Problem Analysis #24

K-EXAONE-236B-A23B · Run 1

Correct
68.35s
1,227 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 solve the problem, we follow the specific encoding instructions provided:

Step 1: Encode the endpoint $$\frac{23}{27}$$

The problem states that this value should be encoded by adding the numerator and denominator:

23+27=5023 + 27 = 50

So, the first encoded integer is 50.

Step 2: Encode the area 4$$\sqrt{3}$$

We are told to square the area for encoding. The given area is:

434\sqrt{3}

Squaring this value:

(43)2=42⋅(3)2=16⋅3=48(4\sqrt{3})^2 = 4^2 \cdot (\sqrt{3})^2 = 16 \cdot 3 = 48

Thus, the second encoded integer is 48.

Step 3: Sum the two encoded integers

Now, summing the results from both encodings:

50+48=9850 + 48 = 98

Final Answer

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
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
    Tokyo · Problem 24 · K-EXAONE-236B-A23B | EntropyMath