Problem Analysis #24

KT Mi:dm 2.0 Base Instruct · Run 1

Correct

1.12s

923 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 cubic problem, one endpoint of the possible range of $\sin\theta$ is $23/27$ , and the relevant area is $4\sqrt3$ . Encode the endpoint $23/27$ by $23+27$ , and encode the area by squaring it. Find the sum of the two encoded integers.

Ground Truth

Recorded model response / solution

Reasoning Process

To solve the problem, we need to encode the endpoint $\frac{23}{27}$ and the area $4\sqrt{3}$ as specified, and then find the sum of the encoded integers.

Encode the endpoint $\frac{23}{27}$ :
- The endpoint is $\frac{23}{27}$ .
- According to the problem, we encode this by adding the numerator and denominator: $23 + 27 = 50$ .
Encode the area $4\sqrt{3}$ :
- The area is $4\sqrt{3}$ .
- According to the problem, we square this value: $(4\sqrt{3})^2 = 16 \times 3 = 48$ .
Sum the two encoded integers:
- The encoded endpoint is $50$ .
- The encoded area is $48$ .
- The sum of these two integers is $50 + 48 = 98$ .

Thus, the final answer is $\boxed{98}$ .

Final Model Output

Comparative Analysis (P24) (Average across runs)

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

Avg Time Taken

K-EXAONE-236B-A23B

27.1

Gemini 3.5 Flash

4.6

DeepSeek V4 Pro

4.0

GPT-5.5

3.6

Claude Opus 4.8

2.3

Solar Pro 3

2.0

KT Mi:dm 2.0 Base Instruct

0.7

Avg Token Usage

K-EXAONE-236B-A23B

1114.3

KT Mi:dm 2.0 Base Instruct

899.7

Gemini 3.5 Flash

850.3

Solar Pro 3

501.3

DeepSeek V4 Pro

372.7

Claude Opus 4.8

321.7

GPT-5.5

285.7