Consider a rectangular array of dots with an even number of rows and an even number of columns. Color the dots, each one red or blue, in such a way so that in each row half the

dots are red and half are blue, and also in each column half are red and half are blue. Now, whenever two points of the same color are adjacent (in a row or column), join them by an edge of that color. Show that the number of red edges is the same as the number of blue edges.