While I was in my school garden, I looked at our noughts and crosses board, and I thought to myself, “How many possibilities are there to win in Noughts and Crosses on a 9 square board?” I thought about how many places you could take the first turn, then the second turn and so on. I then wondered if there was an infinite number of possibilities or whether it was finite. I looked up potential combinations, after working through some myself, and found a formula to figure this out. The Formula is (8*3!*6*5) + (8*3!*6*5*4) – (6*3!*2*3!) + (8*3*6*3!*5*4*3) – (6*3*6*3!*3!) + (8*3*6*3!*5*4*3*2) – (6*3*6*3!*2*4) + (2*3*8*4!*4!) + (6*3*4*4!*4!) + (22*1*4!*4!) = The Answer!
In this sum, the “*” means the multiply sum, so x.
And the exclamation mark in this sum means “the product of the integers from 1 to n” In this formula they only use 4! And 3! 3! means 3x2x1 which is 6 and 4! means 4x3x2x1 which is 24.
After using a smart calculator, I figured out that the answer to this formula is 209,088! So, there are 209,088 possibilities/ways to win in Noughts and Crosses on our board!
