Problem Analysis #0

GPT-5.5 · Run 1

Correct

14.48s

1,032 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 $C$ be the parabola

y=ax^2+bx+c.

For $0^\circ<\theta<90^\circ$ , suppose that $C$ passes through

P(\cos\theta,\sin\theta),\qquad Q(-\cos\theta,\sin\theta),

and that, at both $P$ and $Q$ , it has a common tangent with the unit circle $x^2+y^2=1$ . Let $A$ be the area of the region enclosed by $C$ and the $x$ -axis. Find the minimum possible value of $A^2$ .

Ground Truth

Recorded model response / solution

Reasoning Process

\boxed{3}

Final Model Output

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

7597.7

Gemini 3.5 Flash

4119.7

Solar Pro 3

3702.3

DeepSeek V4 Pro

2671.7

KT Mi:dm 2.0 Base Instruct

1919.0

Claude Opus 4.8

1564.7

GPT-5.5

1053.0