Problem Analysis #15

Gemini 3.5 Flash · Run 1

Correct
4.21s
764 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.

The original limit value is

L=log⁡2−12.L=\log 2-\frac12.

To avoid a logarithmic final answer, compute the integer

eL+1/2.e^{L+1/2}.
Ground Truth
2
Recorded model response / solution
Reasoning Process

To find the value of the expression, we start with the given value of LL:

L=log⁡2−12L = \log 2 - \frac{1}{2}

where log⁡\log represents the natural logarithm.

We want to compute:

eL+1/2e^{L + 1/2}

Substitute LL into the exponent:

L+12=(log⁡2−12)+12=log⁡2L + \frac{1}{2} = \left(\log 2 - \frac{1}{2}\right) + \frac{1}{2} = \log 2

Now, substitute this back into the exponential expression:

eL+1/2=elog⁡2=2e^{L + 1/2} = e^{\log 2} = 2

The final integer value is 2.

\boxed{2}

Final Model Output
2

Comparative Analysis (P15) (Average across runs)

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

Avg Time Taken

K-EXAONE-236B-A23B
34.9
DeepSeek V4 Pro
5.0
Gemini 3.5 Flash
4.3
GPT-5.5
4.1
Claude Opus 4.8
2.7
Solar Pro 3
1.0
KT Mi:dm 2.0 Base Instruct
0.9

Avg Token Usage

K-EXAONE-236B-A23B
2002.0
KT Mi:dm 2.0 Base Instruct
901.0
Gemini 3.5 Flash
795.0
DeepSeek V4 Pro
367.7
Solar Pro 3
299.0
Claude Opus 4.8
243.7
GPT-5.5
223.3
    Tokyo · Problem 15 · Gemini 3.5 Flash | EntropyMath