diff --git a/logs/game24/gpt-4o_0.7_propose5_value1_greedy1_start10_end15.json b/logs/game24/gpt-4o_0.7_propose5_value1_greedy1_start10_end15.json index c3ca6a0..7a29c92 100644 --- a/logs/game24/gpt-4o_0.7_propose5_value1_greedy1_start10_end15.json +++ b/logs/game24/gpt-4o_0.7_propose5_value1_greedy1_start10_end15.json @@ -8,7 +8,7 @@ "" ], "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", + "Here are some possible next steps with the numbers 1, 1, 2, and 8:\n", "\n", "1. \\(1 + 1 = 2\\) (left: 2, 2, 8)\n", "2. \\(1 + 2 = 3\\) (left: 1, 3, 8)\n", @@ -17,14 +17,13 @@ "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", + "8. \\(2 - 1 = 1\\) (left: 1, 1, 8)\n", + "9. \\(8 - 1 = 7\\) (left: 1, 2, 7)\n", + "10. \\(8 - 2 = 6\\) (left: 1, 1, 6)\n", + "11. \\(8 \\div 1 = 8\\) (left: 1, 2, 8)\n", + "12. \\(8 \\div 2 = 4\\) (left: 1, 1, 4)\n", "\n", - "These are the possible next steps using basic arithmetic operations. Note that division operations only result in integer outcomes.\n" + "These are some of the possible operations you can perform with the given numbers.\n" ], "values": [ 0.001, @@ -41,236 +40,141 @@ 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" + "Here are some possible next steps with the numbers 1, 1, 2, and 8:\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" + "Here are some possible next steps with the numbers 1, 1, 2, and 8:\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" + "Here are some possible next steps with the numbers 1, 1, 2, and 8:\n1 + 1 = 2 (left: 2 2 8) \n", + "Here are some possible next steps with the numbers 1, 1, 2, and 8:\n1 + 2 = 3 (left: 1 3 8) \n", + "Here are some possible next steps with the numbers 1, 1, 2, and 8:\n1 + 8 = 9 (left: 1 2 9) \n", + "Here are some possible next steps with the numbers 1, 1, 2, and 8:\n1 + 1 = 2 (left: 2 2 8) \n", + "Here are some possible next steps with the numbers 1, 1, 2, and 8:\n1 + 2 = 3 (left: 1 3 8) \n", + "Here are some possible next steps with the numbers 1, 1, 2, and 8:\n1 + 8 = 9 (left: 1 2 9) \n", + "Here are some possible next steps with the numbers 1, 1, 2, and 8:\n2 + 8 = 10 (left: 1 1 10) \n", + "Here are some possible next steps with the numbers 1, 1, 2, and 8:\n1 - 1 = 0 (left: 0 2 8) \n", + "Here are some possible next steps with the numbers 1, 1, 2, and 8:\n2 - 1 = 1 (left: 1 1 8) \n", + "Here are some possible next steps with the numbers 1, 1, 2, and 8:\n8 - 1 = 7 (left: 1 2 7) \n", + "Here are some possible next steps with the numbers 1, 1, 2, and 8:\n2 - 1 = 1 (left: 1 1 8) \n", + "Here are some possible next steps with the numbers 1, 1, 2, and 8:\n8 - 1 = 7 (left: 1 2 7) \n", + "Here are some possible next steps with the numbers 1, 1, 2, and 8:\n8 - 2 = 6 (left: 1 1 6) \n", + "Here are some possible next steps with the numbers 1, 1, 2, and 8:\n1 * 1 = 1 (left: 1 2 8) \n", + "Here are some possible next steps with the numbers 1, 1, 2, and 8:\n1 * 2 = 2 (left: 1 2 8) \n", + "Here are some possible next steps with the numbers 1, 1, 2, and 8:\n1 * 8 = 8 (left: 1 2 8) \n", + "Here are some possible next steps with the numbers 1, 1, 2, and 8:\n2 * 8 = 16 (left: 1 1 16) \n", + "Here are some possible next steps with the numbers 1, 1, 2, and 8:\n1 / 1 = 1 (left: 1 2 8) \n", + "Here are some possible next steps with the numbers 1, 1, 2, and 8:\n2 / 1 = 2 (left: 1 1 8) \n", + "Here are some possible next steps with the numbers 1, 1, 2, and 8:\n8 / 1 = 8 (left: 1 2 8) \n", + "Here are some possible next steps with the numbers 1, 1, 2, and 8:\n8 / 2 = 4 (left: 1 1 4)\n" ], "values": [ 0.0, - 0.001, - 0.001, - 0.001, 0.0, - 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, - 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, + 0.0, + 0.0, + 0.0, 0, - 0.001 + 0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 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\n" + "Here are some possible next steps with the numbers 1, 1, 2, and 8:\n1 + 1 = 2 (left: 2 2 8) \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" + "Here are some possible next steps with the numbers 1, 1, 2, and 8:\n1 + 1 = 2 (left: 2 2 8) \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" + "Here are some possible next steps with the numbers 1, 1, 2, and 8:\n1 + 1 = 2 (left: 2 2 8) \nHere are the possible next steps for the input `2 2 8`:\n", + "Here are some possible next steps with the numbers 1, 1, 2, and 8:\n1 + 1 = 2 (left: 2 2 8) \n\n", + "Here are some possible next steps with the numbers 1, 1, 2, and 8:\n1 + 1 = 2 (left: 2 2 8) \n1. \\(2 + 2 = 4\\) (left: 4 8)\n", + "Here are some possible next steps with the numbers 1, 1, 2, and 8:\n1 + 1 = 2 (left: 2 2 8) \n2. \\(2 \\times 2 = 4\\) (left: 4 8)\n", + "Here are some possible next steps with the numbers 1, 1, 2, and 8:\n1 + 1 = 2 (left: 2 2 8) \n3. \\(8 - 2 = 6\\) (left: 2 6)\n", + "Here are some possible next steps with the numbers 1, 1, 2, and 8:\n1 + 1 = 2 (left: 2 2 8) \n4. \\(8 - 2 = 6\\) (left: 2 6)\n", + "Here are some possible next steps with the numbers 1, 1, 2, and 8:\n1 + 1 = 2 (left: 2 2 8) \n5. \\(8 / 2 = 4\\) (left: 2 4)\n", + "Here are some possible next steps with the numbers 1, 1, 2, and 8:\n1 + 1 = 2 (left: 2 2 8) \n6. \\(8 / 2 = 4\\) (left: 2 4)\n", + "Here are some possible next steps with the numbers 1, 1, 2, and 8:\n1 + 1 = 2 (left: 2 2 8) \n\n", + "Here are some possible next steps with the numbers 1, 1, 2, and 8:\n1 + 1 = 2 (left: 2 2 8) \nNote: Steps 1 and 2 result in the same state (4 8), and steps 3 and 4 result in the same state (2 6), as do steps 5 and 6, resulting in the state (2 4).\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, + 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\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" + "Here are some possible next steps with the numbers 1, 1, 2, and 8:\n1 + 1 = 2 (left: 2 2 8) \nHere are the possible next steps for the input `2 2 8`:\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" + "Here are some possible next steps with the numbers 1, 1, 2, and 8:\n1 + 1 = 2 (left: 2 2 8) \nHere are the possible next steps for the input `2 2 8`:\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" + "Here are some possible next steps with the numbers 1, 1, 2, and 8:\n1 + 1 = 2 (left: 2 2 8) \nHere are the possible next steps for the input `2 2 8`:\nFor the input `2 2 8`, here are the possible next steps:\n", + "Here are some possible next steps with the numbers 1, 1, 2, and 8:\n1 + 1 = 2 (left: 2 2 8) \nHere are the possible next steps for the input `2 2 8`:\n\n", + "Here are some possible next steps with the numbers 1, 1, 2, and 8:\n1 + 1 = 2 (left: 2 2 8) \nHere are the possible next steps for the input `2 2 8`:\n1. \\(2 + 2 = 4\\) (left: 4 8)\n", + "Here are some possible next steps with the numbers 1, 1, 2, and 8:\n1 + 1 = 2 (left: 2 2 8) \nHere are the possible next steps for the input `2 2 8`:\n2. \\(2 \\times 2 = 4\\) (left: 4 8)\n", + "Here are some possible next steps with the numbers 1, 1, 2, and 8:\n1 + 1 = 2 (left: 2 2 8) \nHere are the possible next steps for the input `2 2 8`:\n3. \\(8 - 2 = 6\\) (left: 2 6)\n", + "Here are some possible next steps with the numbers 1, 1, 2, and 8:\n1 + 1 = 2 (left: 2 2 8) \nHere are the possible next steps for the input `2 2 8`:\n4. \\(8 - 2 = 6\\) (left: 2 6)\n", + "Here are some possible next steps with the numbers 1, 1, 2, and 8:\n1 + 1 = 2 (left: 2 2 8) \nHere are the possible next steps for the input `2 2 8`:\n5. \\(8 \\div 2 = 4\\) (left: 2 4)\n", + "Here are some possible next steps with the numbers 1, 1, 2, and 8:\n1 + 1 = 2 (left: 2 2 8) \nHere are the possible next steps for the input `2 2 8`:\n6. \\(8 \\div 2 = 4\\) (left: 2 4)\n", + "Here are some possible next steps with the numbers 1, 1, 2, and 8:\n1 + 1 = 2 (left: 2 2 8) \nHere are the possible next steps for the input `2 2 8`:\n\n", + "Here are some possible next steps with the numbers 1, 1, 2, and 8:\n1 + 1 = 2 (left: 2 2 8) \nHere are the possible next steps for the input `2 2 8`:\nNote: Since the two `2`s are indistinguishable in operations like addition and multiplication, the results are the same, but I've listed them to show all possible pairings.\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, 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" + "Here are some possible next steps with the numbers 1, 1, 2, and 8:\n1 + 1 = 2 (left: 2 2 8) \nHere are the possible next steps for the input `2 2 8`:\n\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" + "Here are some possible next steps with the numbers 1, 1, 2, and 8:\n1 + 1 = 2 (left: 2 2 8) \nHere are the possible next steps for the input `2 2 8`:\n\n" ], "infos": [ { @@ -278,361 +182,10 @@ } ], "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, - 0.0, - 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 - ], - "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 - } + "completion_tokens": 5961, + "prompt_tokens": 12152, + "cost": 0.7222199999999999 + }, + "total_runtime": 95.51803588000075 } ] \ No newline at end of file diff --git a/run.py b/run.py index 21a4f0b..ae0d671 100644 --- a/run.py +++ b/run.py @@ -22,22 +22,17 @@ def run(args): for i in range(args.task_start_index, args.task_end_index): # solve + start_timer = time.perf_counter() if args.naive_run: ys, info = naive_solve(args, task, i) 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() + runtime = time.perf_counter()-start_timer + print(runtime) # 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)}) + info.update({'idx': i, 'ys': ys, 'infos': infos, 'usage_so_far': gpt_usage(args.backend), 'total_runtime': runtime}) logs.append(info) with open(file, 'w') as f: json.dump(logs, f, indent=4) diff --git a/src/tot/methods/bfs.py b/src/tot/methods/bfs.py index 149506f..61ca5de 100644 --- a/src/tot/methods/bfs.py +++ b/src/tot/methods/bfs.py @@ -14,15 +14,10 @@ def get_value(task, x, y, n_evaluate_sample, cache_value=True): return value def get_values(task, x, ys, n_evaluate_sample, cache_value=True): - - # ys = list(set(ys)) - # print(ys) + 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: @@ -40,10 +35,8 @@ 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...") 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): @@ -72,26 +65,15 @@ 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': values = get_votes(task, x, new_ys, args.n_evaluate_sample) 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("Starting selection!!") # selection if args.method_select == 'sample': ps = np.array(values) / sum(values) diff --git a/src/tot/models.py b/src/tot/models.py index 4ed510a..f59760b 100644 --- a/src/tot/models.py +++ b/src/tot/models.py @@ -25,8 +25,7 @@ def inference_model(prompt, model="gpt-4o", temperature=0.7, max_tokens=1000, n= ''' Driver function for model inference. ''' - # print("made it into driver.") - if model == "llama_3.2" and vllm: + if model == "llama_3.2" and vllm: #will change this later return llama_32(prompt, quant, vllm, temperature, max_tokens, n, stop) else: messages = [{"role": "system", "content": "You are a helpful assistant."}, @@ -56,7 +55,7 @@ def hf_model(model, input_tokens, temperature=0.7, max_tokens=1000, n=1, stop=No outputs = [] while n > 0: - cnt = min(n, 20) #never generate more than 20 outputs per same input + cnt = min(n, 20) n -= cnt outputs = model.generate(**input_tokens, temperature=temperature, max_new_tokens=max_tokens, num_return_sequences=cnt) #might add stopping criteria depending on heuristics experimentation #need to take a look at the specific output format once i get access to the gated repo @@ -79,7 +78,7 @@ def chatgpt(messages, model="gpt-4", temperature=0.7, max_tokens=1000, n=1, stop res = client.chat.completions.create(model=model, messages=messages, temperature=temperature, n=cnt, stop=stop) res_answer = res.choices[0].message.content # print(res_answer) - outputs.extend([res_answer]) #will add in support for generate sample > 1 hyperparam later + outputs.extend([res_answer]) #will add in support for n > 1 hyperparam later # log completion tokens completion_tokens += res.usage.completion_tokens diff --git a/src/tot/tasks/game24.py b/src/tot/tasks/game24.py index 3f5bd59..c1cefaf 100644 --- a/src/tot/tasks/game24.py +++ b/src/tot/tasks/game24.py @@ -74,10 +74,6 @@ 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: ', '')