Here’s a puzzle for you: Take a bunch of pentagons and try to fit them together so that they cover a tabletop perfectly, with no gaps or overlaps. If you try it with ordinary pentagons, with equal sides, you’ll soon see it just won’t work. But loosen the requirements by allowing unequal sides, and all becomes possible. Mathematicians had found 14 different types of pentagons that worked, but for 30 years, no one could find another.