Problem Analysis #37

14.10s
2,683 toks
Problem Statement

There are 1616 balls and six empty boxes labeled with the integers from 11 to 66. Using a single die, the following experiment is performed.If the probability is qp\frac{q}{p}, compute p+qp+q.\

Ground Truth
19
Execution Trace
Reasoning Process

[THOUGHT] The problem statement is incomplete: it describes 16 balls, 6 labeled boxes, and an experiment using a die, but it does not state what event/probability we are supposed to compute (e.g., all boxes nonempty, a specific occupancy pattern, etc.). I need the missing sentence(s) after “the following experiment is performed.” to proceed and compute p+q. [/THOUGHT] [PYTHON] print("Need clarification: the problem statement is missing the description of the experiment's outcome/event whose probability is q/p. Please provide the full sentence(s) after 'the following experiment is performed.'") [/PYTHON]

Tool Output
[PYTHON OUTPUT] Need clarification: the problem statement is missing the description of the experiment's outcome/event whose probability is q/p. Please provide the full sentence(s) after 'the following experiment is performed.' [/PYTHON OUTPUT]
Reasoning Process

[THOUGHT] The experiment/event whose probability should equal (q/p) is missing from the prompt, so (p+q) cannot be determined from the given information. \boxed{0}

Final Model Output
0

Comparative Analysis (P37) (Average across runs)

Avg Time Taken

K-EXAONE-236B-A23B
4193.5
K-EXAONE-236B-A23B
2741.3
EXAONE-4.0.1-32B (high)
1790.1
Solar-Open-100B
624.1
Gemini-3-Pro-Preview
100.4
Llama-VARCO-8B-Instruct
91.8
Deepseek-V3.2
73.4
Kanana-2-30B-Thinking
58.9
Kanana-2-30B-Thinking-2601
29.4
Solar-Pro-2 (31B)(high)
24.1
HCX-007(high)
21.8
Claude-Opus-4.5
20.9
Grok-4.1-fast
17.6
GPT-5.1 (high)
16.4
GPT-5.2 (high)
14.1
A.X-4.0 (72B)
8.7
axk1
4.0

Avg Token Usage

K-EXAONE-236B-A23B
457357.7
K-EXAONE-236B-A23B
262144.0
EXAONE-4.0.1-32B (high)
14344.0
Kanana-2-30B-Thinking
10520.0
Gemini-3-Pro-Preview
6917.0
Kanana-2-30B-Thinking-2601
6777.5
Llama-VARCO-8B-Instruct
6148.0
Solar-Open-100B
5585.0
Grok-4.1-fast
5112.0
Solar-Pro-2 (31B)(high)
5011.0
Claude-Opus-4.5
4102.0
Deepseek-V3.2
4079.0
HCX-007(high)
3437.0
A.X-4.0 (72B)
2706.0
GPT-5.2 (high)
2683.0
GPT-5.1 (high)
2624.0
axk1
2241.0