# I have a 1x8 board...

• Feb 17th 2008, 11:34 AM
bwickfb606
I have a 1x8 board...
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
• Feb 17th 2008, 11:47 AM
galactus
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?.
• Feb 17th 2008, 11:49 AM
bwickfb606
yea....
yeah they are the two previous numbers added together to get the next number so f sub 1 is 1 and f sub 2 is 1 and f sub 3 is 2 then it goes, 3,5,8,13 etc.. so now wut?
• Feb 17th 2008, 12:01 PM
galactus
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?.
• Feb 17th 2008, 01:03 PM
bwickfb606
ok thanks a lot!