25 families live in the squares of a 5 × 5 chessboard, each occupying a square. As it often happens, each family thinks that their neighbors (i. e. those families living in the squares with which their square
shares a side) have better living units. At a town hall meeting it is resolved to make everyone happier
by moving the 25 families around so that each ends up in a square of one of their former neighbors.
Unfortunately try as they might, the families cannot figure out any relocation scheme to carry out this
resolution. Give a very simple reason explaining why they were doomed to fail. (Hint: 25 is odd).