Since this is a challenge for you from your professor I will not give you the answer outright, but I will give you a hint.
Think about the Fibonaaci numbers. Do you know what they are?.
My professor gave us this problem that says that we have a 1x8 board and we have dominoes that are 2 units long and squares that are one unit long. how many different ways can you tile the the board?
If you can help me just know what formula/method to use to solve this problem in any 1xn or mxn board that would be great thanks so much
1-by-1 can only be tiled in 1 way. Right?. Because of the one square.
1-by-2 can be tiled 2 ways: either two squares or one domino.
1-by-3 can be tiled 3 ways: three squares, or a domino and square, or a square and domino.
1-by-4 can be tiled in 5 ways. And so on and so forth.
See the pattern?.