Problem Analysis #0

K-EXAONE-236B-A23B · Run 1

Correct
58.15s
7,255 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 coordinate plane, let CC be the parabola

y=ax2+bx+c.y=ax^2+bx+c.

For 0∘<θ<90∘0^\circ<\theta<90^\circ, suppose that CC passes through

P(cos⁡θ,sin⁡θ),Q(−cos⁡θ,sin⁡θ),P(\cos\theta,\sin\theta),\qquad Q(-\cos\theta,\sin\theta),

and that, at both PP and QQ, it has a common tangent with the unit circle x2+y2=1x^2+y^2=1. Let AA be the area of the region enclosed by CC and the xx-axis. Find the minimum possible value of A2A^2.

Ground Truth
3
Recorded model response / solution
Reasoning Process

3\boxed{3}

Final Model Output
3

Comparative Analysis (P0) (Average across runs)

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

Avg Time Taken

K-EXAONE-236B-A23B
58.1
DeepSeek V4 Pro
39.4
Solar Pro 3
22.8
GPT-5.5
16.6
Gemini 3.5 Flash
15.8
Claude Opus 4.8
12.2
KT Mi:dm 2.0 Base Instruct
2.7

Avg Token Usage

K-EXAONE-236B-A23B
7,598
Gemini 3.5 Flash
4,120
Solar Pro 3
3,702
DeepSeek V4 Pro
2,672
KT Mi:dm 2.0 Base Instruct
1,919
Claude Opus 4.8
1,565
GPT-5.5
1,053
    Tokyo · Problem 0 · K-EXAONE-236B-A23B | EntropyMath