Rithmomachia

Today, Rithmomachia is a little known game, but for 5 centuries it was a popular game across Europe even rivalling chess. It's similar to chess and draughts in that players take turns to move their own pieces on a grid of squares attempting to capture the opponents pieces. In Rithmomachia the board is 8x16 squares and each piece has a number on it. There have been many sets of rules published over the years but they all have one thing in common: they involve mathematical relationships between these numbers. For example in some variants you can win by arranging numbered pieces in an arithmetic, geometric, or harmonic progression. Rithmomachia is a challenging game to play and it seems astonishing that so many people were able to play. But this type of arithmetic formed an important part of the Quadrivium and so would have been part of the knowledge of any well educated person in medieval times.

Anyway, there's no point me writing about it as there's plenty of stuff out there already. Check out what Wikipedia has to say on the subject. There's also an introduction on Kuro5hin. (I contributed to both of those articles.) You can even play a modern version called Ambush on your PC.