Problem Analysis #29

GPT-5.5 · Run 1

Correct

4.56s

263 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=\frac{5\sqrt3}{12}.

Instead of giving $k$ , compute the integer

\frac{(12k)^2}{3}.

Ground Truth

Recorded model response / solution

Reasoning Process

\boxed{25}

Final Model Output

Comparative Analysis (P29) (Average across runs)

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

Avg Time Taken

GPT-5.5

4.6

DeepSeek V4 Pro

4.1

K-EXAONE-236B-A23B

3.9

Gemini 3.5 Flash

3.1

Claude Opus 4.8

2.0

Solar Pro 3

1.2

KT Mi:dm 2.0 Base Instruct

0.4

Avg Token Usage

KT Mi:dm 2.0 Base Instruct

819.0

K-EXAONE-236B-A23B

736.0

Gemini 3.5 Flash

641.3

DeepSeek V4 Pro

403.3

Solar Pro 3

358.0

Claude Opus 4.8

285.0

GPT-5.5

264.3