Problem Analysis #26

K-EXAONE-236B-A23B · Run 1

Correct
3.61s
595 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 revised parabola-area problem, the boundary values for the parameter kk are

19and13.\frac19 \quad\text{and}\quad \frac13.

To avoid a range as the final answer, compute the integer

11/9+11/3.\frac{1}{1/9}+\frac{1}{1/3}.
Ground Truth
12
Recorded model response / solution
Reasoning Process

The problem requires computing the expression:

11/9+11/3\frac{1}{1/9} + \frac{1}{1/3}

Step 1: Evaluate $$\frac{1}{1/9}$$

To divide by a fraction, multiply by its reciprocal:

11/9=1÷19=1×9=9\frac{1}{1/9} = 1 \div \frac{1}{9} = 1 \times 9 = 9

Step 2: Evaluate $$\frac{1}{1/3}$$

Similarly,

11/3=1÷13=1×3=3\frac{1}{1/3} = 1 \div \frac{1}{3} = 1 \times 3 = 3

Step 3: Add the results

9+3=129 + 3 = 12

Final Check

  • The result is an integer.
  • It is not a range, irrational number, or parameterized expression.
  • All constraints are satisfied.
12\boxed{12}
Final Model Output
12

Comparative Analysis (P26) (Average across runs)

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

Avg Time Taken

GPT-5.5
3.7
DeepSeek V4 Pro
3.2
K-EXAONE-236B-A23B
3.0
Gemini 3.5 Flash
2.9
Claude Opus 4.8
1.9
Solar Pro 3
0.8
KT Mi:dm 2.0 Base Instruct
0.6

Avg Token Usage

KT Mi:dm 2.0 Base Instruct
869.7
K-EXAONE-236B-A23B
555.0
Gemini 3.5 Flash
480.0
DeepSeek V4 Pro
346.7
Solar Pro 3
285.0
Claude Opus 4.8
273.0
GPT-5.5
242.7
    Tokyo · Problem 26 · K-EXAONE-236B-A23B | EntropyMath