Chess related to math

Welcome to free math tutoring,
It's a little like what you do when you invent a board game like
chess. You specify that there are such-and-such pieces, and they can
move in such-and-such ways, and then you let people explore which
board positions are possible or impossible to achieve. 

The main difference is that in chess, you're trying to win, while in
math help, you're just trying to figure out what kinds of things can - and
can't - happen. So a 'chessamatician', instead of playing complete
games, might just sit and think about questions like this:

 If I place a knight (the piece that looks like a horse, and moves
 in an L-shaped jump) on any position, can it reach all other
 positions?

 What is the minimum number of moves that would be required to get
 from any position to any other position?

Think, get more examples on free online math tutoring.