Polyopolis
This is one of the most popular places in the world of recreational mathematics. It is inhabited by the Polyominoes. These come in all shapes an dsizes. One type, the Pentominoes , have 12 different shapes, which are often given letter names as shown below.
A favourite pentomino puzzle is the problem of fitting all 12 shapes into a 6 by 10 rectangle. There are more than 2000 ways of doing this, but solvers tend to assume that the I pentomino has to be placed along the edge of the rectangle. However, there are at least ten solutions with the I shape inside the rectangle. One is shown here – can you find more?
Pat Perkins
