lotus

previous page: 167 geometry/coloring/cheese.cube.p
  
page up: Puzzles FAQ
  
next page: 169 geometry/construction/4.triangles.6.lines.p

168 geometry/coloring/triominoes.p




Description

This article is from the Puzzles FAQ, by Chris Cole chris@questrel.questrel.com and Matthew Daly mwdaly@pobox.com with numerous contributions by others.

168 geometry/coloring/triominoes.p


There is a chess board (of course with 64 squares). You are given 21
"triominoes" of size 3-by-1 (the size of an individual square on a
chess board is 1-by-1). Which square on the chess board can you cut out
so that the 21 triominoes exactly cover the remaining 63 squares? Or is
it impossible?

geometry/coloring/triominoes.s

||||||||
||||||||
||||||||
---***+*
---...+*
---*+O+*
---*+...
---*+***

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:

		ABCABCAB
		CABCABCA
		BCABCABC
		ABCABCAB
		CABCABCA
		BCABCABC
		ABCABCAB
		CABCABCA

Every triomino 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:

		CABCABCA
		ABCABCAB
		BCABCABC
		CABCABCA
		ABCABCAB
		BCABCABC
		CABCABCA
		ABCABCAB

The square removed must still be an A. The only squares that got
marked with A both times are these:

		........
		........
		..A..A..
		........
		........
		..A..A..
		........
		........

 

Continue to:













TOP
previous page: 167 geometry/coloring/cheese.cube.p
  
page up: Puzzles FAQ
  
next page: 169 geometry/construction/4.triangles.6.lines.p