[ Classical combinatorics (other) $]$

In the cabinet of Anchuria, there are 100 ministers. Among them, there are both corrupt and honest ministers. It is known that among any ten ministers, at least one minister is a corrupt one. What is the smallest number of corrupt ministers that can be in the cabinet?

#
There cannot be more than nine honest ministers: ten honest ministers would contradict the condition.

On the other hand, the presence of exactly nine honest ministers does not contradict the condition.

## Answer

91.