Question 114
Find, with proof, all ways to write $1$ as a sum of three fractions, each with numerator $1$ and positive integer denominator. (The order of the fractions is irrelevant, so for instance $\frac{1}{2}+\frac{1}{4}+\frac{1}{4}$ is the same as $\frac{1}{4}+\frac{1}{4}+\frac{1}{2}$.)