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Sum of 3 elements are all different

Source: 2012 Indonesia Round 2 TST 4 Problem 3

March 18, 2012

combinatorics proposedcombinatorics

Problem Statement

Let

S

be a subset of

\{1,2,3,4,5,6,7,8,9,10\}

. If

S

has the property that the sums of three elements of

S

are all different, find the maximum number of elements of

S