A rectangular floor is covered entirely by 2×2 and 1×4 tiles. One tile accidentally gets completely broken.
Each of the available spare tiles are corresponds to the other type.

Can that the floor be completely covered by rearranging the tiles?
Justify your answer.

*Assume that there are an unlimited number of spare tiles.

If completely covered includes overlapping then the problem is trivial. Assume then that overlaps are not allowed.

If the floor is size 1x4 then it can't be covered with 2x2 tiles.

If the floor is size 2x2 then it can't be covered with 1x4 tiles.

Posted by broll on 2015-03-20 08:23:51