There are many ways to express the number 9 as a sum of other numbers. One way to think about this is to use the concept of “partitions” of a number. A partition of a number is a way of expressing that number as the sum of one or more positive integers. For example, the partitions of the number 9 are:
9
8 + 1
7 + 2
6 + 3
5 + 4
4 + 5
3 + 6
2 + 7
1 + 8
There are other partitions as well, but these are the distinct ones. These partitions are not ordered, so (5+4) and (4+5) are the same.
In this case, there are 9 distinct partitions of the number 9.
This is just one way to think about the question, but it’s a nice way to think about the different ways that a number can be expressed as a sum of other numbers. If you are interested in the number of partitions of a number in general, you can use the Partition function which is denoted by “p(n)”
If you want more general answer, there is no closed-form solution for the number of partitions of a number in general, there are some asymptotic estimates and some recursive approaches.