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.
[Mailbag] What Do You Do with the Ideas You Used to Call “Mistakes”

Guillaume ParĂ©, in the very interesting comments of my last post where I
urged us to reconsider mistakes: I do agree with what is written, but I am
still w...
1 week ago
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