# Mathematics Exam

**Discrete Mathematics**Level 5

A national math contest consisted of \(11\) multiple choice questions, each having \(11\) possible choices, of which only 1 of the choices is correct. A student's score for the contest is the total number of correct answers.

Suppose that \(111\) students actually wrote the exam, answered every single question, and no two students have more than one answer in common. The highest possible average score for the students can be expressed as \(\frac{a}{b}\) where \(a,b\) are coprime positive integers. What is the value of \(a + b\)?

**Details and assumptions**

Each correct answer is worth 1 points.

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