All the partitions of 6

Text

A partition of an integer is a way of writing it as a sum of positive integers, disregarding order. How many partitions does the number $6$ have?

Solution

List them in decreasing order: $6;\ \ 5{+}1;\ \ 4{+}2;\ \ 3{+}3;\ \ 4{+}1{+}1;\ \ 3{+}2{+}1;\ \ 2{+}2{+}2;$ $3{+}1{+}1{+}1;\ \ 2{+}2{+}1{+}1;\ \ 2{+}1{+}1{+}1{+}1;\ \ 1{+}1{+}1{+}1{+}1{+}1.$ There are $\boxed{11}$ partitions in all.