Question 22
Construct a tetramino by attaching two $2 \times 1$ dominoes along their sides such that the midpoint of the longer side of one domino is a corner of other domino. This construction yields two kinds of the tetraminoes with opposite orientations. Let us call them S- and Z-tetraminoes, respectively.
S-tetraminoes Z-tetraminoes
Assume that a lattice polygon $P$ can be tiled with S-tetraminoes.
Prove that no matter how we tile $P$ using only S- and Z-tetraminoes, we always use even number of Z-tetraminoes.
S-tetraminoes Z-tetraminoes
Assume that a lattice polygon $P$ can be tiled with S-tetraminoes.
Prove that no matter how we tile $P$ using only S- and Z-tetraminoes, we always use even number of Z-tetraminoes.