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smallest sum of perimeters of 100 natural, sides of non-obtuse triangles

Source: Spanish Mathematical Olympiad 1995 P1

July 31, 2018
perimeterminimumSumcombinatoricsalgebra

Problem Statement

Consider all sets AA of one hundred different natural numbers with the property that any three elements a,b,cāˆˆAa,b,c \in A (not necessarily different) are the sides of a non-obtuse triangle. Denote by S(A)S(A) the sum of the perimeters of all such triangles. Compute the smallest possible value of S(A)S(A).
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