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10 distinct numbers from {1, 2, 3, ... , 37 }

Source: 2018 Grand Duchy of Lithuania, Mathematical Contest p2 (Baltic Way TST)

October 3, 2020
combinatoricsSum

Problem Statement

Ten distinct numbers are chosen at random from the set {1,2,3,...,37}\{1, 2, 3, ... , 37\}. Show that one can select four distinct numbers out of those ten so that the sum of two of them is equal to the sum of the other two.
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