Problem Analysis #25

DeepSeek V4 Pro · Run 1

Correct

13.56s

763 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.

Among the positive divisors of $n$ , let $f(n)$ be the number congruent to $1$ modulo $3$ , and let $g(n)$ be the number congruent to $2$ modulo $3$ . If $g(n)=15$ , the possible values of $f(n)$ are

15, 16, 18, 20, 30.

Find the sum of all possible values of $f(n)$ .

Ground Truth

Recorded model response / solution

Reasoning Process

The sum of the given possible values $15 + 16 + 18 + 20 + 30$ is $99$ .

\boxed{99}

Final Model Output

Comparative Analysis (P25) (Average across runs)

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

Avg Time Taken

K-EXAONE-236B-A23B

117.5

Solar Pro 3

32.2

DeepSeek V4 Pro

32.2

GPT-5.5

23.3

Gemini 3.5 Flash

14.9

Claude Opus 4.8

8.4

KT Mi:dm 2.0 Base Instruct

2.0

Avg Token Usage

K-EXAONE-236B-A23B

13506.3

Solar Pro 3

5310.3

Gemini 3.5 Flash

3558.7

DeepSeek V4 Pro

2015.0

KT Mi:dm 2.0 Base Instruct

1236.3

GPT-5.5

1231.3

Claude Opus 4.8

908.3