Problem #PRU-5102

Problems Combinatorics Colorings of the board

Problem

There are \(25\) bugs sitting on the squares of a \(5 \times 5\) board, \(1\) at each square. When I clap my hands, each bug jumps to a square diagonally from where it was before. Show that after I clap my hands, at least \(5\) squares will be empty.