Problem Analysis #24

Gemini 3.5 Flash · Run 1

Correct
3.97s
871 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⁡θ\sin\theta is 23/2723/27, and the relevant area is 434\sqrt3. Encode the endpoint 23/2723/27 by 23+2723+27, and encode the area by squaring it. Find the sum of the two encoded integers.

Ground Truth
98
Recorded model response / solution
Reasoning Process

To find the sum of the two encoded integers, we follow the encoding instructions step-by-step:

  1. Encode the endpoint 2327\frac{23}{27}: The encoding is defined as the sum of the numerator and the denominator:
23+27=5023 + 27 = 50
  1. Encode the area 434\sqrt{3}: The encoding is defined by squaring the area:
(43)2=16×3=48(4\sqrt{3})^2 = 16 \times 3 = 48
  1. Find the sum of the two encoded integers:
50+48=9850 + 48 = 98

98\boxed{98}

Final Model Output
98

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
1,114
KT Mi:dm 2.0 Base Instruct
900
Gemini 3.5 Flash
850
Solar Pro 3
501
DeepSeek V4 Pro
373
Claude Opus 4.8
322
GPT-5.5
286
    Tokyo · Problem 24 · Gemini 3.5 Flash | EntropyMath