Let \(q(n)\) be the number of partitions of \(n\) into distinct parts. What is \(q(6)\), and which value makes \(q(6)=p(6)-\)(number of partitions of \(6\) with a repeated part) true?
The partitions of 6 into distinct parts are 6, 5+1, 4+2 and 3+2+1, so q(6)=4. Since p(6)=11, the number with a repeated part is 7. The option giving three omits the partition 3+2+1.
A partition of an integer n is a way of writing n as a sum of positive integers, where the order of the summands does not matter. The number of partitions of n is denoted p(n).