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Determine all values of 'e'

Source: ItaMO 2009, p1

February 22, 2012
number theory proposednumber theory

Problem Statement

Let a<b<c<d<ea < b < c < d < e be real numbers. We calculate all possible sums in pairs of these 5 numbers. Of these 10 sums, the three smaller ones are 32, 36, 37, while the two larger ones are 48 and 51. Determine all possible values ​​that ee can take.
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