# Magic Combinations

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• May 1st 2009, 08:17 AM
Aquafina
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
• May 1st 2009, 04:23 PM
awkward
Quote:

Originally Posted by aquafina
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?