I'm having trouble regarding the application of the Pigeonhole Principle. I understand $f:A \to B$ but I don't know how to apply it in questions that require it. Example:
Ten bullets are all shot on a square target of $900~\text{cm}^2$. The statement is: If there are $10$ disjoint holes which are entirely on the target, then there are at least $2$ of them with the distance between their centres less than $10\sqrt{2}~\text{cm}$.
Best Answer
Divide the square into nine $100$ cm$^2$ squares. By the pigeonhole principle, one of the squares contains at least two holes, and the maximal distance between any two points in the same square is $10\sqrt 2$ cm.