Challenge Level

Consider the equation ${1\over a} +{1\over b}+{1\over c} = 1$ where $a$, $b$ and $c$ are natural numbers and $0 < a < b < c$. Prove that $a< 3$ and also that $b< 4$ and hence that there is only one set of values which satisfy this equation.

Find the six sets of values which satisfy the equation ${1\over a} +{1\over b}+{1\over c} +{1\over d}= 1$ where $a$, $b$, $c$ and $d$ are natural numbers and $0 < a < b < c < d$.