Problem Analysis #1

GPT-5.5 · Run 1

Correct

5.61s

414 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 $n$ be the smallest natural number such that $5^n>10^9$ , and let $m$ be the smallest natural number such that $5^m+4^m>10^9$ . Find $n+m$ .

Ground Truth

Recorded model response / solution

Reasoning Process

\boxed{26}

Final Model Output

Comparative Analysis (P1) (Average across runs)

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

Avg Time Taken

K-EXAONE-236B-A23B

48.3

DeepSeek V4 Pro

12.1

Gemini 3.5 Flash

10.6

Solar Pro 3

7.3

GPT-5.5

6.8

Claude Opus 4.8

3.3

KT Mi:dm 2.0 Base Instruct

1.7

Avg Token Usage

K-EXAONE-236B-A23B

7598.7

Gemini 3.5 Flash

2446.3

Solar Pro 3

1316.0

KT Mi:dm 2.0 Base Instruct

1259.0

DeepSeek V4 Pro

1017.0

GPT-5.5

424.7

Claude Opus 4.8

410.3