Friday, September 25, 2009

Writing 20 as a sum of odd numbers

There are three ways to write 10 as the sum of four odd positive integers, assuming that order does not matter. They are 1+1+1+7, 1+1+3+5, and 1+3+3+3. In how many ways can 20 be written as the sum of eight odd positive integers?

Source: The Moscow Puzzles, by Boris Kordemsky.
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1 comment:

  1. DavidSeptember 26, 2009 at 12:34 PM

    Answer: 11

    This problem is not hard if you list the solutions systematically.

    1+1+1+1+1+1+1+13
    1+1+1+1+1+1+3+11
    1+1+1+1+1+1+5+9
    1+1+1+1+1+1+7+7
    1+1+1+1+1+3+3+9
    1+1+1+1+1+3+5+7
    1+1+1+1+1+5+5+5
    1+1+1+1+3+3+3+7
    1+1+1+1+3+3+5+5
    1+1+1+3+3+3+3+5
    1+1+3+3+3+3+3+3

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