If 51 mosquitoes are sitting on a square with side 1m, are at least 3 of them within a disk of radius 1/7?

Question

There are 51 mosquitoes on a square-shaped window with side 1 m. Can Stephen kill 3 mosquitoes with a circular plastic disk of radius 1/7 m in a single strike?

I know this can be solved by applying Dirichlet principle, but can't put whole proof together - I can't focus, since my room is full of mosquitoes. ;)

Answer 1

Divide the square into $5 \times 5$ squares of side $0.2$m. The diagonal of each square is $\frac {\sqrt 2}5 \lt \frac 27$, so each square can be covered by a disk of radius $\frac 17$ Two mosquitoes per square is $50$, there must be a third one in a square so squash that square.