Problem Analysis #29

KT Mi:dm 2.0 Base Instruct · Run 1

Correct
0.40s
819 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

To solve the problem, we need to compute the integer value of (12k)23\frac{(12k)^2}{3} where k=5312k = \frac{5\sqrt{3}}{12}.

Step 1: Substitute kk into the expression (12k)2(12k)^2.

(12k)2=(12⋅5312)2=(53)2=25⋅3=75.(12k)^2 = (12 \cdot \frac{5\sqrt{3}}{12})^2 = (5\sqrt{3})^2 = 25 \cdot 3 = 75.

Step 2: Divide the result by 3.

753=25.\frac{75}{3} = 25.

Final Answer: 25\boxed{25}

Final Model Output
25

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
    Tokyo · Problem 29 · KT Mi:dm 2.0 Base Instruct | EntropyMath