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 I think this is a solution... by KC)

Minor quibble that I'm sure you can fix.  If you have checkers in columns 1, 2, and 4 of row 1, then you have three "gaps", 1=2-1, 2=4-2, and 3=4-1, but only 3 checkers in row 1.  So, "number of different gaps is either k or k - 1" is false.

Posted by McWorter on 2005-07-31 18:15:11