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.
It's not too hard to find the 15-piece counter example shown
below. This only disproves it for the 15-piece case, not the
16-piece case. It seems that if any more pieces are added, a
parallelogram with positive area is formed.
X-------
XX------
X-X-----
X--X----
X---X---
X----X--
X-----X-
X------X
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Posted by Tristan
on 2005-06-12 19:36:20 |
15-piece counter-example
