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Math Help - Magic Combinations

  1. #1
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    Magic Combinations

    How many ways are there of spelling out “ABRACADABRA” by traversing the following diamond, always going from one letter to an adjacent one? (ignore the underscores, theyre just there to make it look like a diamond)

    _____A
    ____B B
    ___R R R
    __A A A A
    _C C C C C
    A A A A A A
    _D D D D D
    __A A A A
    ___B B B
    ____R R
    _____A
    Last edited by Aquafina; May 1st 2009 at 08:19 AM. Reason: typed it wrong
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  2. #2
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    Quote Originally Posted by aquafina View Post
    how many ways are there of spelling out “abracadabra” by traversing the following diamond, always going from one letter to an adjacent one? (ignore the underscores, theyre just there to make it look like a diamond)

    _____a
    ____b b
    ___r r r
    __a a a a
    _c c c c c
    a a a a a a
    _d d d d d
    __a a a a
    ___b b b
    ____r r
    _____a
    If by "ways of spelling out abracadaba" you mean the number of paths from the top of the diamond to the bottom, the answer is 252.

    Code:
                  1
               1    1
            1     2    1
         1     3    3     1
      1     4     6    4     1
    1    5    10    10    5    1
      6    15    20    15    6
        21    35    35    21
           56    70    56
              126   126
                 252
    Do you see why?
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