How many unique ways can thirteen be obtained from the sum of 5 odd numbers?

Answer 1

I count 5, not counting the different orders that they are added as different ways. Here they are. If I missed some, then somebody else can add to it:

1. 3 + 3 + 3 + 3 + 1 = 13
2. 3 + 3 + 5 + 1 + 1 = 13
3. 5 + 5 + 1 + 1 + 1
4. 7 + 3 + 1 + 1 + 1
5. 9 + 1 + 1 + 1 + 1

If you want to count different orders as unique, For #1, there are 4 additional ways (I wouldn't say that the different 3's are unique, so the 1 in each position).

For #2, I count 13 additional ways. For # 3, I count 8 additional. For #4, I count 7 additional ways. And for #5, I count 4 additional ways. So that would be 36 additional ways, rearranging the orders, for a total of 41 ways.