Joseph has $$100$$ mice. Each of them is either white or grey. At least one of the mice is grey, and out of any seven of Joseph\textquotesingle s mice at least four are white. How many grey mice does Joseph have at the most? 
Overseas Competition->Knowledge Point->Combinatorics->Pigeonhole Principle->Worst Case in Pigeonhole Principle Problems
The maximum is $3$ since any group of $7$ at most $3$ are grey. 