# Blue and Red

• Apr 28th 2009, 08:40 AM
Fayyaz
Blue and Red
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.
• Apr 28th 2009, 09:04 AM
mollymcf2009
Quote:

Originally Posted by Fayyaz
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.

Here is what your picture should probably look like. Looking at this picture, do you think you an come up with an explanation as to why the number of edges might be the same?

Attachment 11152
• May 4th 2009, 06:38 AM
Fayyaz
hi i didnt understand what to do next..

another person said that this is the way to proceed:

Two Colors in Two Rows from Interactive Mathematics Miscellany and Puzzles