Is it possible to find tiling of a square into an odd number of non-rectangular pieces each having identical shapes and the same area? (Regard a given piece as identical to another if the rotation and/or reflection of the first piece is identical to the second)

If so, provide an example. If not, prove that it can’t be done.

It is possible; for example, a 45*45 square can be exactly tiled with 675 congruent L-shaped pieces of size 3.

Doubtless smaller solutions exist.

Posted by broll on 2014-07-25 10:30:28