Tic Tac Toe¹ is one of those games that all of us remember from our childhood. We all have fond memories of marking boxes in an attempt to win knowing we could end up in a draw quite easily. The game is usually played in two dimensions, but it is quite easy to imagine it being extended up into three or more. This is the heart of the Tic Tac Toe problem being set here. To create a generalised game in any number of dimensions. Post ideas, proofs and questions in the forum below.

The Minimum Playable Grid problem

What size of row provides the minimum playable² grid in n dimensions?

Experience and experiment suggests a grid of row size n+1 but can this be proven and if so, how?

The Number of Scoring Rows problem

How many scoring³ rows are there in n dimensions.

Ideas for further research

The problems above are generalised for a square grid. What would happen if the playing surface weren't square but rectangular, triangular etc? What would happen to the game rules and game itself? Could rules be generalised for these surfaces in n dimensions as for the n dimensional hypercubic grid.

Please feel free to submit any ideas for further research below.