Date: 2024/09/04
Configurations for Orchestrator
LLM: gpt-4-turbo-2024-04-09
Sage LLM: gpt-4-turbo-2024-04-09
File consolidation LLM: gpt-4o
{
"initial_expansion": 3,
"first_expansion": 3,
"first_try_temperature": 0,
"alternative_temperature": 0.7,
"max_search_expansion": 2,
"votes": 1,
"n_final_checks": 5,
"ask_questions": true,
"ask_genie": true,
"file_support": true,
"optimized_sequential_next_step": false,
"summarize": true,
"max_tokens": 200000,
"max_tokens_for_sage_llm": 200000,
"max_retries": 3,
"use_sage_llm_for_initial_expansion": true,
"ask_user_questions_in_one_prompt": false,
"ask_user_before_execute_codes": true,
"pause_after_initial_solving_expansion": false,
"pause_on_backtrack": true,
"review_file_merges": false,
"collapse_long_prompts": true
}[..tao_intro..]
[at step#0: task statement]
Solve this Game of 24: 7, 6, 2, 1.
Use every number exactly once.
Tao, proceed to work at the next step "[step#0: task statement]" of the plan root.
Following strictly the "Problem Solving Instructions" and templates. Make sure to start with one of the supported headers.
[..tao_template..]
As we're at the start, it is often a good time to ask questions for clarification.
I_NEED_TO_ASK_SOME_QUESTIONS_BEFORE_I_PROCEED:
- Are there any specific operations (addition, subtraction, multiplication, division) that must be used or avoided in solving the Game of 24 with the numbers 7, 6, 2, 1?
- Is the use of parentheses to dictate the order of operations allowed in the solution?
- Should the solution be presented in a specific format, such as a step-by-step calculation or a single mathematical expression?
temperature=0. context tokens: 1050, subtotal: 1153. cumulative total: 1153
[..tao_intro..]
[at step#0: task statement]
Solve this Game of 24: 7, 6, 2, 1.
Use every number exactly once.
Tao, proceed to work at the next step "[step#0: task statement]" of the plan root.
Following strictly the "Problem Solving Instructions" and templates. Make sure to start with one of the supported headers.
[..tao_template..]
These are prior proposals attempted:
[Proposal#1] I_NEED_TO_ASK_SOME_QUESTIONS_BEFORE_I_PROCEED:
- Are there any specific operations (addition, subtraction, multiplication, division) that must be used or avoided in solving the Game of 24 with the numbers 7, 6, 2, 1?
- Is the use of parentheses to dictate the order of operations allowed in the solution?
- Should the solution be presented in a specific format, such as a step-by-step calculation or a single mathematical expression?
Think of an improved proposal.
MY_THOUGHT: To solve the Game of 24 using the numbers 7, 6, 2, 1, where each number must be used exactly once to total 24, we can use the combination of basic arithmetic operations: addition, subtraction, multiplication, and division, along with the appropriate use of parentheses to control the order of operations. Here is one possible solution:
[ (7 - (1 + 2)) \times 6 = 24 ]
Explanation:
- Add 1 and 2 together: (1 + 2 = 3).
- Subtract the result from 7: (7 - 3 = 4).
- Multiply the result by 6: (4 \times 6 = 24).
This achieves the target of 24 using each of the numbers exactly once.
temperature=0.7. context tokens: 1152, subtotal: 1326. cumulative total: 2479
[..tao_intro..]
[at step#0: task statement]
Solve this Game of 24: 7, 6, 2, 1.
Use every number exactly once.
Tao, proceed to work at the next step "[step#0: task statement]" of the plan root.
Following strictly the "Problem Solving Instructions" and templates. Make sure to start with one of the supported headers.
[..tao_template..]
These are prior proposals attempted:
[Proposal#1] I_NEED_TO_ASK_SOME_QUESTIONS_BEFORE_I_PROCEED:
- Are there any specific operations (addition, subtraction, multiplication, division) that must be used or avoided in solving the Game of 24 with the numbers 7, 6, 2, 1?
- Is the use of parentheses to dictate the order of operations allowed in the solution?
- Should the solution be presented in a specific format, such as a step-by-step calculation or a single mathematical expression?
[Proposal#2] MY_THOUGHT:
To solve the Game of 24 using the numbers 7, 6, 2, 1, where each number must be used exactly once to total 24, we can use the combination of basic arithmetic operations: addition, subtraction, multiplication, and division, along with the appropriate use of parentheses to control the order of operations. Here is one possible solution:
[ (7 - (1 + 2)) \times 6 = 24 ]
Explanation:
- Add 1 and 2 together: (1 + 2 = 3).
- Subtract the result from 7: (7 - 3 = 4).
- Multiply the result by 6: (4 \times 6 = 24).
This achieves the target of 24 using each of the numbers exactly once.
Think of an improved proposal.
MY_THOUGHT: The solution provided in Proposal#2 is correct and efficiently solves the Game of 24 using the numbers 7, 6, 2, 1. It uses basic arithmetic operations and parentheses effectively to reach the target of 24. Here’s a reiteration and slight elaboration of the solution with a clear breakdown:
- Addition: Start by adding 1 and 2. This gives: [ 1 + 2 = 3 ]
- Subtraction: Subtract the sum obtained from 7. This calculation proceeds as: [ 7 - 3 = 4 ]
- Multiplication: Finally, multiply the result by 6 to achieve the target: [ 4 \times 6 = 24 ]
This method utilizes each number exactly once and correctly adheres to the rules of the Game of 24, achieving the target number through a simple and logical sequence of operations.
temperature=0.7. context tokens: 1332, subtotal: 1541. cumulative total: 4020
[..sage_intro..]
[at step#0: task statement]
Solve this Game of 24: 7, 6, 2, 1.
Use every number exactly once.
[at step#1: ]
Tao has proposed the following different choices:
[Proposal 1] I_NEED_TO_ASK_SOME_QUESTIONS_BEFORE_I_PROCEED:
- Are there any specific operations (addition, subtraction, multiplication, division) that must be used or avoided in solving the Game of 24 with the numbers 7, 6, 2, 1?
- Is the use of parentheses to dictate the order of operations allowed in the solution?
- Should the solution be presented in a specific format, such as a step-by-step calculation or a single mathematical expression?
[Proposal 2] MY_THOUGHT:
To solve the Game of 24 using the numbers 7, 6, 2, 1, where each number must be used exactly once to total 24, we can use the combination of basic arithmetic operations: addition, subtraction, multiplication, and division, along with the appropriate use of parentheses to control the order of operations. Here is one possible solution:
[ (7 - (1 + 2)) \times 6 = 24 ]
Explanation:
- Add 1 and 2 together: (1 + 2 = 3).
- Subtract the result from 7: (7 - 3 = 4).
- Multiply the result by 6: (4 \times 6 = 24).
This achieves the target of 24 using each of the numbers exactly once.
[Proposal 3] MY_THOUGHT:
The solution provided in Proposal#2 is correct and efficiently solves the Game of 24 using the numbers 7, 6, 2, 1. It uses basic arithmetic operations and parentheses effectively to reach the target of 24. Here’s a reiteration and slight elaboration of the solution with a clear breakdown:
- Addition: Start by adding 1 and 2. This gives: [ 1 + 2 = 3 ]
- Subtraction: Subtract the sum obtained from 7. This calculation proceeds as: [ 7 - 3 = 4 ]
- Multiplication: Finally, multiply the result by 6 to achieve the target: [ 4 \times 6 = 24 ]
This method utilizes each number exactly once and correctly adheres to the rules of the Game of 24, achieving the target number through a simple and logical sequence of operations.
[..sage_rank_instructions..]
{
"1": {
"score": 2.0,
"reason": "The choice to ask questions before attempting a solution is generally prudent. However, the specific questions asked here are not particularly useful as the Game of 24 inherently allows all basic arithmetic operations and the use of parentheses. The format of the solution is typically straightforward and does not require clarification."
},
"2": {
"score": 9.8,
"reason": "This choice directly provides a correct and efficient solution to the Game of 24 using the given numbers. The use of basic arithmetic operations and the clear explanation of each step make this a high-quality response."
},
"3": {
"score": 9.65,
"duplicate_of": 2,
"reason": "This choice essentially reiterates the solution provided in Proposal 2 with additional breakdowns. While it adds clarity, it does not fundamentally change or improve the solution, making it slightly less original."
}
}temperature=0. context tokens: 1119, subtotal: 1331. cumulative total: 5351
[..tao_intro..]
[at step#0: task statement]
Solve this Game of 24: 7, 6, 2, 1.
Use every number exactly once.
MY_THOUGHT: [at step#2: top-level plan/answer]
To solve the Game of 24 using the numbers 7, 6, 2, 1, where each number must be used exactly once to total 24, we can use the combination of basic arithmetic operations: addition, subtraction, multiplication, and division, along with the appropriate use of parentheses to control the order of operations. Here is one possible solution:
[ (7 - (1 + 2)) \times 6 = 24 ]
Explanation:
- Add 1 and 2 together: (1 + 2 = 3).
- Subtract the result from 7: (7 - 3 = 4).
- Multiply the result by 6: (4 \times 6 = 24).
This achieves the target of 24 using each of the numbers exactly once.
[..tao_summarize..]
To solve the Game of 24 using the numbers 7, 6, 2, 1, you can use the following calculation:
[ (7 - (1 + 2)) \times 6 = 24 ]
Here's the step-by-step breakdown:
- Add 1 and 2 together: (1 + 2 = 3).
- Subtract the result from 7: (7 - 3 = 4).
- Multiply the result by 6: (4 \times 6 = 24).
This solution uses each of the numbers exactly once and successfully reaches the target of 24.
temperature=0.0. context tokens: 351, subtotal: 484. cumulative total: 5835
[..sage_intro..]
[at step#0: task statement]
Solve this Game of 24: 7, 6, 2, 1.
Use every number exactly once.
MY_THOUGHT: [at step#2: top-level plan/answer]
To solve the Game of 24 using the numbers 7, 6, 2, 1, where each number must be used exactly once to total 24, we can use the combination of basic arithmetic operations: addition, subtraction, multiplication, and division, along with the appropriate use of parentheses to control the order of operations. Here is one possible solution:
[ (7 - (1 + 2)) \times 6 = 24 ]
Explanation:
- Add 1 and 2 together: (1 + 2 = 3).
- Subtract the result from 7: (7 - 3 = 4).
- Multiply the result by 6: (4 \times 6 = 24).
This achieves the target of 24 using each of the numbers exactly once.
[at step#3: Summarize final answer]
To solve the Game of 24 using the numbers 7, 6, 2, 1, you can use the following calculation:
[ (7 - (1 + 2)) \times 6 = 24 ]
Here's the step-by-step breakdown:
- Add 1 and 2 together: (1 + 2 = 3).
- Subtract the result from 7: (7 - 3 = 4).
- Multiply the result by 6: (4 \times 6 = 24).
This solution uses each of the numbers exactly once and successfully reaches the target of 24.
Is the solution correct? Report errors and warnings found, but avoid nitpicking, in this format:
At step#: : . Severity: error or warning.
Already fixed in subsequentstep: yes/no;
Recommendation: .
...
At step#: affected by issue found at step#: .
where "step#<ID>: <step description>" can be found in the bracket "[at step#: <step_description>]" of the steps
(without the brackets.)
Directions:
- Worship Occam's razor. Prefer specific solution according to the scope of the task step, neither too generic nor excessively detailed.
- For any step, do NOT report issues that should be, or already been, taken care of by different/subsequent step. For example, dummy/placeholder/temporary values that are to be taken care of later.
- A
HERE_IS_MY_STEP_BY_STEP_PLANplan itself does not provide any answer; its sub-steps should. - We should generally respect user's assumptions even if they are inaccurate as assumptions are meant to simplify the problem.
- Subsequent steps depending on the issue should be reported an step as
affected byonly if it must be changed or fixed; if a step depends on this step but not affected by the particular issue, no need to report.
At step#2: top-level plan/answer: The solution provided is correct and achieves the target of 24 using each of the numbers exactly once. Severity: error.
Already fixed in subsequent step: no;
Recommendation: No action needed as the solution is valid.
At step#3: affected by issue found at step#2: Summarize final answer.
temperature=0. context tokens: 723, subtotal: 801. cumulative total: 6636
Critic 1:
At step#2: top-level plan/answer: The solution provided is correct and achieves the target of 24 using each of the numbers exactly once. Severity: error.
Already fixed in subsequent step: no;
Recommendation: No action needed as the solution is valid.
At step#3: affected by issue found at step#2: Summarize final answer.
[..sage_merge_criticisms..]
{
"Step#2 solution validity": {
"ok": "The solution provided is correct and achieves the target of 24 using each of the numbers exactly once."
}
}temperature=0. context tokens: 272, subtotal: 314. cumulative total: 6950