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5-tuple with property sum of any 3 is divisible by the sum of the other 2

Source: 2000 German Federal - Bundeswettbewerb Mathematik - BWM - Round 1 p2

January 27, 2020
number theorySumdivisible

Problem Statement

A 55-tuple (1,1,1,1,2)(1,1,1,1,2) has the property that the sum of any three of them is divisible by the sum of the remaining two. Is there a 55-tuple with this property whose all terms are distinct?
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