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Problem 250

Combinatorics Difficulty 2.0 Find the answer Junior Mathematical Olympiad, September · Netherlands · 2019

In a class, $30$ students did a test. Every student got a grade that was an integer from $1$ to $10$ . The grade $8$ was given more often than any of the other grades.
What is the smallest possible average grade of the students?
A) $3\frac{8}{15}$
B) $3\frac{2}{3}$
C) $3\frac{5}{6}$
D) $4\frac{11}{30}$
E) $4\frac{8}{15}$

This was a multiple-choice question, but the options didn't survive into the source we have, so there is nothing here to pick from. Work it on paper and mark yourself against the solution below.

Official solution

B) $3^{\frac{2}{3}}$

Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.