Problem Analysis #13

KT Mi:dm 2.0 Base Instruct · Run 1

Correct
0.72s
771 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.

For the relevant optimization problem, the maximum value is 19/619/6. If the maximum is p/qp/q in lowest terms, find p+qp+q.

Ground Truth
25
Recorded model response / solution
Reasoning Process

To solve the problem, we need to determine the sum p+qp + q where the maximum value p/qp/q is given as 19/619/6.

  1. Identify the fraction: The maximum value is 19/619/6, which is already in lowest terms. Here, p=19p = 19 and q=6q = 6.

  2. Calculate the sum: Add the numerator and the denominator:

    p+q=19+6=25p + q = 19 + 6 = 25

Final Answer: 25\boxed{25}

Final Model Output
25

Comparative Analysis (P13) (Average across runs)

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

Avg Time Taken

K-EXAONE-236B-A23B
24.2
Gemini 3.5 Flash
5.3
DeepSeek V4 Pro
4.7
GPT-5.5
4.1
Solar Pro 3
2.4
Claude Opus 4.8
1.7
KT Mi:dm 2.0 Base Instruct
0.5

Avg Token Usage

Gemini 3.5 Flash
956.3
KT Mi:dm 2.0 Base Instruct
777.0
K-EXAONE-236B-A23B
639.3
Solar Pro 3
464.0
DeepSeek V4 Pro
367.3
GPT-5.5
254.3
Claude Opus 4.8
229.7
    Tokyo · Problem 13 · KT Mi:dm 2.0 Base Instruct | EntropyMath