Credit for this problem goes to jlevinson. Thanks!

## N-dimensional Tic-Tac-Toe

How many winning lines can you make on a normal 3x3 tic-tac-toe board? 8 (3 verticial, 3 horizontal, 2 diagonal)

What about on a 3x3x3 tic-tac-toe cube?

How about a \(3^n\) tic-tac-toe hypercube?

Solution