As an exercise, in college, a couple colleagues and me started to play 4D Tic Tac Toe. We started with a 4x4x4x4 cube on the assumption that, when the game became too easy, we'd have grasped the idea and would move to a 5x5x5x5 cube. It took us many hours of play, explanations and headaches before we could move on, but we did it.

Its a lot of work to represent it, even ias a series of 3d projections