A triangle, made up of different building blocks, is either perfectly filled or, when rearranged, has a section missing. How is this possible? Welcome to Curry's Triangle Paradox.

Curry's Paradox was invented in New York City in 1953 by Paul Curry. Curry was a magician, and so you might expect some sleight of hand. But none seems apparent. It's a very simple-seeming object. A triangle is made up of a bunch of different polygons. All of the polygons fit together perfectly, with no gaps between them. No problem.

Until you rearrange the thing, switching the triangles and rearranging the blocks, it fits together again - with one missing space in the middle. This makes no sense. The entire thing is generally done on graph paper, so there can be no sneakily hiding a square in one of the blocks in the middle. And the entire shape keeps the same size at the beginning and at the end. There's just no space where an extra square can go, but you count up the dimensions and they're all the same in each triangle. What's happening?