thought_cache_error.json

{"accepted": {"To obtain 24 using the numbers 14, 8, 8, and 2, we can decompose the task into the following subtasks:\n\n1. Explore all possible combinations of the given numbers.\n2. Apply basic arithmetic operations to each combination to evaluate if it can result in 24.\n3. If a combination results in 24, return it as the solution.\n4. If no combination results in 24, continue exploring other combinations.\n\nSubtask 1: Explore all possible combinations of the given numbers.\n1. Combine the numbers in all possible orders:\n   - 14, 8, 8, 2\n   - 14, 8, 2, 8\n   - 14, 2, 8, 8\n   - 8, 14, 8, 2\n   - 8, 14, 2, 8\n   - 8, 8, 14, 2\n   - 8, 8, 2, 14\n   - 8, 2, 14, 8\n   - 8, 2, 8, 14\n   - 2, 14, 8, 8\n   - 2, 8, 14, 8\n   - 2, 8, 8, 14\n\nSubtask 2: Apply basic arithmetic operations to each combination to evaluate if it can result in 24.\n1. For each combination, apply the four basic arithmetic operations (+, -, *, /) to evaluate if it equals 24.\n   - 14 + 8 + 8 + 2 = 32\n   - 14 + 8 + 2 + 8 = 32\n   - 14 + 2 + 8 + 8 = 32\n   - 8 + 14 + 8 + 2 = 32": 0.5, "To decompose the task into subtasks, we can follow the following steps:\n\n1. Identify the given numbers: 14, 8, 8, 2\n2. Determine all possible combinations of the given numbers.\n3. For each combination, perform basic arithmetic operations (+, -, *, /) to obtain 24.\n4. Check if any of the combinations result in 24.\n5. If a combination results in 24, return that combination as the solution.\n6. If none of the combinations result in 24, go back to step 2 and try different combinations.\n\nSubtask 1: Identify the given numbers\n- Given numbers: 14, 8, 8, 2\n\nSubtask 2: Determine all possible combinations of the given numbers\n- Possible combinations:\n    - 14 8 8 2\n    - 14 8 2 8\n    - 14 2 8 8\n    - 8 14 8 2\n    - 8 14 2 8\n    - 8 8 14 2\n    - 8 8 2 14\n    - 8 2 14 8\n    - 8 2 8 14\n    - 2 14 8 8\n    - 2 8 14 8\n    - 2 8 8 14\n\nSubtask 3: For each combination, perform basic arithmetic operations to obtain 24\n- Combination: 14 8 8 2\n    - 14 + 8 + 8 + 2 = 32 (not equal to 24)\n    - 14 + 8 + 8 - 2 = 28 (not equal to 24)\n    - 14 + 8 + 8 * 2 = 46 (not equal to 24)\n    - 14 +": 0.7}, "pruned": {"To obtain 24 using the numbers 14, 8, 8, and 2, we can decompose the task into the following subtasks:\n\n1. Explore all possible combinations of the given numbers.\n2. Apply basic arithmetic operations to each combination to evaluate if it can result in 24.\n3. If a combination results in 24, return it as the solution.\n4. If no combination results in 24, continue exploring other combinations.\n\nSubtask 1: Explore all possible combinations of the given numbers.\n1. Combine the numbers in all possible orders:\n   - 14, 8, 8, 2\n   - 14, 8, 2, 8\n   - 14, 2, 8, 8\n   - 8, 14, 8, 2\n   - 8, 14, 2, 8\n   - 8, 8, 14, 2\n   - 8, 8, 2, 14\n   - 8, 2, 14, 8\n   - 8, 2, 8, 14\n   - 2, 14, 8, 8\n   - 2, 8, 14, 8\n   - 2, 8, 8, 14\n\nSubtask 2: Apply basic arithmetic operations to each combination to evaluate if it can result in 24.\n1. For each combination, apply the four basic arithmetic operations (+, -, *, /) to evaluate if it equals 24.\n   - 14 + 8 + 8 + 2 = 32\n   - 14 + 8 + 2 + 8 = 32\n   - 14 + 2 + 8 + 8 = 32\n   - 8 + 14 + 8 + 2 = 32": 0.5, "To decompose the task into subtasks, we can follow the following steps:\n\n1. Identify the given numbers: 14, 8, 8, 2\n2. Determine all possible combinations of the given numbers.\n3. For each combination, perform basic arithmetic operations (+, -, *, /) to obtain 24.\n4. Check if any of the combinations result in 24.\n5. If a combination results in 24, return that combination as the solution.\n6. If none of the combinations result in 24, go back to step 2 and try different combinations.\n\nSubtask 1: Identify the given numbers\n- Given numbers: 14, 8, 8, 2\n\nSubtask 2: Determine all possible combinations of the given numbers\n- Possible combinations:\n    - 14 8 8 2\n    - 14 8 2 8\n    - 14 2 8 8\n    - 8 14 8 2\n    - 8 14 2 8\n    - 8 8 14 2\n    - 8 8 2 14\n    - 8 2 14 8\n    - 8 2 8 14\n    - 2 14 8 8\n    - 2 8 14 8\n    - 2 8 8 14\n\nSubtask 3: For each combination, perform basic arithmetic operations to obtain 24\n- Combination: 14 8 8 2\n    - 14 + 8 + 8 + 2 = 32 (not equal to 24)\n    - 14 + 8 + 8 - 2 = 28 (not equal to 24)\n    - 14 + 8 + 8 * 2 = 46 (not equal to 24)\n    - 14 +": 0.7}}{"accepted": {"To decompose the task into explicit subtasks, we can follow the steps below:\n\n1. Evaluate the given numbers and determine if any of them can be used directly to obtain 24 without any operations. If so, return the solution.\n\n2. Generate all possible combinations of the given numbers. This can be done by permuting the numbers and grouping them into pairs.\n\n3. For each combination, apply the four basic arithmetic operations (+, -, *, /) to the pair of numbers and evaluate if any of the results equal 24. If so, return the solution.\n\n4. If none of the combinations from step 3 yield a solution, generate all possible combinations of three numbers from the given set.\n\n5. For each combination of three numbers, apply the four basic arithmetic operations to the numbers in all possible orders and evaluate if any of the results equal 24. If so, return the solution.\n\n6. If none of the combinations from step 5 yield a solution, generate all possible combinations of four numbers from the given set.\n\n7. For each combination of four numbers, apply the four basic arithmetic operations to the numbers in all possible orders and evaluate if any of the results equal 24. If so, return the solution.\n\n8. If none of the combinations from step 7 yield a solution, repeat the process with different orders of operations (e.g., changing the order of addition, subtraction, multiplication, and division).\n\n9. If none of the combinations from step 8 yield a solution, return that there is no solution for the given set of numbers.\n\nProspective search steps:\n1. Check if any of the given numbers (14, 8, 8, 2) can be used directly to obtain 24.\n2. Generate all possible combinations of the given numbers: (14, 8), (14, 8), (14, 2), (8, 8), (8, 2), (8, 2).\n": 0.75}, "pruned": {"To decompose the task and find a solution, we can follow these subtasks:\n\n1. Explore all possible combinations of the given numbers (14, 8, 8, 2) to form equations using basic arithmetic operations (+ - * /).\n2. Check if any of the combinations result in 24 without using negative or fractional numbers.\n3. If no combination satisfies the condition in step 2, backtrack to a viable subtree and continue exploring.\n4. Repeat steps 1-3 until all possible combinations have been explored.\n5. Return the definitive end result, which is the equation that equals 24.\n\nNow let's go through the subtasks in detail:\n\n1. Explore all possible combinations of the given numbers (14, 8, 8, 2) to form equations using basic arithmetic operations (+ - * /):\n\n   - 14 + 8 + 8 + 2\n   - 14 + 8 + 8 - 2\n   - 14 + 8 + 8 * 2\n   - 14 + 8 + 8 / 2\n   - 14 + 8 - 8 + 2\n   - 14 + 8 - 8 - 2\n   - 14 + 8 - 8 * 2\n   - 14 + 8 - 8 / 2\n   - 14 + 8 * 8 + 2\n   - 14 + 8 * 8 - 2\n   - 14 + 8 * 8 * 2\n   - 14 + 8 * 8 / 2\n   - 14 + 8 / 8 + 2\n   - 14 + 8 / 8 - 2\n   - 14 + 8 / 8 * 2\n   - 14 + 8 / 8 / 2\n   - 14 - ": 0.4, "To decompose the task into explicit subtasks, we can follow the steps below:\n\n1. Evaluate the given numbers and determine if any of them can be used directly to obtain 24 without any operations. If so, return the solution.\n\n2. Generate all possible combinations of the given numbers. This can be done by permuting the numbers and grouping them into pairs.\n\n3. For each combination, apply the four basic arithmetic operations (+, -, *, /) to the pair of numbers and evaluate if any of the results equal 24. If so, return the solution.\n\n4. If none of the combinations from step 3 yield a solution, generate all possible combinations of three numbers from the given set.\n\n5. For each combination of three numbers, apply the four basic arithmetic operations to the numbers in all possible orders and evaluate if any of the results equal 24. If so, return the solution.\n\n6. If none of the combinations from step 5 yield a solution, generate all possible combinations of four numbers from the given set.\n\n7. For each combination of four numbers, apply the four basic arithmetic operations to the numbers in all possible orders and evaluate if any of the results equal 24. If so, return the solution.\n\n8. If none of the combinations from step 7 yield a solution, repeat the process with different orders of operations (e.g., changing the order of addition, subtraction, multiplication, and division).\n\n9. If none of the combinations from step 8 yield a solution, return that there is no solution for the given set of numbers.\n\nProspective search steps:\n1. Check if any of the given numbers (14, 8, 8, 2) can be used directly to obtain 24.\n2. Generate all possible combinations of the given numbers: (14, 8), (14, 8), (14, 2), (8, 8), (8, 2), (8, 2).\n": 0.75}}