# How many possible combinations of this stage given its a n * n grid?

Lets say you have n x n grid, and each square on the grid is either black or white. How many different combinations of this grid can exist?

I figured 9! would be for the grid, but I don't know how to incorporate the fact each tile can be 2 different things.

• Is there anything other than black or white going on? Like numbered squares or something? – Glen_b -Reinstate Monica Sep 13 '17 at 22:49
• nope there isnt – Itachi San Sep 13 '17 at 22:50
• 1. Where did the "9" come from? 2. Each square can be in two states. Start with one square. Two possibilities (B or W). Add a square (BB, BW,WB,WW) etc. Every new square simply doubles how many possibilities there are. – Glen_b -Reinstate Monica Sep 13 '17 at 22:52
• @Glen_b I think the OP meant 9 factorial. It still wouldn't make sense. – Michael R. Chernick Sep 14 '17 at 0:43
• @Michael Yes thanks, I saw the "!", but the question is what any specific number would be doing in a question about $n$. – Glen_b -Reinstate Monica Sep 14 '17 at 1:00

Each square can have one of two possible values. There are $n^2$ squares. Therefore the number of possibilities is $2^{n^2}$