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Math Help - I have a 1x8 board...

  1. #1
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    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
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  2. #2
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    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?.
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  3. #3
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    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?
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  4. #4
    Eater of Worlds
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    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?.
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  5. #5
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    ok thanks a lot!
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