Problem Analysis #23

Claude Opus 4.8 · Run 1

Correct
1.45s
287 toks

API · no tools. This is the prompt and response recorded for this attempt; a full solution may not have been returned.

Problem Statement

Return a single integer only. The problem has been revised so that no final answer is an irrational number, a parameterized expression, a range, a proof, a drawing, a graph, a locus equation, or a region description.

In the cubic tangent problem, the special value satisfying the area-ratio condition is

k=5312.k=\frac{5\sqrt3}{12}.

Instead of giving kk, compute the integer

(12k)23.\frac{(12k)^2}{3}.
Ground Truth
25
Recorded model response / solution
Reasoning Process

(12k)² = (5√3)² = 75. Divide by 3 = 25.

\boxed{25}

Final Model Output
25

Comparative Analysis (P23) (Average across runs)

Averages use reported measurements only. Missing usage is not treated as zero.

Avg Time Taken

K-EXAONE-236B-A23B
24.6
DeepSeek V4 Pro
5.0
GPT-5.5
4.1
Gemini 3.5 Flash
4.1
Claude Opus 4.8
1.7
Solar Pro 3
1.3
KT Mi:dm 2.0 Base Instruct
0.7

Avg Token Usage

K-EXAONE-236B-A23B
828.3
KT Mi:dm 2.0 Base Instruct
828.0
Gemini 3.5 Flash
640.0
DeepSeek V4 Pro
395.0
Solar Pro 3
366.3
Claude Opus 4.8
285.0
GPT-5.5
258.3
    Tokyo · Problem 23 · Claude Opus 4.8 | EntropyMath