16 checkers are placed on an 8 by 8 checkerboard, no two checkers on the same square. Show that some four of the 16 checkers are on the vertices of a parallelogram with positive area.

(In reply to Direct me to a Website by Charley)

Use the "Pigeonhole Principle": if more than n pigeons are placed into n pigeonholes, some pigeonhole has at least two pigeons.  The trick is to decide for this problem what you want the "pigeons" and "pigeonholes"  to be.

Posted by McWorter on 2005-06-12 18:48:20