Problem 44850. X O X O

On a noughts and crosses board, how many possible unique combinations are there given a square grid of length n?

Assumptions/constraints:

• All squares are populated.
• Number of naughts and number of crosses can only differ by a maximum of 1. I.E. The game was played until the board was full
• Minimum Grid size (n) = 1x1

This is a discrete maths question, which can be simplified by focussing on one of the options. If we look at the options for locating just the crosses on the grid, we know that the remaining locations must contain naughts and so similarly for the opposite condition. The maths is relatively simple, and is the solution to "choose k from n".

19-Feb-19 - Test suite updated to take into account solutions where the opposing player goes first.