On Tue, 19 Nov 2002, Richard Guy wrote:
On Tue, 19 Nov 2002, Richard Guy wrote:
On Tue, 19 Nov 2002 asimovd@aol.com wrote:
Clearly any portion of a checkered board that can be covered by dominoes must have an equal number of squares of each color, but does the converse hold? d No! --- bc| | --------------- a| | | | |a --------------- | |cb --- R. d
I recall Bill Thurston's showing me an exact characterization of the regions that CAN be filled by dominos, in terms of some property of the boundary curve. It's easier for fillability by rhombs in the "cubix" pattern, in which "the move" replaces __ __ /\_\ by /_/\ \/_/ \_\/ There, the condition is that if you regard the boundary path as 3-dimensional, then it still closes. The solution in the domino case is essentially the same, but I've forgotten the details. JHC