Bakayev E.V.

At the beginning of the school year, Andrey started recording his math grades. Upon receiving a new grade (2, 3, 4, or 5), he called it unexpected if, up to that point, it had occurred less frequently than each of the other possible grades. (For example, if he had received the grades 3, 4, 2, 5, 5, 5, 2, 3, 4, 3 in sequence, the first 5 and the second 4 would have been unexpected.) Over the entire school year, Andrey received 40 grades - 10 fives, fours, threes, and twos (the order is unknown). Can we determine exactly how many grades were unexpected for him?
The first unexpected grade will be the last one received for the first time. The second unexpected grade will be the last one received for the second time, and so on. Therefore, there will be a total of 10 unexpected grades.

## Answer

It can be.