Just today I had a bet with my friend over the following problem:
How many winning configurations can you have in a nxn Tic-Tac-Toe game where players win if a they get n/2 in either a row or column, consecutively.
n is even.
For example, in a 4x4 game, players win if a they get 2 of their symbols in either a row or column, consecutively.
I bet the figure to be "2 * ( 2 * n ) * ( 3 ** ( n / 2 ) )"
Do I win?
How to proceed if we were to count only draws? ( how many board configurations can there be so that they are always draws - i.e. no one wins )