Covering a chessboard (Posted on 2005-11-12)

	Submitted by pcbouhid
Rating: 3.6667 (6 votes)
Solution:	(Hide)
There is only one way to remove a square, aside from rotations and reflections. To see that there is at most one way, do this: Label all the squares of the chessboard with A, B or C in sequence by rows starting from the top: A B C A B C A B C A B C A B C A B C A B C A B C A B C A B C A B C A B C A B C A B C A B C A B C A B C A B C A B C A B C A B C A Every piece must cover one A, one B and one C. There is one extra A square, so an A must be removed. Now label the board again by rows starting from the bottom: C A B C A B C A A B C A B C A B B C A B C A B C C A B C A B C A A B C A B C A B B C A B C A B C C A B C A B C A A B C A B C A B The square removed must still be an A. The only squares that got marked with A both times are these: . . . . . . . . . . . . . . . . . . A . . A . . . . . . . . . . . . . . . . . . . . A . . A . . . . . . . . . . . . . . . . . .

	Subject	Author	Date
	re: Count the Ways	Charlie	2005-11-14 08:24:58
	re: Count the Ways	Charlie	2005-11-13 19:22:35
	Count the Ways	Charlie	2005-11-13 19:18:14
	re(6): spoiler	Mindy Rodriguez	2005-11-13 12:49:01
	A solution	Ken Haley	2005-11-13 08:14:48
	re(6): spoiler	Vernon Lewis	2005-11-13 08:07:17
	re(5): spoiler	pcbouhid	2005-11-13 05:21:43
	re(4): spoiler	Mindy Rodriguez	2005-11-12 22:37:31
	re(3): spoiler	pcbouhid	2005-11-12 21:54:42
	re(2): spoiler	Mindy Rodriguez	2005-11-12 21:28:54
	re: spoiler	pcbouhid	2005-11-12 20:27:42
	spoiler	Mindy Rodriguez	2005-11-12 18:08:40
	early thoughts.	Vernon Lewis	2005-11-12 14:40:32
	solution	Charlie	2005-11-12 13:53:23
	My thoughts:	Joe	2005-11-12 11:03:45