`:\nTo determine the possible next steps, we can apply basic arithmetic operations (addition, subtraction, multiplication, and division) to any pair of numbers from the list. Here are the possible next steps for the input list `2 8 8 14`:\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"step": 2,
|
||||
"x": "6 6 6 6",
|
||||
"ys": [
|
||||
"To determine the possible next steps, we can apply basic arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers in the list. Here are the possible next steps for the input `6 6 6 6`:\nTo determine the possible next steps, we can apply basic arithmetic operations (addition, subtraction, multiplication, and division) to any pair of numbers from the list. Here are the possible next steps for the input list `2 8 8 14`:\n"
|
||||
],
|
||||
"new_ys": [
|
||||
"To determine the possible next steps, we can apply basic arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers in the list. Here are the possible next steps for the input `6 6 6 6`:\nTo determine the possible next steps, we can apply basic arithmetic operations (addition, subtraction, multiplication, and division) to any pair of numbers from the list. Here are the possible next steps for the input list `2 8 8 14`:\nTo determine the possible next steps, we can apply basic arithmetic operations (addition, subtraction, multiplication, and division) to any pair of numbers from the list. Here are the possible next steps for the input numbers 2, 8, 8, and 14:\n"
|
||||
],
|
||||
"values": [
|
||||
0.0
|
||||
],
|
||||
"select_new_ys": [
|
||||
"To determine the possible next steps, we can apply basic arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers in the list. Here are the possible next steps for the input `6 6 6 6`:\nTo determine the possible next steps, we can apply basic arithmetic operations (addition, subtraction, multiplication, and division) to any pair of numbers from the list. Here are the possible next steps for the input list `2 8 8 14`:\nTo determine the possible next steps, we can apply basic arithmetic operations (addition, subtraction, multiplication, and division) to any pair of numbers from the list. Here are the possible next steps for the input numbers 2, 8, 8, and 14:\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"step": 3,
|
||||
"x": "6 6 6 6",
|
||||
"ys": [
|
||||
"To determine the possible next steps, we can apply basic arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers in the list. Here are the possible next steps for the input `6 6 6 6`:\nTo determine the possible next steps, we can apply basic arithmetic operations (addition, subtraction, multiplication, and division) to any pair of numbers from the list. Here are the possible next steps for the input list `2 8 8 14`:\nTo determine the possible next steps, we can apply basic arithmetic operations (addition, subtraction, multiplication, and division) to any pair of numbers from the list. Here are the possible next steps for the input numbers 2, 8, 8, and 14:\n"
|
||||
],
|
||||
"new_ys": [
|
||||
"To determine the possible next steps, we can apply basic arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers in the list. Here are the possible next steps for the input `6 6 6 6`:\nTo determine the possible next steps, we can apply basic arithmetic operations (addition, subtraction, multiplication, and division) to any pair of numbers from the list. Here are the possible next steps for the input list `2 8 8 14`:\nTo determine the possible next steps, we can apply basic arithmetic operations (addition, subtraction, multiplication, and division) to any pair of numbers from the list. Here are the possible next steps for the input numbers 2, 8, 8, and 14:\nTo determine the possible next steps, we can apply basic arithmetic operations (addition, subtraction, multiplication, and division) to any pair of numbers from the list. Here are the possible next steps for the input list `2 8 8 14`:\n"
|
||||
],
|
||||
"values": [
|
||||
0.0
|
||||
],
|
||||
"select_new_ys": [
|
||||
"To determine the possible next steps, we can apply basic arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers in the list. Here are the possible next steps for the input `6 6 6 6`:\nTo determine the possible next steps, we can apply basic arithmetic operations (addition, subtraction, multiplication, and division) to any pair of numbers from the list. Here are the possible next steps for the input list `2 8 8 14`:\nTo determine the possible next steps, we can apply basic arithmetic operations (addition, subtraction, multiplication, and division) to any pair of numbers from the list. Here are the possible next steps for the input numbers 2, 8, 8, and 14:\nTo determine the possible next steps, we can apply basic arithmetic operations (addition, subtraction, multiplication, and division) to any pair of numbers from the list. Here are the possible next steps for the input list `2 8 8 14`:\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"idx": 4,
|
||||
"ys": [
|
||||
"To determine the possible next steps, we can apply basic arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers in the list. Here are the possible next steps for the input `6 6 6 6`:\nTo determine the possible next steps, we can apply basic arithmetic operations (addition, subtraction, multiplication, and division) to any pair of numbers from the list. Here are the possible next steps for the input list `2 8 8 14`:\nTo determine the possible next steps, we can apply basic arithmetic operations (addition, subtraction, multiplication, and division) to any pair of numbers from the list. Here are the possible next steps for the input numbers 2, 8, 8, and 14:\nTo determine the possible next steps, we can apply basic arithmetic operations (addition, subtraction, multiplication, and division) to any pair of numbers from the list. Here are the possible next steps for the input list `2 8 8 14`:\n"
|
||||
],
|
||||
"infos": [
|
||||
{
|
||||
"r": 0
|
||||
}
|
||||
],
|
||||
"usage_so_far": {
|
||||
"completion_tokens": 15200,
|
||||
"prompt_tokens": 10228,
|
||||
"cost": 1.21884
|
||||
}
|
||||
}
|
||||
]
|
||||
@ -0,0 +1,638 @@
|
||||
[
|
||||
{
|
||||
"steps": [
|
||||
{
|
||||
"step": 0,
|
||||
"x": "1 1 2 8",
|
||||
"ys": [
|
||||
""
|
||||
],
|
||||
"new_ys": [
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n",
|
||||
"\n",
|
||||
"1. \\(1 + 1 = 2\\) (left: 2, 2, 8)\n",
|
||||
"2. \\(1 + 2 = 3\\) (left: 1, 3, 8)\n",
|
||||
"3. \\(1 + 8 = 9\\) (left: 1, 2, 9)\n",
|
||||
"4. \\(1 \\times 1 = 1\\) (left: 1, 2, 8)\n",
|
||||
"5. \\(1 \\times 2 = 2\\) (left: 1, 2, 8)\n",
|
||||
"6. \\(1 \\times 8 = 8\\) (left: 1, 2, 8)\n",
|
||||
"7. \\(2 + 8 = 10\\) (left: 1, 1, 10)\n",
|
||||
"8. \\(8 - 1 = 7\\) (left: 1, 2, 7)\n",
|
||||
"9. \\(8 - 2 = 6\\) (left: 1, 1, 6)\n",
|
||||
"10. \\(2 - 1 = 1\\) (left: 1, 1, 8)\n",
|
||||
"11. \\(8 / 1 = 8\\) (left: 1, 2, 8) \n",
|
||||
"12. \\(8 / 2 = 4\\) (left: 1, 1, 4)\n",
|
||||
"13. \\(2 / 1 = 2\\) (left: 1, 1, 8)\n",
|
||||
"\n",
|
||||
"These are the possible next steps using basic arithmetic operations. Note that division operations only result in integer outcomes.\n"
|
||||
],
|
||||
"values": [
|
||||
0.001,
|
||||
0.001,
|
||||
0.0,
|
||||
0.0,
|
||||
0.0,
|
||||
0.0,
|
||||
0.0,
|
||||
0.0,
|
||||
0.0,
|
||||
0.0,
|
||||
0.0,
|
||||
0.0,
|
||||
0.0,
|
||||
0.0,
|
||||
0.0,
|
||||
0,
|
||||
0.001
|
||||
],
|
||||
"select_new_ys": [
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"step": 1,
|
||||
"x": "1 1 2 8",
|
||||
"ys": [
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n"
|
||||
],
|
||||
"new_ys": [
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\nLet's explore the possible next steps for the input numbers 1, 1, 2, and 8 by performing arithmetic operations between any two numbers and replacing them with the result. Here are the possible operations and resulting sets of numbers:\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n1. **Addition:**\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n - \\(1 + 1 = 2\\) (remaining: 2, 2, 8)\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n - \\(1 + 2 = 3\\) (remaining: 1, 3, 8)\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n - \\(1 + 8 = 9\\) (remaining: 1, 2, 9)\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n - \\(1 + 2 = 3\\) (remaining: 1, 3, 8) *(repeated operation)*\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n - \\(1 + 8 = 9\\) (remaining: 1, 2, 9) *(repeated operation)*\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n - \\(2 + 8 = 10\\) (remaining: 1, 1, 10)\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n2. **Subtraction:**\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n - \\(1 - 1 = 0\\) (remaining: 0, 2, 8)\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n - \\(1 - 2 = -1\\) (remaining: 1, -1, 8)\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n - \\(1 - 8 = -7\\) (remaining: 1, 2, -7)\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n - \\(2 - 1 = 1\\) (remaining: 1, 1, 8)\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n - \\(8 - 1 = 7\\) (remaining: 1, 2, 7)\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n - \\(8 - 2 = 6\\) (remaining: 1, 1, 6)\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n3. **Multiplication:**\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n - \\(1 \\times 1 = 1\\) (remaining: 1, 2, 8)\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n - \\(1 \\times 2 = 2\\) (remaining: 1, 2, 8)\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n - \\(1 \\times 8 = 8\\) (remaining: 1, 2, 8)\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n - \\(2 \\times 1 = 2\\) (remaining: 1, 2, 8)\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n - \\(2 \\times 8 = 16\\) (remaining: 1, 1, 16)\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n4. **Division:**\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n - \\(1 \\div 1 = 1\\) (remaining: 1, 2, 8)\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n - \\(2 \\div 1 = 2\\) (remaining: 1, 2, 8)\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n - \\(8 \\div 1 = 8\\) (remaining: 1, 2, 8)\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n - \\(8 \\div 2 = 4\\) (remaining: 1, 1, 4)\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\nThese are all the possible next steps by performing arithmetic operations on the input numbers 1, 1, 2, and 8.\n"
|
||||
],
|
||||
"values": [
|
||||
0.0,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.0,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0,
|
||||
0.001
|
||||
],
|
||||
"select_new_ys": [
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"step": 2,
|
||||
"x": "1 1 2 8",
|
||||
"ys": [
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\n"
|
||||
],
|
||||
"new_ys": [
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\nTo find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\n\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\n1. **Addition:**\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\n - 1 + 1 = 2 (remaining: 2, 2, 8)\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\n - 1 + 2 = 3 (remaining: 1, 3, 8)\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\n - 1 + 8 = 9 (remaining: 1, 2, 9)\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\n - 2 + 8 = 10 (remaining: 1, 1, 10)\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\n\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\n2. **Subtraction:**\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\n - 1 - 1 = 0 (remaining: 0, 2, 8)\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\n - 1 - 2 = -1 (remaining: 1, -1, 8)\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\n - 1 - 8 = -7 (remaining: 1, 2, -7)\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\n - 2 - 1 = 1 (remaining: 1, 1, 8)\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\n - 8 - 1 = 7 (remaining: 1, 2, 7)\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\n - 8 - 2 = 6 (remaining: 1, 1, 6)\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\n\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\n3. **Multiplication:**\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\n - 1 * 1 = 1 (remaining: 1, 2, 8)\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\n - 1 * 2 = 2 (remaining: 1, 2, 8)\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\n - 1 * 8 = 8 (remaining: 1, 2, 8)\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\n - 2 * 8 = 16 (remaining: 1, 1, 16)\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\n\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\n4. **Division:**\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\n - 1 / 1 = 1 (remaining: 1, 2, 8)\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\n - 2 / 1 = 2 (remaining: 1, 1, 8)\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\n - 8 / 1 = 8 (remaining: 1, 2, 8)\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\n - 8 / 2 = 4 (remaining: 1, 1, 4)\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\n\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\nThese are all the possible operations and resulting sets of numbers that can be achieved from the given input numbers 1, 1, 2, and 8. Note that unnecessary operations that result in no change (e.g., multiplying by 1 or dividing by 1) can be omitted if desired.\n"
|
||||
],
|
||||
"values": [
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0,
|
||||
0.001
|
||||
],
|
||||
"select_new_ys": [
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\nTo find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"step": 3,
|
||||
"x": "1 1 2 8",
|
||||
"ys": [
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\nTo find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n"
|
||||
],
|
||||
"new_ys": [
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\nTo find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\nTo find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\nTo find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\nTo find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n1. **Addition:**\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\nTo find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n - \\( 1 + 1 = 2 \\) (left: 2, 2, 8)\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\nTo find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n - \\( 1 + 2 = 3 \\) (left: 1, 1, 3, 8)\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\nTo find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n - \\( 1 + 8 = 9 \\) (left: 1, 1, 2, 9)\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\nTo find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n - \\( 2 + 8 = 10 \\) (left: 1, 1, 10)\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\nTo find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\nTo find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n2. **Subtraction:**\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\nTo find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n - \\( 1 - 1 = 0 \\) (left: 0, 2, 8)\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\nTo find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n - \\( 2 - 1 = 1 \\) (left: 1, 1, 8)\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\nTo find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n - \\( 8 - 1 = 7 \\) (left: 1, 2, 7)\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\nTo find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n - \\( 8 - 2 = 6 \\) (left: 1, 1, 6)\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\nTo find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\nTo find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n3. **Multiplication:**\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\nTo find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n - \\( 1 \\times 1 = 1 \\) (left: 1, 2, 8)\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\nTo find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n - \\( 1 \\times 2 = 2 \\) (left: 1, 1, 8)\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\nTo find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n - \\( 1 \\times 8 = 8 \\) (left: 1, 1, 2)\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\nTo find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n - \\( 2 \\times 8 = 16 \\) (left: 1, 1, 16)\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\nTo find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\nTo find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n4. **Division:**\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\nTo find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n - \\( 1 \\div 1 = 1 \\) (left: 1, 2, 8)\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\nTo find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n - \\( 2 \\div 1 = 2 \\) (left: 1, 1, 8)\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\nTo find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n - \\( 8 \\div 1 = 8 \\) (left: 1, 1, 2)\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\nTo find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n - \\( 8 \\div 2 = 4 \\) (left: 1, 1, 4)\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\nTo find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\n",
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\nTo find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\nNote: Division is only performed when it results in an integer.\n"
|
||||
],
|
||||
"values": [
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.0,
|
||||
0,
|
||||
0,
|
||||
0.0,
|
||||
0,
|
||||
0.001,
|
||||
0,
|
||||
0.0,
|
||||
0.0,
|
||||
0.0,
|
||||
0,
|
||||
0.001,
|
||||
0.0,
|
||||
0.0,
|
||||
0,
|
||||
0,
|
||||
0,
|
||||
0.001,
|
||||
0.0,
|
||||
0.0,
|
||||
0,
|
||||
0.0,
|
||||
0,
|
||||
0
|
||||
],
|
||||
"select_new_ys": [
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\nTo find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\nTo find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"idx": 10,
|
||||
"ys": [
|
||||
"To find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n\nTo find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\nTo find the possible next steps for the input numbers 1, 1, 2, and 8, we can perform arithmetic operations between any two numbers and replace them with the result. Here are the possible operations and the resulting sets of numbers:\n"
|
||||
],
|
||||
"infos": [
|
||||
{
|
||||
"r": 0
|
||||
}
|
||||
],
|
||||
"usage_so_far": {
|
||||
"completion_tokens": 5801,
|
||||
"prompt_tokens": 22299,
|
||||
"cost": 1.0170299999999999
|
||||
}
|
||||
},
|
||||
{
|
||||
"steps": [
|
||||
{
|
||||
"step": 0,
|
||||
"x": "1 1 4 8",
|
||||
"ys": [
|
||||
""
|
||||
],
|
||||
"new_ys": [
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n",
|
||||
"\n",
|
||||
"1. **Addition:**\n",
|
||||
" - 1 + 1 = 2 (left: 2, 4, 8)\n",
|
||||
" - 1 + 4 = 5 (left: 1, 5, 8)\n",
|
||||
" - 1 + 8 = 9 (left: 1, 4, 9)\n",
|
||||
" - 4 + 8 = 12 (left: 1, 1, 12)\n",
|
||||
"\n",
|
||||
"2. **Subtraction:**\n",
|
||||
" - 1 - 1 = 0 (left: 0, 4, 8)\n",
|
||||
" - 4 - 1 = 3 (left: 1, 3, 8)\n",
|
||||
" - 8 - 1 = 7 (left: 1, 4, 7)\n",
|
||||
" - 4 - 8 = -4 (left: 1, 1, -4)\n",
|
||||
" - 8 - 4 = 4 (left: 1, 1, 4)\n",
|
||||
"\n",
|
||||
"3. **Multiplication:**\n",
|
||||
" - 1 * 1 = 1 (left: 1, 4, 8)\n",
|
||||
" - 1 * 4 = 4 (left: 1, 4, 8)\n",
|
||||
" - 1 * 8 = 8 (left: 1, 4, 8)\n",
|
||||
" - 4 * 8 = 32 (left: 1, 1, 32)\n",
|
||||
"\n",
|
||||
"4. **Division:**\n",
|
||||
" - 1 / 1 = 1 (left: 1, 4, 8)\n",
|
||||
" - 4 / 1 = 4 (left: 1, 4, 8)\n",
|
||||
" - 8 / 1 = 8 (left: 1, 4, 8)\n",
|
||||
" - 8 / 4 = 2 (left: 1, 1, 2)\n",
|
||||
" - 4 / 8 = 0.5 (left: 1, 1, 0.5)\n",
|
||||
"\n",
|
||||
"These are the possible operations that can be performed with the numbers 1, 1, 4, and 8.\n"
|
||||
],
|
||||
"values": [
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.0,
|
||||
0.0,
|
||||
0.0,
|
||||
0.0,
|
||||
0,
|
||||
0.001,
|
||||
0.0,
|
||||
0.0,
|
||||
0.0,
|
||||
0.0,
|
||||
0.0,
|
||||
0,
|
||||
0.001,
|
||||
0.0,
|
||||
0.0,
|
||||
0.0,
|
||||
0.0,
|
||||
0,
|
||||
0.001,
|
||||
0.0,
|
||||
0.0,
|
||||
0.0,
|
||||
0,
|
||||
0.0,
|
||||
0,
|
||||
0.001
|
||||
],
|
||||
"select_new_ys": [
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"step": 1,
|
||||
"x": "1 1 4 8",
|
||||
"ys": [
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n"
|
||||
],
|
||||
"new_ys": [
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n1. Add 1 and 1:\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n - 1 + 1 = 2 (remaining numbers: 2, 4, 8)\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n2. Add 1 and 4:\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n - 1 + 4 = 5 (remaining numbers: 1, 5, 8)\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n3. Add 1 and 8:\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n - 1 + 8 = 9 (remaining numbers: 1, 4, 9)\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n4. Add 4 and 8:\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n - 4 + 8 = 12 (remaining numbers: 1, 1, 12)\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n5. Subtract 1 from 1:\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n - 1 - 1 = 0 (remaining numbers: 0, 4, 8)\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n6. Subtract 1 from 4:\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n - 4 - 1 = 3 (remaining numbers: 1, 1, 3)\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n7. Subtract 1 from 8:\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n - 8 - 1 = 7 (remaining numbers: 1, 4, 7)\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n8. Subtract 4 from 8:\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n - 8 - 4 = 4 (remaining numbers: 1, 1, 4)\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n9. Multiply 1 and 1:\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n - 1 * 1 = 1 (remaining numbers: 1, 4, 8)\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n10. Multiply 1 and 4:\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n - 1 * 4 = 4 (remaining numbers: 1, 4, 8)\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n11. Multiply 1 and 8:\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n - 1 * 8 = 8 (remaining numbers: 1, 4, 8)\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n12. Multiply 4 and 8:\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n - 4 * 8 = 32 (remaining numbers: 1, 1, 32)\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n13. Divide 1 by 1:\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n - 1 / 1 = 1 (remaining numbers: 1, 4, 8)\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n14. Divide 4 by 1:\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n - 4 / 1 = 4 (remaining numbers: 1, 1, 8)\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n15. Divide 8 by 1:\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n - 8 / 1 = 8 (remaining numbers: 1, 1, 4)\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n16. Divide 8 by 4:\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n - 8 / 4 = 2 (remaining numbers: 1, 1, 2)\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nNote: Dividing 1 by 4 or 1 by 8 results in fractions, which are not included here as they may not be considered valid operations in some contexts.\n"
|
||||
],
|
||||
"values": [
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0,
|
||||
0.001,
|
||||
0.001,
|
||||
0,
|
||||
0.001,
|
||||
0.001,
|
||||
0,
|
||||
0.001,
|
||||
0.001,
|
||||
0,
|
||||
0.001,
|
||||
0.001,
|
||||
0,
|
||||
0.001,
|
||||
0.001,
|
||||
0,
|
||||
0.001,
|
||||
0.001,
|
||||
0,
|
||||
0.001,
|
||||
0.001,
|
||||
0,
|
||||
0.001,
|
||||
0.001,
|
||||
0,
|
||||
0.001,
|
||||
0.001,
|
||||
0,
|
||||
0.001,
|
||||
0.001,
|
||||
0,
|
||||
0.001,
|
||||
0.001,
|
||||
0,
|
||||
0.001,
|
||||
0.001,
|
||||
0,
|
||||
0.001,
|
||||
0.001,
|
||||
0,
|
||||
0.001,
|
||||
0.001,
|
||||
0,
|
||||
0.001,
|
||||
0.001,
|
||||
0,
|
||||
0.001
|
||||
],
|
||||
"select_new_ys": [
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"step": 2,
|
||||
"x": "1 1 4 8",
|
||||
"ys": [
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n"
|
||||
],
|
||||
"new_ys": [
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers in the sequence. Here are the possible next steps:\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n1. Addition:\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n - 1 + 1 = 2 (left: 2, 4, 8)\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n - 1 + 4 = 5 (left: 1, 1, 5, 8)\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n - 1 + 8 = 9 (left: 1, 1, 4, 9)\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n - 4 + 8 = 12 (left: 1, 1, 12)\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n2. Subtraction:\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n - 1 - 1 = 0 (left: 0, 4, 8)\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n - 4 - 1 = 3 (left: 1, 1, 3, 8)\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n - 8 - 1 = 7 (left: 1, 1, 4, 7)\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n - 8 - 4 = 4 (left: 1, 1, 4, 4)\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n3. Multiplication:\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n - 1 * 1 = 1 (left: 1, 4, 8)\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n - 1 * 4 = 4 (left: 1, 1, 4, 8)\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n - 1 * 8 = 8 (left: 1, 1, 4, 8)\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n - 4 * 8 = 32 (left: 1, 1, 32)\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n4. Division (only when the result is an integer):\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n - 8 / 1 = 8 (left: 1, 1, 4, 8)\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n - 4 / 1 = 4 (left: 1, 1, 4, 8)\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n - 8 / 4 = 2 (left: 1, 1, 2)\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\n\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nThese are the possible next steps you can take using arithmetic operations on the sequence 1, 1, 4, 8.\n"
|
||||
],
|
||||
"values": [
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.0,
|
||||
0.0,
|
||||
0.0,
|
||||
0.0,
|
||||
0,
|
||||
0.001,
|
||||
0.0,
|
||||
0,
|
||||
0.0,
|
||||
0.0,
|
||||
0,
|
||||
0.001,
|
||||
0.0,
|
||||
0.0,
|
||||
0.0,
|
||||
0.0,
|
||||
0,
|
||||
0.001,
|
||||
0.0,
|
||||
0.0,
|
||||
0,
|
||||
0,
|
||||
0.001
|
||||
],
|
||||
"select_new_ys": [
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers in the sequence. Here are the possible next steps:\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"step": 3,
|
||||
"x": "1 1 4 8",
|
||||
"ys": [
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers in the sequence. Here are the possible next steps:\n"
|
||||
],
|
||||
"new_ys": [
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers in the sequence. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8 using arithmetic operations (addition, subtraction, multiplication, and division), we need to consider each pair of numbers and apply the operations. Here are the possible next steps:\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers in the sequence. Here are the possible next steps:\n\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers in the sequence. Here are the possible next steps:\n1. **Addition:**\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers in the sequence. Here are the possible next steps:\n - \\(1 + 1 = 2\\) (left: 2, 4, 8)\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers in the sequence. Here are the possible next steps:\n - \\(1 + 4 = 5\\) (left: 1, 5, 8)\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers in the sequence. Here are the possible next steps:\n - \\(1 + 8 = 9\\) (left: 1, 4, 9)\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers in the sequence. Here are the possible next steps:\n - \\(1 + 4 = 5\\) (left: 1, 5, 8)\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers in the sequence. Here are the possible next steps:\n - \\(1 + 8 = 9\\) (left: 1, 4, 9)\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers in the sequence. Here are the possible next steps:\n - \\(4 + 8 = 12\\) (left: 1, 1, 12)\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers in the sequence. Here are the possible next steps:\n\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers in the sequence. Here are the possible next steps:\n2. **Subtraction:**\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers in the sequence. Here are the possible next steps:\n - \\(1 - 1 = 0\\) (left: 0, 4, 8)\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers in the sequence. Here are the possible next steps:\n - \\(1 - 4 = -3\\) (left: 1, -3, 8)\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers in the sequence. Here are the possible next steps:\n - \\(1 - 8 = -7\\) (left: 1, 4, -7)\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers in the sequence. Here are the possible next steps:\n - \\(4 - 1 = 3\\) (left: 1, 3, 8)\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers in the sequence. Here are the possible next steps:\n - \\(8 - 1 = 7\\) (left: 1, 4, 7)\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers in the sequence. Here are the possible next steps:\n - \\(4 - 8 = -4\\) (left: 1, 1, -4)\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers in the sequence. Here are the possible next steps:\n - \\(8 - 4 = 4\\) (left: 1, 1, 4)\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers in the sequence. Here are the possible next steps:\n\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers in the sequence. Here are the possible next steps:\n3. **Multiplication:**\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers in the sequence. Here are the possible next steps:\n - \\(1 \\times 1 = 1\\) (left: 1, 4, 8)\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers in the sequence. Here are the possible next steps:\n - \\(1 \\times 4 = 4\\) (left: 1, 4, 8)\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers in the sequence. Here are the possible next steps:\n - \\(1 \\times 8 = 8\\) (left: 1, 4, 8)\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers in the sequence. Here are the possible next steps:\n - \\(4 \\times 8 = 32\\) (left: 1, 1, 32)\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers in the sequence. Here are the possible next steps:\n\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers in the sequence. Here are the possible next steps:\n4. **Division:**\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers in the sequence. Here are the possible next steps:\n - \\(1 / 1 = 1\\) (left: 1, 4, 8)\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers in the sequence. Here are the possible next steps:\n - \\(4 / 1 = 4\\) (left: 1, 1, 8)\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers in the sequence. Here are the possible next steps:\n - \\(8 / 1 = 8\\) (left: 1, 4, 1)\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers in the sequence. Here are the possible next steps:\n - \\(4 / 8 = 0.5\\) (left: 1, 1, 0.5)\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers in the sequence. Here are the possible next steps:\n - \\(8 / 4 = 2\\) (left: 1, 1, 2)\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers in the sequence. Here are the possible next steps:\n\n",
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers in the sequence. Here are the possible next steps:\nThese are the immediate next steps available by pairing and applying operations to the numbers in the sequence 1, 1, 4, 8.\n"
|
||||
],
|
||||
"values": [
|
||||
0,
|
||||
0.001,
|
||||
0.001,
|
||||
0.0,
|
||||
0.0,
|
||||
0.0,
|
||||
0,
|
||||
0,
|
||||
0.0,
|
||||
0,
|
||||
0.001,
|
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0.0,
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0,
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0,
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0.0,
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||||
0.0,
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0.0,
|
||||
0.0,
|
||||
0,
|
||||
0.001,
|
||||
0.0,
|
||||
0.0,
|
||||
0.0,
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0.0,
|
||||
0,
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0.001,
|
||||
0.0,
|
||||
0.0,
|
||||
0,
|
||||
0.0,
|
||||
0,
|
||||
0,
|
||||
0
|
||||
],
|
||||
"select_new_ys": [
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers in the sequence. Here are the possible next steps:\n\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"idx": 11,
|
||||
"ys": [
|
||||
"To determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, you can perform arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers. After performing an operation, the two numbers are replaced with the result of the operation, reducing the total count of numbers by one. Here are the possible next steps:\nTo determine the possible next steps with the sequence 1, 1, 4, 8, we can perform arithmetic operations (addition, subtraction, multiplication, and division) on any two numbers in the sequence. Here are the possible next steps:\n\n"
|
||||
],
|
||||
"infos": [
|
||||
{
|
||||
"r": 0
|
||||
}
|
||||
],
|
||||
"usage_so_far": {
|
||||
"completion_tokens": 12723,
|
||||
"prompt_tokens": 45580,
|
||||
"cost": 2.13078
|
||||
}
|
||||
}
|
||||
]
|
||||
@ -1,412 +0,0 @@
|
||||
[
|
||||
{
|
||||
"steps": [
|
||||
{
|
||||
"step": 0,
|
||||
"x": "1 1 2 12",
|
||||
"ys": [
|
||||
""
|
||||
],
|
||||
"new_ys": [
|
||||
"Given the input numbers 1, 1, 2, and 12, let's consider the possible operations and the resulting sets of numbers. You can use addition (+), subtraction (-), multiplication (*), and division (/), but only between two numbers at a time. Here are the possible next steps:\n"
|
||||
],
|
||||
"values": [
|
||||
0.001
|
||||
],
|
||||
"select_new_ys": [
|
||||
"Given the input numbers 1, 1, 2, and 12, let's consider the possible operations and the resulting sets of numbers. You can use addition (+), subtraction (-), multiplication (*), and division (/), but only between two numbers at a time. Here are the possible next steps:\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"step": 1,
|
||||
"x": "1 1 2 12",
|
||||
"ys": [
|
||||
"Given the input numbers 1, 1, 2, and 12, let's consider the possible operations and the resulting sets of numbers. You can use addition (+), subtraction (-), multiplication (*), and division (/), but only between two numbers at a time. Here are the possible next steps:\n"
|
||||
],
|
||||
"new_ys": [
|
||||
"Given the input numbers 1, 1, 2, and 12, let's consider the possible operations and the resulting sets of numbers. You can use addition (+), subtraction (-), multiplication (*), and division (/), but only between two numbers at a time. Here are the possible next steps:\nGiven the input numbers 1, 1, 2, and 12, let's consider the possible operations and the resulting sets of numbers. You can use addition (+), subtraction (-), multiplication (*), and division (/) for any two numbers in the set. Here are some possible next steps:\n"
|
||||
],
|
||||
"values": [
|
||||
0.001
|
||||
],
|
||||
"select_new_ys": [
|
||||
"Given the input numbers 1, 1, 2, and 12, let's consider the possible operations and the resulting sets of numbers. You can use addition (+), subtraction (-), multiplication (*), and division (/), but only between two numbers at a time. Here are the possible next steps:\nGiven the input numbers 1, 1, 2, and 12, let's consider the possible operations and the resulting sets of numbers. You can use addition (+), subtraction (-), multiplication (*), and division (/) for any two numbers in the set. Here are some possible next steps:\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"step": 2,
|
||||
"x": "1 1 2 12",
|
||||
"ys": [
|
||||
"Given the input numbers 1, 1, 2, and 12, let's consider the possible operations and the resulting sets of numbers. You can use addition (+), subtraction (-), multiplication (*), and division (/), but only between two numbers at a time. Here are the possible next steps:\nGiven the input numbers 1, 1, 2, and 12, let's consider the possible operations and the resulting sets of numbers. You can use addition (+), subtraction (-), multiplication (*), and division (/) for any two numbers in the set. Here are some possible next steps:\n"
|
||||
],
|
||||
"new_ys": [
|
||||
"Given the input numbers 1, 1, 2, and 12, let's consider the possible operations and the resulting sets of numbers. You can use addition (+), subtraction (-), multiplication (*), and division (/), but only between two numbers at a time. Here are the possible next steps:\nGiven the input numbers 1, 1, 2, and 12, let's consider the possible operations and the resulting sets of numbers. You can use addition (+), subtraction (-), multiplication (*), and division (/) for any two numbers in the set. Here are some possible next steps:\nGiven the input numbers 1, 1, 2, and 12, let's consider the possible operations and the resulting sets of numbers you can perform using addition (+), subtraction (-), multiplication (*), and division (/) on any two numbers. Here are some possible next steps:\n"
|
||||
],
|
||||
"values": [
|
||||
0.0
|
||||
],
|
||||
"select_new_ys": [
|
||||
"Given the input numbers 1, 1, 2, and 12, let's consider the possible operations and the resulting sets of numbers. You can use addition (+), subtraction (-), multiplication (*), and division (/), but only between two numbers at a time. Here are the possible next steps:\nGiven the input numbers 1, 1, 2, and 12, let's consider the possible operations and the resulting sets of numbers. You can use addition (+), subtraction (-), multiplication (*), and division (/) for any two numbers in the set. Here are some possible next steps:\nGiven the input numbers 1, 1, 2, and 12, let's consider the possible operations and the resulting sets of numbers you can perform using addition (+), subtraction (-), multiplication (*), and division (/) on any two numbers. Here are some possible next steps:\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"step": 3,
|
||||
"x": "1 1 2 12",
|
||||
"ys": [
|
||||
"Given the input numbers 1, 1, 2, and 12, let's consider the possible operations and the resulting sets of numbers. You can use addition (+), subtraction (-), multiplication (*), and division (/), but only between two numbers at a time. Here are the possible next steps:\nGiven the input numbers 1, 1, 2, and 12, let's consider the possible operations and the resulting sets of numbers. You can use addition (+), subtraction (-), multiplication (*), and division (/) for any two numbers in the set. Here are some possible next steps:\nGiven the input numbers 1, 1, 2, and 12, let's consider the possible operations and the resulting sets of numbers you can perform using addition (+), subtraction (-), multiplication (*), and division (/) on any two numbers. Here are some possible next steps:\n"
|
||||
],
|
||||
"new_ys": [
|
||||
"Given the input numbers 1, 1, 2, and 12, let's consider the possible operations and the resulting sets of numbers. You can use addition (+), subtraction (-), multiplication (*), and division (/), but only between two numbers at a time. Here are the possible next steps:\nGiven the input numbers 1, 1, 2, and 12, let's consider the possible operations and the resulting sets of numbers. You can use addition (+), subtraction (-), multiplication (*), and division (/) for any two numbers in the set. Here are some possible next steps:\nGiven the input numbers 1, 1, 2, and 12, let's consider the possible operations and the resulting sets of numbers you can perform using addition (+), subtraction (-), multiplication (*), and division (/) on any two numbers. Here are some possible next steps:\nLet's consider the possible operations using the numbers 1, 1, 2, and 12. We can use addition (+), subtraction (-), multiplication (*), and division (/), and we perform these operations on two numbers at a time, replacing them with the result. Here are the possible next steps:\n"
|
||||
],
|
||||
"values": [
|
||||
0
|
||||
],
|
||||
"select_new_ys": [
|
||||
"Given the input numbers 1, 1, 2, and 12, let's consider the possible operations and the resulting sets of numbers. You can use addition (+), subtraction (-), multiplication (*), and division (/), but only between two numbers at a time. Here are the possible next steps:\nGiven the input numbers 1, 1, 2, and 12, let's consider the possible operations and the resulting sets of numbers. You can use addition (+), subtraction (-), multiplication (*), and division (/) for any two numbers in the set. Here are some possible next steps:\nGiven the input numbers 1, 1, 2, and 12, let's consider the possible operations and the resulting sets of numbers you can perform using addition (+), subtraction (-), multiplication (*), and division (/) on any two numbers. Here are some possible next steps:\nLet's consider the possible operations using the numbers 1, 1, 2, and 12. We can use addition (+), subtraction (-), multiplication (*), and division (/), and we perform these operations on two numbers at a time, replacing them with the result. Here are the possible next steps:\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"idx": 5,
|
||||
"ys": [
|
||||
"Given the input numbers 1, 1, 2, and 12, let's consider the possible operations and the resulting sets of numbers. You can use addition (+), subtraction (-), multiplication (*), and division (/), but only between two numbers at a time. Here are the possible next steps:\nGiven the input numbers 1, 1, 2, and 12, let's consider the possible operations and the resulting sets of numbers. You can use addition (+), subtraction (-), multiplication (*), and division (/) for any two numbers in the set. Here are some possible next steps:\nGiven the input numbers 1, 1, 2, and 12, let's consider the possible operations and the resulting sets of numbers you can perform using addition (+), subtraction (-), multiplication (*), and division (/) on any two numbers. Here are some possible next steps:\nLet's consider the possible operations using the numbers 1, 1, 2, and 12. We can use addition (+), subtraction (-), multiplication (*), and division (/), and we perform these operations on two numbers at a time, replacing them with the result. Here are the possible next steps:\n"
|
||||
],
|
||||
"infos": [
|
||||
{
|
||||
"r": 0
|
||||
}
|
||||
],
|
||||
"usage_so_far": {
|
||||
"completion_tokens": 2736,
|
||||
"prompt_tokens": 2250,
|
||||
"cost": 0.23166
|
||||
}
|
||||
},
|
||||
{
|
||||
"steps": [
|
||||
{
|
||||
"step": 0,
|
||||
"x": "1 2 2 6",
|
||||
"ys": [
|
||||
""
|
||||
],
|
||||
"new_ys": [
|
||||
"1 + 2 = 3 (left: 2 3 6) \n"
|
||||
],
|
||||
"values": [
|
||||
0.0
|
||||
],
|
||||
"select_new_ys": [
|
||||
"1 + 2 = 3 (left: 2 3 6) \n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"step": 1,
|
||||
"x": "1 2 2 6",
|
||||
"ys": [
|
||||
"1 + 2 = 3 (left: 2 3 6) \n"
|
||||
],
|
||||
"new_ys": [
|
||||
"1 + 2 = 3 (left: 2 3 6) \nTo determine the possible next steps, we need to consider combinations of two numbers from the list and apply basic arithmetic operations (addition, subtraction, multiplication, and division) to them. Let's go through each pair:\n"
|
||||
],
|
||||
"values": [
|
||||
0.0
|
||||
],
|
||||
"select_new_ys": [
|
||||
"1 + 2 = 3 (left: 2 3 6) \nTo determine the possible next steps, we need to consider combinations of two numbers from the list and apply basic arithmetic operations (addition, subtraction, multiplication, and division) to them. Let's go through each pair:\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"step": 2,
|
||||
"x": "1 2 2 6",
|
||||
"ys": [
|
||||
"1 + 2 = 3 (left: 2 3 6) \nTo determine the possible next steps, we need to consider combinations of two numbers from the list and apply basic arithmetic operations (addition, subtraction, multiplication, and division) to them. Let's go through each pair:\n"
|
||||
],
|
||||
"new_ys": [
|
||||
"1 + 2 = 3 (left: 2 3 6) \nTo determine the possible next steps, we need to consider combinations of two numbers from the list and apply basic arithmetic operations (addition, subtraction, multiplication, and division) to them. Let's go through each pair:\nTo determine the possible next steps from the list of numbers 2, 8, 8, and 14, we need to consider combinations of two numbers and apply basic arithmetic operations (addition, subtraction, multiplication, and division). Here are the possible next steps:\n"
|
||||
],
|
||||
"values": [
|
||||
0.001
|
||||
],
|
||||
"select_new_ys": [
|
||||
"1 + 2 = 3 (left: 2 3 6) \nTo determine the possible next steps, we need to consider combinations of two numbers from the list and apply basic arithmetic operations (addition, subtraction, multiplication, and division) to them. Let's go through each pair:\nTo determine the possible next steps from the list of numbers 2, 8, 8, and 14, we need to consider combinations of two numbers and apply basic arithmetic operations (addition, subtraction, multiplication, and division). Here are the possible next steps:\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"step": 3,
|
||||
"x": "1 2 2 6",
|
||||
"ys": [
|
||||
"1 + 2 = 3 (left: 2 3 6) \nTo determine the possible next steps, we need to consider combinations of two numbers from the list and apply basic arithmetic operations (addition, subtraction, multiplication, and division) to them. Let's go through each pair:\nTo determine the possible next steps from the list of numbers 2, 8, 8, and 14, we need to consider combinations of two numbers and apply basic arithmetic operations (addition, subtraction, multiplication, and division). Here are the possible next steps:\n"
|
||||
],
|
||||
"new_ys": [
|
||||
"1 + 2 = 3 (left: 2 3 6) \nTo determine the possible next steps, we need to consider combinations of two numbers from the list and apply basic arithmetic operations (addition, subtraction, multiplication, and division) to them. Let's go through each pair:\nTo determine the possible next steps from the list of numbers 2, 8, 8, and 14, we need to consider combinations of two numbers and apply basic arithmetic operations (addition, subtraction, multiplication, and division). Here are the possible next steps:\nTo determine the possible next steps from the list of numbers 2, 8, 8, and 14, let's consider all combinations of two numbers and apply basic arithmetic operations (addition, subtraction, multiplication, and division) where applicable.\n"
|
||||
],
|
||||
"values": [
|
||||
0
|
||||
],
|
||||
"select_new_ys": [
|
||||
"1 + 2 = 3 (left: 2 3 6) \nTo determine the possible next steps, we need to consider combinations of two numbers from the list and apply basic arithmetic operations (addition, subtraction, multiplication, and division) to them. Let's go through each pair:\nTo determine the possible next steps from the list of numbers 2, 8, 8, and 14, we need to consider combinations of two numbers and apply basic arithmetic operations (addition, subtraction, multiplication, and division). Here are the possible next steps:\nTo determine the possible next steps from the list of numbers 2, 8, 8, and 14, let's consider all combinations of two numbers and apply basic arithmetic operations (addition, subtraction, multiplication, and division) where applicable.\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"idx": 6,
|
||||
"ys": [
|
||||
"1 + 2 = 3 (left: 2 3 6) \nTo determine the possible next steps, we need to consider combinations of two numbers from the list and apply basic arithmetic operations (addition, subtraction, multiplication, and division) to them. Let's go through each pair:\nTo determine the possible next steps from the list of numbers 2, 8, 8, and 14, we need to consider combinations of two numbers and apply basic arithmetic operations (addition, subtraction, multiplication, and division). Here are the possible next steps:\nTo determine the possible next steps from the list of numbers 2, 8, 8, and 14, let's consider all combinations of two numbers and apply basic arithmetic operations (addition, subtraction, multiplication, and division) where applicable.\n"
|
||||
],
|
||||
"infos": [
|
||||
{
|
||||
"r": 0
|
||||
}
|
||||
],
|
||||
"usage_so_far": {
|
||||
"completion_tokens": 6159,
|
||||
"prompt_tokens": 4465,
|
||||
"cost": 0.50349
|
||||
}
|
||||
},
|
||||
{
|
||||
"steps": [
|
||||
{
|
||||
"step": 0,
|
||||
"x": "1 1 10 12",
|
||||
"ys": [
|
||||
""
|
||||
],
|
||||
"new_ys": [
|
||||
"To determine the possible next steps, we combine two numbers from the list and replace them with the result of one of the basic arithmetic operations: addition, subtraction, multiplication, or division (if applicable). Here's how you can proceed with the input \"1 1 10 12\":\n"
|
||||
],
|
||||
"values": [
|
||||
0.0
|
||||
],
|
||||
"select_new_ys": [
|
||||
"To determine the possible next steps, we combine two numbers from the list and replace them with the result of one of the basic arithmetic operations: addition, subtraction, multiplication, or division (if applicable). Here's how you can proceed with the input \"1 1 10 12\":\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"step": 1,
|
||||
"x": "1 1 10 12",
|
||||
"ys": [
|
||||
"To determine the possible next steps, we combine two numbers from the list and replace them with the result of one of the basic arithmetic operations: addition, subtraction, multiplication, or division (if applicable). Here's how you can proceed with the input \"1 1 10 12\":\n"
|
||||
],
|
||||
"new_ys": [
|
||||
"To determine the possible next steps, we combine two numbers from the list and replace them with the result of one of the basic arithmetic operations: addition, subtraction, multiplication, or division (if applicable). Here's how you can proceed with the input \"1 1 10 12\":\nTo determine the possible next steps, you can combine two numbers from the list and replace them with the result of one of the basic arithmetic operations: addition, subtraction, multiplication, or division (if applicable). Here's how you can do it with the input list [2, 8, 8, 14]:\n"
|
||||
],
|
||||
"values": [
|
||||
0.001
|
||||
],
|
||||
"select_new_ys": [
|
||||
"To determine the possible next steps, we combine two numbers from the list and replace them with the result of one of the basic arithmetic operations: addition, subtraction, multiplication, or division (if applicable). Here's how you can proceed with the input \"1 1 10 12\":\nTo determine the possible next steps, you can combine two numbers from the list and replace them with the result of one of the basic arithmetic operations: addition, subtraction, multiplication, or division (if applicable). Here's how you can do it with the input list [2, 8, 8, 14]:\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"step": 2,
|
||||
"x": "1 1 10 12",
|
||||
"ys": [
|
||||
"To determine the possible next steps, we combine two numbers from the list and replace them with the result of one of the basic arithmetic operations: addition, subtraction, multiplication, or division (if applicable). Here's how you can proceed with the input \"1 1 10 12\":\nTo determine the possible next steps, you can combine two numbers from the list and replace them with the result of one of the basic arithmetic operations: addition, subtraction, multiplication, or division (if applicable). Here's how you can do it with the input list [2, 8, 8, 14]:\n"
|
||||
],
|
||||
"new_ys": [
|
||||
"To determine the possible next steps, we combine two numbers from the list and replace them with the result of one of the basic arithmetic operations: addition, subtraction, multiplication, or division (if applicable). Here's how you can proceed with the input \"1 1 10 12\":\nTo determine the possible next steps, you can combine two numbers from the list and replace them with the result of one of the basic arithmetic operations: addition, subtraction, multiplication, or division (if applicable). Here's how you can do it with the input list [2, 8, 8, 14]:\nGiven the input numbers 2, 8, 8, and 14, you can combine two of these numbers using basic arithmetic operations (addition, subtraction, multiplication, or division, where applicable) to determine the possible next steps. Below are the possible combinations and their results:\n"
|
||||
],
|
||||
"values": [
|
||||
0.001
|
||||
],
|
||||
"select_new_ys": [
|
||||
"To determine the possible next steps, we combine two numbers from the list and replace them with the result of one of the basic arithmetic operations: addition, subtraction, multiplication, or division (if applicable). Here's how you can proceed with the input \"1 1 10 12\":\nTo determine the possible next steps, you can combine two numbers from the list and replace them with the result of one of the basic arithmetic operations: addition, subtraction, multiplication, or division (if applicable). Here's how you can do it with the input list [2, 8, 8, 14]:\nGiven the input numbers 2, 8, 8, and 14, you can combine two of these numbers using basic arithmetic operations (addition, subtraction, multiplication, or division, where applicable) to determine the possible next steps. Below are the possible combinations and their results:\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"step": 3,
|
||||
"x": "1 1 10 12",
|
||||
"ys": [
|
||||
"To determine the possible next steps, we combine two numbers from the list and replace them with the result of one of the basic arithmetic operations: addition, subtraction, multiplication, or division (if applicable). Here's how you can proceed with the input \"1 1 10 12\":\nTo determine the possible next steps, you can combine two numbers from the list and replace them with the result of one of the basic arithmetic operations: addition, subtraction, multiplication, or division (if applicable). Here's how you can do it with the input list [2, 8, 8, 14]:\nGiven the input numbers 2, 8, 8, and 14, you can combine two of these numbers using basic arithmetic operations (addition, subtraction, multiplication, or division, where applicable) to determine the possible next steps. Below are the possible combinations and their results:\n"
|
||||
],
|
||||
"new_ys": [
|
||||
"To determine the possible next steps, we combine two numbers from the list and replace them with the result of one of the basic arithmetic operations: addition, subtraction, multiplication, or division (if applicable). Here's how you can proceed with the input \"1 1 10 12\":\nTo determine the possible next steps, you can combine two numbers from the list and replace them with the result of one of the basic arithmetic operations: addition, subtraction, multiplication, or division (if applicable). Here's how you can do it with the input list [2, 8, 8, 14]:\nGiven the input numbers 2, 8, 8, and 14, you can combine two of these numbers using basic arithmetic operations (addition, subtraction, multiplication, or division, where applicable) to determine the possible next steps. Below are the possible combinations and their results:\nGiven the input numbers 2, 8, 8, and 14, you can choose two numbers and combine them using basic arithmetic operations. Here are the possible combinations and their outcomes:\n"
|
||||
],
|
||||
"values": [
|
||||
0
|
||||
],
|
||||
"select_new_ys": [
|
||||
"To determine the possible next steps, we combine two numbers from the list and replace them with the result of one of the basic arithmetic operations: addition, subtraction, multiplication, or division (if applicable). Here's how you can proceed with the input \"1 1 10 12\":\nTo determine the possible next steps, you can combine two numbers from the list and replace them with the result of one of the basic arithmetic operations: addition, subtraction, multiplication, or division (if applicable). Here's how you can do it with the input list [2, 8, 8, 14]:\nGiven the input numbers 2, 8, 8, and 14, you can combine two of these numbers using basic arithmetic operations (addition, subtraction, multiplication, or division, where applicable) to determine the possible next steps. Below are the possible combinations and their results:\nGiven the input numbers 2, 8, 8, and 14, you can choose two numbers and combine them using basic arithmetic operations. Here are the possible combinations and their outcomes:\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"idx": 7,
|
||||
"ys": [
|
||||
"To determine the possible next steps, we combine two numbers from the list and replace them with the result of one of the basic arithmetic operations: addition, subtraction, multiplication, or division (if applicable). Here's how you can proceed with the input \"1 1 10 12\":\nTo determine the possible next steps, you can combine two numbers from the list and replace them with the result of one of the basic arithmetic operations: addition, subtraction, multiplication, or division (if applicable). Here's how you can do it with the input list [2, 8, 8, 14]:\nGiven the input numbers 2, 8, 8, and 14, you can combine two of these numbers using basic arithmetic operations (addition, subtraction, multiplication, or division, where applicable) to determine the possible next steps. Below are the possible combinations and their results:\nGiven the input numbers 2, 8, 8, and 14, you can choose two numbers and combine them using basic arithmetic operations. Here are the possible combinations and their outcomes:\n"
|
||||
],
|
||||
"infos": [
|
||||
{
|
||||
"r": 0
|
||||
}
|
||||
],
|
||||
"usage_so_far": {
|
||||
"completion_tokens": 8576,
|
||||
"prompt_tokens": 6708,
|
||||
"cost": 0.7158
|
||||
}
|
||||
},
|
||||
{
|
||||
"steps": [
|
||||
{
|
||||
"step": 0,
|
||||
"x": "2 2 10 10",
|
||||
"ys": [
|
||||
""
|
||||
],
|
||||
"new_ys": [
|
||||
"Here's the list of possible next steps for the input `2 2 10 10`:\n"
|
||||
],
|
||||
"values": [
|
||||
0.0
|
||||
],
|
||||
"select_new_ys": [
|
||||
"Here's the list of possible next steps for the input `2 2 10 10`:\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"step": 1,
|
||||
"x": "2 2 10 10",
|
||||
"ys": [
|
||||
"Here's the list of possible next steps for the input `2 2 10 10`:\n"
|
||||
],
|
||||
"new_ys": [
|
||||
"Here's the list of possible next steps for the input `2 2 10 10`:\nTo find the possible next steps for the input `2 2 10 10`, we can consider applying basic arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers and replacing them with the result. Here are the possible next steps:\n"
|
||||
],
|
||||
"values": [
|
||||
0.0
|
||||
],
|
||||
"select_new_ys": [
|
||||
"Here's the list of possible next steps for the input `2 2 10 10`:\nTo find the possible next steps for the input `2 2 10 10`, we can consider applying basic arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers and replacing them with the result. Here are the possible next steps:\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"step": 2,
|
||||
"x": "2 2 10 10",
|
||||
"ys": [
|
||||
"Here's the list of possible next steps for the input `2 2 10 10`:\nTo find the possible next steps for the input `2 2 10 10`, we can consider applying basic arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers and replacing them with the result. Here are the possible next steps:\n"
|
||||
],
|
||||
"new_ys": [
|
||||
"Here's the list of possible next steps for the input `2 2 10 10`:\nTo find the possible next steps for the input `2 2 10 10`, we can consider applying basic arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers and replacing them with the result. Here are the possible next steps:\nTo find the possible next steps for the input `2 2 10 10`, we can apply basic arithmetic operations (addition, subtraction, multiplication, and division) on any pair of numbers from the list. Here are the possible next steps:\n"
|
||||
],
|
||||
"values": [
|
||||
0.0
|
||||
],
|
||||
"select_new_ys": [
|
||||
"Here's the list of possible next steps for the input `2 2 10 10`:\nTo find the possible next steps for the input `2 2 10 10`, we can consider applying basic arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers and replacing them with the result. Here are the possible next steps:\nTo find the possible next steps for the input `2 2 10 10`, we can apply basic arithmetic operations (addition, subtraction, multiplication, and division) on any pair of numbers from the list. Here are the possible next steps:\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"step": 3,
|
||||
"x": "2 2 10 10",
|
||||
"ys": [
|
||||
"Here's the list of possible next steps for the input `2 2 10 10`:\nTo find the possible next steps for the input `2 2 10 10`, we can consider applying basic arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers and replacing them with the result. Here are the possible next steps:\nTo find the possible next steps for the input `2 2 10 10`, we can apply basic arithmetic operations (addition, subtraction, multiplication, and division) on any pair of numbers from the list. Here are the possible next steps:\n"
|
||||
],
|
||||
"new_ys": [
|
||||
"Here's the list of possible next steps for the input `2 2 10 10`:\nTo find the possible next steps for the input `2 2 10 10`, we can consider applying basic arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers and replacing them with the result. Here are the possible next steps:\nTo find the possible next steps for the input `2 2 10 10`, we can apply basic arithmetic operations (addition, subtraction, multiplication, and division) on any pair of numbers from the list. Here are the possible next steps:\nTo find the possible next steps for the input `2 2 10 10`, we can apply basic arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers, and replace those two numbers with the result of the operation. Here are the possible next steps:\n"
|
||||
],
|
||||
"values": [
|
||||
0
|
||||
],
|
||||
"select_new_ys": [
|
||||
"Here's the list of possible next steps for the input `2 2 10 10`:\nTo find the possible next steps for the input `2 2 10 10`, we can consider applying basic arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers and replacing them with the result. Here are the possible next steps:\nTo find the possible next steps for the input `2 2 10 10`, we can apply basic arithmetic operations (addition, subtraction, multiplication, and division) on any pair of numbers from the list. Here are the possible next steps:\nTo find the possible next steps for the input `2 2 10 10`, we can apply basic arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers, and replace those two numbers with the result of the operation. Here are the possible next steps:\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"idx": 8,
|
||||
"ys": [
|
||||
"Here's the list of possible next steps for the input `2 2 10 10`:\nTo find the possible next steps for the input `2 2 10 10`, we can consider applying basic arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers and replacing them with the result. Here are the possible next steps:\nTo find the possible next steps for the input `2 2 10 10`, we can apply basic arithmetic operations (addition, subtraction, multiplication, and division) on any pair of numbers from the list. Here are the possible next steps:\nTo find the possible next steps for the input `2 2 10 10`, we can apply basic arithmetic operations (addition, subtraction, multiplication, and division) between any two numbers, and replace those two numbers with the result of the operation. Here are the possible next steps:\n"
|
||||
],
|
||||
"infos": [
|
||||
{
|
||||
"r": 0
|
||||
}
|
||||
],
|
||||
"usage_so_far": {
|
||||
"completion_tokens": 11716,
|
||||
"prompt_tokens": 8883,
|
||||
"cost": 0.9694499999999999
|
||||
}
|
||||
},
|
||||
{
|
||||
"steps": [
|
||||
{
|
||||
"step": 0,
|
||||
"x": "1 1 1 12",
|
||||
"ys": [
|
||||
""
|
||||
],
|
||||
"new_ys": [
|
||||
"Given the input numbers 1, 1, 1, and 12, here are the possible next steps you can take by performing arithmetic operations (addition, subtraction, multiplication, division) between any two numbers:\n"
|
||||
],
|
||||
"values": [
|
||||
0.001
|
||||
],
|
||||
"select_new_ys": [
|
||||
"Given the input numbers 1, 1, 1, and 12, here are the possible next steps you can take by performing arithmetic operations (addition, subtraction, multiplication, division) between any two numbers:\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"step": 1,
|
||||
"x": "1 1 1 12",
|
||||
"ys": [
|
||||
"Given the input numbers 1, 1, 1, and 12, here are the possible next steps you can take by performing arithmetic operations (addition, subtraction, multiplication, division) between any two numbers:\n"
|
||||
],
|
||||
"new_ys": [
|
||||
"Given the input numbers 1, 1, 1, and 12, here are the possible next steps you can take by performing arithmetic operations (addition, subtraction, multiplication, division) between any two numbers:\nGiven the input numbers 1, 1, 1, and 12, here are the possible next steps you can take by performing basic arithmetic operations (addition, subtraction, multiplication, and division):\n"
|
||||
],
|
||||
"values": [
|
||||
0.001
|
||||
],
|
||||
"select_new_ys": [
|
||||
"Given the input numbers 1, 1, 1, and 12, here are the possible next steps you can take by performing arithmetic operations (addition, subtraction, multiplication, division) between any two numbers:\nGiven the input numbers 1, 1, 1, and 12, here are the possible next steps you can take by performing basic arithmetic operations (addition, subtraction, multiplication, and division):\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"step": 2,
|
||||
"x": "1 1 1 12",
|
||||
"ys": [
|
||||
"Given the input numbers 1, 1, 1, and 12, here are the possible next steps you can take by performing arithmetic operations (addition, subtraction, multiplication, division) between any two numbers:\nGiven the input numbers 1, 1, 1, and 12, here are the possible next steps you can take by performing basic arithmetic operations (addition, subtraction, multiplication, and division):\n"
|
||||
],
|
||||
"new_ys": [
|
||||
"Given the input numbers 1, 1, 1, and 12, here are the possible next steps you can take by performing arithmetic operations (addition, subtraction, multiplication, division) between any two numbers:\nGiven the input numbers 1, 1, 1, and 12, here are the possible next steps you can take by performing basic arithmetic operations (addition, subtraction, multiplication, and division):\nGiven the input numbers 1, 1, 1, and 12, here are the possible next steps you can take by performing basic arithmetic operations:\n"
|
||||
],
|
||||
"values": [
|
||||
0.001
|
||||
],
|
||||
"select_new_ys": [
|
||||
"Given the input numbers 1, 1, 1, and 12, here are the possible next steps you can take by performing arithmetic operations (addition, subtraction, multiplication, division) between any two numbers:\nGiven the input numbers 1, 1, 1, and 12, here are the possible next steps you can take by performing basic arithmetic operations (addition, subtraction, multiplication, and division):\nGiven the input numbers 1, 1, 1, and 12, here are the possible next steps you can take by performing basic arithmetic operations:\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"step": 3,
|
||||
"x": "1 1 1 12",
|
||||
"ys": [
|
||||
"Given the input numbers 1, 1, 1, and 12, here are the possible next steps you can take by performing arithmetic operations (addition, subtraction, multiplication, division) between any two numbers:\nGiven the input numbers 1, 1, 1, and 12, here are the possible next steps you can take by performing basic arithmetic operations (addition, subtraction, multiplication, and division):\nGiven the input numbers 1, 1, 1, and 12, here are the possible next steps you can take by performing basic arithmetic operations:\n"
|
||||
],
|
||||
"new_ys": [
|
||||
"Given the input numbers 1, 1, 1, and 12, here are the possible next steps you can take by performing arithmetic operations (addition, subtraction, multiplication, division) between any two numbers:\nGiven the input numbers 1, 1, 1, and 12, here are the possible next steps you can take by performing basic arithmetic operations (addition, subtraction, multiplication, and division):\nGiven the input numbers 1, 1, 1, and 12, here are the possible next steps you can take by performing basic arithmetic operations:\n1 + 1 = 2 (left: 1 1 2 12)\n"
|
||||
],
|
||||
"values": [
|
||||
0
|
||||
],
|
||||
"select_new_ys": [
|
||||
"Given the input numbers 1, 1, 1, and 12, here are the possible next steps you can take by performing arithmetic operations (addition, subtraction, multiplication, division) between any two numbers:\nGiven the input numbers 1, 1, 1, and 12, here are the possible next steps you can take by performing basic arithmetic operations (addition, subtraction, multiplication, and division):\nGiven the input numbers 1, 1, 1, and 12, here are the possible next steps you can take by performing basic arithmetic operations:\n1 + 1 = 2 (left: 1 1 2 12)\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"idx": 9,
|
||||
"ys": [
|
||||
"Given the input numbers 1, 1, 1, and 12, here are the possible next steps you can take by performing arithmetic operations (addition, subtraction, multiplication, division) between any two numbers:\nGiven the input numbers 1, 1, 1, and 12, here are the possible next steps you can take by performing basic arithmetic operations (addition, subtraction, multiplication, and division):\nGiven the input numbers 1, 1, 1, and 12, here are the possible next steps you can take by performing basic arithmetic operations:\n1 + 1 = 2 (left: 1 1 2 12)\n"
|
||||
],
|
||||
"infos": [
|
||||
{
|
||||
"r": 0
|
||||
}
|
||||
],
|
||||
"usage_so_far": {
|
||||
"completion_tokens": 13066,
|
||||
"prompt_tokens": 11097,
|
||||
"cost": 1.11687
|
||||
}
|
||||
}
|
||||
]
|
||||
378
logs/game24/gpt-4o_0.7_propose5_value1_greedy1_start5_end6.json
Normal file
378
logs/game24/gpt-4o_0.7_propose5_value1_greedy1_start5_end6.json
Normal file
@ -0,0 +1,378 @@
|
||||
[
|
||||
{
|
||||
"steps": [
|
||||
{
|
||||
"step": 0,
|
||||
"x": "1 1 2 12",
|
||||
"ys": [
|
||||
""
|
||||
],
|
||||
"new_ys": [
|
||||
"Here are the possible next steps with the numbers 1, 1, 2, and 12:\n",
|
||||
"\n",
|
||||
"1. Add 1 and 1:\n",
|
||||
" - 1 + 1 = 2 (left: 2, 2, 12)\n",
|
||||
"\n",
|
||||
"2. Subtract 1 from 2:\n",
|
||||
" - 2 - 1 = 1 (left: 1, 1, 12)\n",
|
||||
"\n",
|
||||
"3. Multiply 1 and 1:\n",
|
||||
" - 1 * 1 = 1 (left: 1, 2, 12)\n",
|
||||
"\n",
|
||||
"4. Add 1 and 2:\n",
|
||||
" - 1 + 2 = 3 (left: 1, 3, 12)\n",
|
||||
"\n",
|
||||
"5. Subtract 1 from 12:\n",
|
||||
" - 12 - 1 = 11 (left: 1, 1, 11)\n",
|
||||
"\n",
|
||||
"6. Subtract 2 from 12:\n",
|
||||
" - 12 - 2 = 10 (left: 1, 1, 10)\n",
|
||||
"\n",
|
||||
"7. Divide 12 by 2:\n",
|
||||
" - 12 / 2 = 6 (left: 1, 1, 6)\n",
|
||||
"\n",
|
||||
"8. Add 1 and 12:\n",
|
||||
" - 1 + 12 = 13 (left: 1, 2, 13)\n",
|
||||
"\n",
|
||||
"9. Add 2 and 12:\n",
|
||||
" - 2 + 12 = 14 (left: 1, 1, 14)\n",
|
||||
"\n",
|
||||
"10. Multiply 2 and 12:\n",
|
||||
" - 2 * 12 = 24 (left: 1, 1, 24)\n",
|
||||
"\n",
|
||||
"These are the possible operations you can perform with the numbers 1, 1, 2, and 12.\n"
|
||||
],
|
||||
"values": [
|
||||
0.0,
|
||||
0.001,
|
||||
0.001,
|
||||
0.0,
|
||||
0,
|
||||
0.001,
|
||||
0.0,
|
||||
0,
|
||||
0.001,
|
||||
0.0,
|
||||
0,
|
||||
0.0,
|
||||
0.0,
|
||||
0,
|
||||
0.001,
|
||||
0.0,
|
||||
0,
|
||||
0.001,
|
||||
0.0,
|
||||
0,
|
||||
0.001,
|
||||
0.0,
|
||||
0,
|
||||
0.001,
|
||||
0.0,
|
||||
0,
|
||||
0.001,
|
||||
0.0,
|
||||
0,
|
||||
0.001,
|
||||
0.0,
|
||||
0,
|
||||
0.001
|
||||
],
|
||||
"select_new_ys": [
|
||||
"\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"step": 1,
|
||||
"x": "1 1 2 12",
|
||||
"ys": [
|
||||
"\n"
|
||||
],
|
||||
"new_ys": [
|
||||
"\nTo generate possible next steps, follow a similar process as the example and apply basic arithmetic operations to pairs of numbers. Here's how you can do it:\n",
|
||||
"\n\n",
|
||||
"\nGiven a list of numbers, you can select any two numbers and apply one of the following operations: addition, subtraction, multiplication, or division (if divisible). After applying an operation, replace the two numbers with the result, and list the remaining numbers along with the result.\n",
|
||||
"\n\n",
|
||||
"\nLet's illustrate this with a new input:\n",
|
||||
"\n\n",
|
||||
"\nInput: 3 5 9 15\n",
|
||||
"\n\n",
|
||||
"\nPossible next steps:\n",
|
||||
"\n\n",
|
||||
"\n1. **3 + 5 = 8** (left: 8 9 15)\n",
|
||||
"\n2. **3 - 5 = -2** (left: -2 9 15)\n",
|
||||
"\n3. **5 - 3 = 2** (left: 2 9 15)\n",
|
||||
"\n4. **3 * 5 = 15** (left: 9 15 15)\n",
|
||||
"\n5. **9 + 3 = 12** (left: 5 12 15)\n",
|
||||
"\n6. **9 - 3 = 6** (left: 5 6 15)\n",
|
||||
"\n7. **3 * 9 = 27** (left: 5 15 27)\n",
|
||||
"\n8. **15 + 3 = 18** (left: 5 9 18)\n",
|
||||
"\n9. **15 - 3 = 12** (left: 5 9 12)\n",
|
||||
"\n10. **3 * 15 = 45** (left: 5 9 45)\n",
|
||||
"\n11. **5 + 9 = 14** (left: 3 14 15)\n",
|
||||
"\n12. **9 - 5 = 4** (left: 3 4 15)\n",
|
||||
"\n13. **5 * 9 = 45** (left: 3 15 45)\n",
|
||||
"\n14. **15 + 5 = 20** (left: 3 9 20)\n",
|
||||
"\n15. **15 - 5 = 10** (left: 3 9 10)\n",
|
||||
"\n16. **5 * 15 = 75** (left: 3 9 75)\n",
|
||||
"\n17. **9 + 15 = 24** (left: 3 5 24)\n",
|
||||
"\n18. **15 - 9 = 6** (left: 3 5 6)\n",
|
||||
"\n19. **9 * 15 = 135** (left: 3 5 135)\n",
|
||||
"\n\n",
|
||||
"\nThese are just some of the possible operations. You can continue to explore other combinations and operations based on the context and goals of your problem.\n"
|
||||
],
|
||||
"values": [
|
||||
0.0,
|
||||
0.001,
|
||||
0.001,
|
||||
0,
|
||||
0.001,
|
||||
0,
|
||||
0.001,
|
||||
0,
|
||||
20.0,
|
||||
0,
|
||||
0.0,
|
||||
0.0,
|
||||
0.0,
|
||||
0.0,
|
||||
0.0,
|
||||
0.0,
|
||||
0.0,
|
||||
0.0,
|
||||
0.0,
|
||||
0.0,
|
||||
0.0,
|
||||
0.0,
|
||||
0.0,
|
||||
0.0,
|
||||
0.0,
|
||||
0.0,
|
||||
0.0,
|
||||
0.0,
|
||||
0.0,
|
||||
0,
|
||||
0.001
|
||||
],
|
||||
"select_new_ys": [
|
||||
"\nPossible next steps:\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"step": 2,
|
||||
"x": "1 1 2 12",
|
||||
"ys": [
|
||||
"\nPossible next steps:\n"
|
||||
],
|
||||
"new_ys": [
|
||||
"\nPossible next steps:\nTo generate the possible next steps from a given set of numbers, you can consider each pair of numbers and apply the basic arithmetic operations: addition, subtraction, multiplication, and division (when applicable). Here are the steps for generating possible next steps with the numbers you provided:\n",
|
||||
"\nPossible next steps:\n\n",
|
||||
"\nPossible next steps:\nInput: 2 8 8 14\n",
|
||||
"\nPossible next steps:\n\n",
|
||||
"\nPossible next steps:\n1. **Addition:**\n",
|
||||
"\nPossible next steps:\n\n",
|
||||
"\nPossible next steps:\n - 2 + 8 = 10 (remaining: 8 10 14)\n",
|
||||
"\nPossible next steps:\n - 2 + 8 (second 8) = 10 (remaining: 8 10 14)\n",
|
||||
"\nPossible next steps:\n - 2 + 14 = 16 (remaining: 8 8 16)\n",
|
||||
"\nPossible next steps:\n - 8 + 8 = 16 (remaining: 2 14 16)\n",
|
||||
"\nPossible next steps:\n - 8 + 14 = 22 (remaining: 2 8 22)\n",
|
||||
"\nPossible next steps:\n - 8 (second 8) + 14 = 22 (remaining: 2 8 22)\n",
|
||||
"\nPossible next steps:\n\n",
|
||||
"\nPossible next steps:\n2. **Subtraction:**\n",
|
||||
"\nPossible next steps:\n\n",
|
||||
"\nPossible next steps:\n - 8 - 2 = 6 (remaining: 6 8 14)\n",
|
||||
"\nPossible next steps:\n - 8 (second 8) - 2 = 6 (remaining: 6 8 14)\n",
|
||||
"\nPossible next steps:\n - 14 - 2 = 12 (remaining: 8 8 12)\n",
|
||||
"\nPossible next steps:\n - 14 - 8 = 6 (remaining: 2 8 6)\n",
|
||||
"\nPossible next steps:\n - 14 - 8 (second 8) = 6 (remaining: 2 8 6)\n",
|
||||
"\nPossible next steps:\n - 8 - 8 = 0 (remaining: 2 14 0)\n",
|
||||
"\nPossible next steps:\n - 2 - 8 = -6 (remaining: -6 8 14)\n",
|
||||
"\nPossible next steps:\n - 8 - 14 = -6 (remaining: 2 8 -6)\n",
|
||||
"\nPossible next steps:\n\n",
|
||||
"\nPossible next steps:\n3. **Multiplication:**\n",
|
||||
"\nPossible next steps:\n\n",
|
||||
"\nPossible next steps:\n - 2 * 8 = 16 (remaining: 8 14 16)\n",
|
||||
"\nPossible next steps:\n - 2 * 8 (second 8) = 16 (remaining: 8 14 16)\n",
|
||||
"\nPossible next steps:\n - 2 * 14 = 28 (remaining: 8 8 28)\n",
|
||||
"\nPossible next steps:\n - 8 * 8 = 64 (remaining: 2 14 64)\n",
|
||||
"\nPossible next steps:\n - 8 * 14 = 112 (remaining: 2 8 112)\n",
|
||||
"\nPossible next steps:\n\n",
|
||||
"\nPossible next steps:\n4. **Division** (only when the result is an integer):\n",
|
||||
"\nPossible next steps:\n\n",
|
||||
"\nPossible next steps:\n - 8 / 2 = 4 (remaining: 4 8 14)\n",
|
||||
"\nPossible next steps:\n - 14 / 2 = 7 (remaining: 8 8 7)\n",
|
||||
"\nPossible next steps:\n - 8 / 8 = 1 (remaining: 2 14 1)\n",
|
||||
"\nPossible next steps:\n - 14 / 8 = 1.75 (not an integer, so not considered)\n",
|
||||
"\nPossible next steps:\n\n",
|
||||
"\nPossible next steps:\nThese are the possible next steps you can take from the given set of numbers. Each operation reduces the set of numbers by one while adding the result of the operation back to the list.\n"
|
||||
],
|
||||
"values": [
|
||||
0.001,
|
||||
20.0,
|
||||
0.001,
|
||||
0,
|
||||
0.001,
|
||||
0,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0,
|
||||
0.001,
|
||||
0,
|
||||
0.0,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0,
|
||||
0.001,
|
||||
0,
|
||||
0.001,
|
||||
0.0,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0,
|
||||
0.001,
|
||||
0,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0,
|
||||
0.001
|
||||
],
|
||||
"select_new_ys": [
|
||||
"\nPossible next steps:\n\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"step": 3,
|
||||
"x": "1 1 2 12",
|
||||
"ys": [
|
||||
"\nPossible next steps:\n\n"
|
||||
],
|
||||
"new_ys": [
|
||||
"\nPossible next steps:\n\nTo determine the possible next steps, we take each pair of numbers and apply the basic arithmetic operations (addition, subtraction, multiplication, and division where applicable) to see what new set of numbers we can create. Let's consider the set of numbers you provided: \\(2, 8, 8, 14\\).\n",
|
||||
"\nPossible next steps:\n\n\n",
|
||||
"\nPossible next steps:\n\n### Current Set: 2, 8, 8, 14\n",
|
||||
"\nPossible next steps:\n\nWe'll evaluate each pair of numbers:\n",
|
||||
"\nPossible next steps:\n\n\n",
|
||||
"\nPossible next steps:\n\n1. **2 and 8**\n",
|
||||
"\nPossible next steps:\n\n - Addition: \\(2 + 8 = 10\\) \u2192 New set: 8, 10, 14\n",
|
||||
"\nPossible next steps:\n\n - Subtraction: \\(8 - 2 = 6\\) \u2192 New set: 6, 8, 14\n",
|
||||
"\nPossible next steps:\n\n - Multiplication: \\(2 \\times 8 = 16\\) \u2192 New set: 8, 14, 16\n",
|
||||
"\nPossible next steps:\n\n - Division: \\(8 \\div 2 = 4\\) \u2192 New set: 4, 8, 14\n",
|
||||
"\nPossible next steps:\n\n\n",
|
||||
"\nPossible next steps:\n\n2. **2 and 14**\n",
|
||||
"\nPossible next steps:\n\n - Addition: \\(2 + 14 = 16\\) \u2192 New set: 8, 8, 16\n",
|
||||
"\nPossible next steps:\n\n - Subtraction: \\(14 - 2 = 12\\) \u2192 New set: 8, 8, 12\n",
|
||||
"\nPossible next steps:\n\n - Multiplication: \\(2 \\times 14 = 28\\) \u2192 New set: 8, 8, 28\n",
|
||||
"\nPossible next steps:\n\n - Division: \\(14 \\div 2 = 7\\) \u2192 New set: 7, 8, 8\n",
|
||||
"\nPossible next steps:\n\n\n",
|
||||
"\nPossible next steps:\n\n3. **8 and 8**\n",
|
||||
"\nPossible next steps:\n\n - Addition: \\(8 + 8 = 16\\) \u2192 New set: 2, 14, 16\n",
|
||||
"\nPossible next steps:\n\n - Subtraction: \\(8 - 8 = 0\\) \u2192 New set: 2, 0, 14\n",
|
||||
"\nPossible next steps:\n\n - Multiplication: \\(8 \\times 8 = 64\\) \u2192 New set: 2, 14, 64\n",
|
||||
"\nPossible next steps:\n\n - Division: \\(8 \\div 8 = 1\\) \u2192 New set: 2, 14, 1\n",
|
||||
"\nPossible next steps:\n\n\n",
|
||||
"\nPossible next steps:\n\n4. **8 and 14**\n",
|
||||
"\nPossible next steps:\n\n - Addition: \\(8 + 14 = 22\\) \u2192 New set: 2, 8, 22\n",
|
||||
"\nPossible next steps:\n\n - Subtraction: \\(14 - 8 = 6\\) \u2192 New set: 2, 6, 8\n",
|
||||
"\nPossible next steps:\n\n - Multiplication: \\(8 \\times 14 = 112\\) \u2192 New set: 2, 8, 112\n",
|
||||
"\nPossible next steps:\n\n - Division: \\(14 \\div 8 = 1.75\\) (not an integer, usually not considered unless fractional results are allowed)\n",
|
||||
"\nPossible next steps:\n\n\n",
|
||||
"\nPossible next steps:\n\n### Summary of Possible Next Steps:\n",
|
||||
"\nPossible next steps:\n\n- New set: 8, 10, 14\n",
|
||||
"\nPossible next steps:\n\n- New set: 6, 8, 14\n",
|
||||
"\nPossible next steps:\n\n- New set: 8, 14, 16\n",
|
||||
"\nPossible next steps:\n\n- New set: 4, 8, 14\n",
|
||||
"\nPossible next steps:\n\n- New set: 8, 8, 16\n",
|
||||
"\nPossible next steps:\n\n- New set: 8, 8, 12\n",
|
||||
"\nPossible next steps:\n\n- New set: 8, 8, 28\n",
|
||||
"\nPossible next steps:\n\n- New set: 7, 8, 8\n",
|
||||
"\nPossible next steps:\n\n- New set: 2, 14, 16\n",
|
||||
"\nPossible next steps:\n\n- New set: 2, 0, 14\n",
|
||||
"\nPossible next steps:\n\n- New set: 2, 14, 64\n",
|
||||
"\nPossible next steps:\n\n- New set: 2, 14, 1\n",
|
||||
"\nPossible next steps:\n\n- New set: 2, 8, 22\n",
|
||||
"\nPossible next steps:\n\n- New set: 2, 6, 8\n",
|
||||
"\nPossible next steps:\n\n- New set: 2, 8, 112\n",
|
||||
"\nPossible next steps:\n\n\n",
|
||||
"\nPossible next steps:\n\nThese are all the possible next steps using the given numbers.\n"
|
||||
],
|
||||
"values": [
|
||||
0.001,
|
||||
20.0,
|
||||
0.001,
|
||||
0.0,
|
||||
0,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.0,
|
||||
0,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0,
|
||||
0.0,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0.001,
|
||||
0,
|
||||
0.001
|
||||
],
|
||||
"select_new_ys": [
|
||||
"\nPossible next steps:\n\n\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"idx": 5,
|
||||
"ys": [
|
||||
"\nPossible next steps:\n\n\n"
|
||||
],
|
||||
"infos": [
|
||||
{
|
||||
"r": 0
|
||||
}
|
||||
],
|
||||
"usage_so_far": {
|
||||
"completion_tokens": 11939,
|
||||
"prompt_tokens": 39972,
|
||||
"cost": 1.9155
|
||||
}
|
||||
}
|
||||
]
|
||||
8
run.py
8
run.py
@ -27,6 +27,14 @@ def run(args):
|
||||
else:
|
||||
ys, info = solve(args, task, i)
|
||||
|
||||
|
||||
# print("HEY IM IN RUN AND I SOLVED")
|
||||
# print("THIS IS THE Y")
|
||||
# print(ys)
|
||||
# print("ThIS IS THE INFO")
|
||||
# print(info)
|
||||
# exit()
|
||||
|
||||
# log
|
||||
infos = [task.test_output(i, y) for y in ys]
|
||||
info.update({'idx': i, 'ys': ys, 'infos': infos, 'usage_so_far': gpt_usage(args.backend)})
|
||||
|
||||
@ -20,6 +20,9 @@ def get_values(task, x, ys, n_evaluate_sample, cache_value=True):
|
||||
values = []
|
||||
local_value_cache = {}
|
||||
for y in ys: # each partial output
|
||||
# print("THIS IS THE Y")
|
||||
# print(y)
|
||||
# print("*****")
|
||||
if y in local_value_cache: # avoid duplicate candidates
|
||||
value = 0
|
||||
else:
|
||||
@ -37,8 +40,10 @@ def get_votes(task, x, ys, n_evaluate_sample):
|
||||
|
||||
def get_proposals(task, x, y):
|
||||
propose_prompt = task.propose_prompt_wrap(x, y)
|
||||
print("prompt proposed -- now running inference...")
|
||||
# print("prompt proposed -- now running inference...")
|
||||
proposals = inference_model(propose_prompt, n=1, stop=None)[0].split('\n')
|
||||
# print(proposals)
|
||||
# print("*****=======")
|
||||
return [y + _ + '\n' for _ in proposals]
|
||||
|
||||
def get_samples(task, x, y, n_generate_sample, prompt_sample, stop):
|
||||
@ -67,9 +72,14 @@ def solve(args, task, idx, to_print=True):
|
||||
# elif args.method_generate == 'propose':
|
||||
else:
|
||||
new_ys = [get_proposals(task, x, y) for y in ys]
|
||||
# print("NEW YS BEFORE ITERTOOl")
|
||||
# print(new_ys)
|
||||
# print("**********")
|
||||
new_ys = list(itertools.chain(*new_ys))
|
||||
ids = list(range(len(new_ys)))
|
||||
|
||||
# print("THESE ARE THE NEW YS")
|
||||
# print(new_ys)
|
||||
# print("**********")
|
||||
print("Starting eval!!")
|
||||
# evaluation
|
||||
if args.method_evaluate == 'vote':
|
||||
@ -77,9 +87,9 @@ def solve(args, task, idx, to_print=True):
|
||||
elif args.method_evaluate == 'value':
|
||||
values = get_values(task, x, new_ys, args.n_evaluate_sample)
|
||||
|
||||
print("THESE ARE THE VALUES")
|
||||
print(values)
|
||||
print("********")
|
||||
# print("THESE ARE THE VALUES")
|
||||
# print(values)
|
||||
# print("********")
|
||||
|
||||
print("Starting selection!!")
|
||||
# selection
|
||||
|
||||
@ -73,22 +73,14 @@ def chatgpt(messages, model="gpt-4", temperature=0.7, max_tokens=1000, n=1, stop
|
||||
outputs = []
|
||||
client = OpenAI()
|
||||
while n > 0:
|
||||
cnt = min(n, 20) #never generate more than 20 outputs per same input
|
||||
cnt = min(n, 20)
|
||||
n -= cnt
|
||||
|
||||
# print("made it into n loop")
|
||||
# res = completions_with_backoff(model=model, messages=messages, temperature=temperature, n=cnt, stop=stop)
|
||||
# print(messages)
|
||||
|
||||
res = client.chat.completions.create(model=model, messages=messages, temperature=temperature, n=cnt, stop=stop)
|
||||
# print("got result from chatgpt")
|
||||
# print(cnt)
|
||||
# print(res)
|
||||
res_answer = res.choices[0].message.content
|
||||
# print(res_answer)
|
||||
outputs.extend(res_answer.split('\n'))
|
||||
# print(outputs)
|
||||
|
||||
# print(f"{n} inference complete. now logging...")
|
||||
outputs.extend([res_answer]) #will add in support for generate sample > 1 hyperparam later
|
||||
|
||||
# log completion tokens
|
||||
completion_tokens += res.usage.completion_tokens
|
||||
prompt_tokens += res.usage.prompt_tokens
|
||||
|
||||
@ -74,6 +74,10 @@ class Game24Task(Task):
|
||||
|
||||
@staticmethod
|
||||
def value_prompt_wrap(x: str, y: str) -> str:
|
||||
# print("IM IN VALUE PROMPT WRAP")
|
||||
# print(y)
|
||||
# print(x)
|
||||
# print("******")
|
||||
last_line = y.strip().split('\n')[-1]
|
||||
if 'left: ' not in last_line: # last step
|
||||
ans = last_line.lower().replace('answer: ', '')
|
||||
|
||||
Loading…
Reference in New Issue
Block a user