Richard P. Stanley
Consider the following puzzle. The goal is to
cover the region
using the following seven tiles.
2 3 4
The region must be covered entirely with-
out any overlap. It is allowed to shift and
rotate the seven pieces in any way, but each
piece must be used exactly once.
One could start by observing that some
This paper is based on the second author's Clay
Public Lecture at the IAS/Park City Mathematics
Institute in July, 2004.