But first, here's a matchstick puzzle from the back of a box of Redheads:

This hexagon shows six triangles. Move four matches to make it show only four triangles.

The Jigsaw 1 and Jigsaw 2 problems are based cutting up the T-hexagon, while Jigsaw 3 is a bit like the famous 'How many squares on a chessboard?" problem. As well as cutting up hexagons, there are a number of puzzles that call for a given shape to cut cut into pieces that can be formed into a hexagon. Wolfgang Stöcher has an interesting collection of examples in which it is a triangle that it cut up. 

I also came across a version of Nim that is played on a hexagon - it's called Sim, after it's author. And in the 2004 Naturally Mathematical competition, we posed a questions about the triangles made by the diagonals of a T-hexagon. The solution provided by one student team was ... well worth having a look at!

On the other hand, the H-hexagon is an old favourite with the 2-D domino style problems, where you have to match the colours of joining edges. By the way, these problems are notoriously hard to solve, so be wary of starting on them if you value your leisure! We'll specify some of these later.

For example, you can have a look at some quite old versions of the hexagon matching problems by visiting the Nemmelgeb Murr site. An example of a 7-hexagon matching puzzle is shown on the site and is called Pair It. A more recent version of the same puzzle appeared in Origami by David Petty (ISBN 1 903327 35 0), complete with instructions on how to make the puzzle pieces in the origami way. Then ... if you enjoy such challenges, check out the way in which MacMahon's Triangles can be fitted into a T-hexagon.