Problem Analysis #10

K-EXAONE-236B-A23B · Run 1

Correct
79.77s
11,169 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 a>0a>0, and consider the parabola y=x2y=x^2. Starting from P(a,a2)P(a,a^2), let Q≠PQ\ne P be the other intersection of the normal line to the parabola at PP with the parabola. Let R≠QR\ne Q be the other intersection of the normal line at QQ with the parabola.

If the minimum possible xx-coordinate of RR is MM, write M2=p/qM^2=p/q in lowest terms and find p+qp+q.

Ground Truth
33
Recorded model response / solution
Reasoning Process

The minimum possible xx-coordinate of RR is M=524M = \frac{5\sqrt{2}}{4}. Then M2=258M^2 = \frac{25}{8}. In lowest terms, p=25p = 25, q=8q = 8, and p+q=33p+q = 33.

\boxed{33}

Final Model Output
33

Comparative Analysis (P10) (Average across runs)

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

Avg Time Taken

K-EXAONE-236B-A23B
77.5
DeepSeek V4 Pro
55.9
Solar Pro 3
41.5
Gemini 3.5 Flash
13.5
GPT-5.5
11.2
Claude Opus 4.8
9.0
KT Mi:dm 2.0 Base Instruct
3.3

Avg Token Usage

K-EXAONE-236B-A23B
11966.0
Solar Pro 3
6444.7
DeepSeek V4 Pro
3794.7
Gemini 3.5 Flash
3138.3
KT Mi:dm 2.0 Base Instruct
1946.7
Claude Opus 4.8
1157.7
GPT-5.5
811.0
    Tokyo · Problem 10 · K-EXAONE-236B-A23B | EntropyMath