The touring knight problem is a maths problem that takes the movement of a knight in chess and attempts to find a path around a two dimensional board such that every single square is visited exactly once.
There are more sofisicated solutions but as you might have imagined, brute forcing is the most naive approach to solving this problem.
By trying every possible combination of legal move from your current position you can follow through every legal path and check whether you've completed the board or not.