Problem Analysis #12

Claude Opus 4.8 · Run 1

Correct
1.76s
223 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 coin-and-balls process, the probability for the first requested event is 5/85/8. If this probability is p/qp/q in lowest terms, find p+qp+q.

Ground Truth
13
Recorded model response / solution
Reasoning Process

13\boxed{13}

Final Model Output
13

Comparative Analysis (P12) (Average across runs)

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

Avg Time Taken

DeepSeek V4 Pro
16.3
Solar Pro 3
6.5
Gemini 3.5 Flash
5.1
K-EXAONE-236B-A23B
5.0
GPT-5.5
4.4
Claude Opus 4.8
1.7
KT Mi:dm 2.0 Base Instruct
0.8

Avg Token Usage

Solar Pro 3
1,139
DeepSeek V4 Pro
984
Gemini 3.5 Flash
960
KT Mi:dm 2.0 Base Instruct
846
K-EXAONE-236B-A23B
773
GPT-5.5
284
Claude Opus 4.8
223
    Tokyo · Problem 12 · Claude Opus 4.8 | EntropyMath