An algebra problem by Alf-archie Sangkula

Algebra Level pending

Let a < b < c < d < e be real numbers. Among the 10 sums of the pairs of these numbers, the least three are 32, 36 and 37 while the largest two are 48 and 51. Find all possible values of e

Hint: List out the pairwise sums in a systematic manner. It should be clear which sums are the smallest, 2nd smallest, largest, and 2nd largest.

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