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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Answer: 11
ReplyDeleteThis 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