Let $a<b<c<d<e$ be real numbers. Among the $10$ sums of the pairs of these numbers, the least $3$ are $32,36,37$, while the largest two are $48$ and $51$. Find all possible values of $e$
Source: Singapore Junior Math Olympiad 2013 2nd Round p1 SMO
Tags: algebra, Sum
Let $a<b<c<d<e$ be real numbers. Among the $10$ sums of the pairs of these numbers, the least $3$ are $32,36,37$, while the largest two are $48$ and $51$. Find all possible values of $e$