Saw an interesting brain teser today that I had never before thought about ...
Q. How many knights can you place on a chessboard so that none of the knights attack one another?
A. (drum roll) 32! Knights always attack squares of opposite color so if you out 32 knights on all the black or the white squares they can't capture each other! I didn't really have time to think about this problem before I was given the answer. I wonder how long it would have taken me otherwise?
Also, here is an older idea but still a huge challenge if you don't have the answer (and by answer I mean the concept to victory). The knights tour ... from any square on the board move a knight to all the other squares without moving to a single square more than once.

(that's a touring knight, btw)
Here is
a simple knight's tour from the corner