Problem Analysis #22

Claude Opus 4.8 · Run 1

Correct
1.78s
310 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.

A maximum area has value 1008100\sqrt8. Write this value in the form

pqr,\frac{p\sqrt q}{r},

where p,q,rp,q,r are positive integers, qq is squarefree, and gcd⁡(p,r)=1\gcd(p,r)=1. Find p+q+rp+q+r.

Ground Truth
203
Recorded model response / solution
Reasoning Process

100√8 = 100·2√2 = 200√2.

So p=200, q=2, r=1. Sum = 203.

\boxed{203}

Final Model Output
203

Comparative Analysis (P22) (Average across runs)

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

Avg Time Taken

K-EXAONE-236B-A23B
13.1
DeepSeek V4 Pro
10.5
Gemini 3.5 Flash
6.7
GPT-5.5
4.3
Solar Pro 3
2.7
Claude Opus 4.8
1.8
KT Mi:dm 2.0 Base Instruct
1.0

Avg Token Usage

K-EXAONE-236B-A23B
2093.3
Gemini 3.5 Flash
1482.0
KT Mi:dm 2.0 Base Instruct
990.3
DeepSeek V4 Pro
729.0
Solar Pro 3
580.0
Claude Opus 4.8
314.7
GPT-5.5
308.3
    Tokyo · Problem 22 · Claude Opus 4.8 | EntropyMath