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maximal number (x, y, z) of 7 elements with x < y & x + y=z

Source: Nordic Mathematical Contest 1997 #1

October 4, 2017

combinatoricsmaximizationtripletsExtremal combinatorics

Problem Statement

Let

A

be a set of seven positive numbers. Determine the maximal number of triples

(x, y, z)

of elements of

A

satisfying

x < y

and

x + y = z