Problem Analysis #7

K-EXAONE-236B-A23B · Run 1

Correct
14.77s
1,944 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.

Let f(x)=2x3−4x2+3f(x)=2x^3-4x^2+3. For 0<t<40<t<4, let CtC_t be the circle passing through (t,f(t))(t,f(t)), having the same tangent there as y=f(x)y=f(x), and having its center on the xx-axis. If the center is (c(t),0)(c(t),0) and the radius is r(t)r(t), find

c(1)+r(1)2.c(1)+r(1)^2.
Ground Truth
4
Recorded model response / solution
Reasoning Process

\boxed{4}

Final Model Output
4

Comparative Analysis (P7) (Average across runs)

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

Avg Time Taken

DeepSeek V4 Pro
20.2
K-EXAONE-236B-A23B
19.9
Gemini 3.5 Flash
9.1
GPT-5.5
7.4
Solar Pro 3
6.1
Claude Opus 4.8
3.7
KT Mi:dm 2.0 Base Instruct
3.3

Avg Token Usage

K-EXAONE-236B-A23B
2869.7
Gemini 3.5 Flash
2161.0
KT Mi:dm 2.0 Base Instruct
1865.7
Solar Pro 3
1143.3
DeepSeek V4 Pro
995.7
Claude Opus 4.8
551.0
GPT-5.5
523.3
    Tokyo · Problem 7 · K-EXAONE-236B-A23B | EntropyMath