Problem Analysis #19

KT Mi:dm 2.0 Base Instruct · Run 1

Correct
0.79s
839 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 complex-plane circle problem, the constant value of Re⁡(1/z)\operatorname{Re}(1/z) on the circle is 1/21/2, and the area of the sum-region is 4π4\pi. Encode 1/21/2 as 1+21+2, and encode 4π4\pi as 4+14+1. Find the sum of these two encoded integers.

Ground Truth
8
Recorded model response / solution
Reasoning Process

To solve the problem, we need to encode the given values and find their sum.

  1. Encode 1/21/2:
    According to the problem, 1/21/2 is encoded as 1+21 + 2.
    Therefore, the encoded value is 33.

  2. Encode 4π4\pi:
    According to the problem, 4π4\pi is encoded as 4+14 + 1.
    Therefore, the encoded value is 55.

  3. Sum the encoded integers:
    Add the two encoded values: 3+5=83 + 5 = 8.

The final answer is 8\boxed{8}.

Final Model Output
8

Comparative Analysis (P19) (Average across runs)

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

Avg Time Taken

K-EXAONE-236B-A23B
27.6
DeepSeek V4 Pro
12.5
Solar Pro 3
12.4
Gemini 3.5 Flash
6.1
GPT-5.5
3.8
Claude Opus 4.8
2.0
KT Mi:dm 2.0 Base Instruct
0.6

Avg Token Usage

Solar Pro 3
2249.7
Gemini 3.5 Flash
1254.7
K-EXAONE-236B-A23B
1164.7
DeepSeek V4 Pro
866.7
KT Mi:dm 2.0 Base Instruct
849.0
GPT-5.5
315.3
Claude Opus 4.8
310.0
    Tokyo · Problem 19 · KT Mi:dm 2.0 Base Instruct | EntropyMath