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 How about this? by Liz)

Your placement of checkers exhibits lots of groups four checkers that are vertices of parallelograms.  Can you place the 16 checkers to avoid four vertices of a parallelogram?  Or prove that 16 checkers is just too many checkers to escape forming four vertices of a parallelogram?

Posted by McWorter on 2005-07-24 22:43:02