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I got different answers...ah. how many paths are there to spell this word? watch

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    rule: start from the top, and you can only move diagonally to the row below.

    B
    I I
    N N N
    O O O O
    M M M
    I I
    A
    L L

    Is there a mathematical way to do this? Or do we just count? I've tried counting and I got 24 and then 26 the second time And I have to do another question like this too.
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    Is that the correct shape for the letters? If not, use [code][/code] tags.
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    could you space the letters a little better please.
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    I'm not 100% sure, but I believe it is this:

    1 * 2 * 3 * 4 * 3 * 2 * 1 * 2 = 288
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    (Original post by mahaneap)
    I'm not 100% sure, but I believe it is this:

    1 * 2 * 3 * 4 * 3 * 2 * 1 * 2 = 288
    You can only chose letters going diagonally...

    I think the best way of doing this is just to be systematic with how you list out the number of ways of getting BINOMIAL. Maybe give each letter a subscript (from 1-4) and keep in mind that the subscripts of adjacent letters can only differ by 1...
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    There's a very easy, standard way of doing problems like this. Basically do the same as you would calculating Pascal's triangle to get something like:

    Code:
    1
               1    1
             1   2   1
          1   3    3  1
             4   6   4
              10  10 
                 20
    (the correct diagram for this problem would be a bit bigger, but the principle is the same).
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    That's...ingenious!
 
 
 
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