A tile is a finite subset of . We can ask if can or cannot be partitioned into copies of . If can be partitioned into copies of we say that tiles .
Here is a simpe example. Let consists of 24 points of the 5 by 5 planar grid minus the center point. cannot tile .
Test your intuition: Does tiles for some ?
If you prefer you can think about the simpler case of consisting of eight points: the 3 by 3 grid minus the center.
I forgot to add polls…