  If n is a multiple of 4, then a square of side n can be tiled with
T-tetrominos, using a well-known construction. If n is even but not a multiple
of four, then there exists an equally well-known construction for tiling a
square of side n with T-tetrominos and exactly 4 monominos. On the other hand,
it was shown by Walkup that it is not possible to tile the square using only
T-tetrominos. Now consider the remaining cases, where n is odd. It was shown by
Zhan that it is not possible to tile such a square using only one monomino.
Hochberg showed that no more than 9 monominos are ever needed. We give a
construction for all odd n which uses exactly 5 monominos, thereby resolving
this question.
