Question

A partition of a positive integer $n$ is any way of writing $n$ as a sum of one or more positive integers, in which we don't care about the order of the numbers in the sum. for example, the number 4 can be written as a sum of one or more positive integers (where we don't care about the order of the numbers in the sum) in exactly five ways: \[4,\; 3 + 1,\; 2 + 2,\; 2 + 1 + 1,\; 1 + 1 + 1 + 1.\] so 4 has five partitions. what is the number of partitions of the number 7? aops

Answer 1

1*7 
1+1+1+1+1+1+1
[7]
5+2
10-3