A math problem with ... fleas

[kate]

In every field of a square board with 5x5 fields there is one flea. When I say 'hop' every flea jumps to a neighboring square. Two squares a neighboring when they have a common side. Prove that, if I say 'hop' there will be at least one square without a flea.

[Fed_BG]

Let's mark the fields of the board with alternate "+" and "-". Let's suppose that the edjes are marked with "+". The we have 12 x "-" and 13 x "+". Every "hop" sends a flea from "+" to "-" or from "-" to "+". Then it's true that 13 x "+" will be send to 13 x "-". But we have only 12 x "-". Then at least 2 fleas will be send to the same field. So at least 1 field will be without flea.