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set and subset

Source: China south east mathematical olympiad 2008 day1 problem 1

July 14, 2013
combinatorics unsolvedcombinatoricsSet systemsAdditive combinatoricsRamsey Theory

Problem Statement

Given a set S={1,2,3,…,3n},(n∈N∗)S=\{1,2,3,\ldots,3n\},(n\in N^*), let TT be a subset of SS, such that for any x,y,z∈Tx, y, z\in T (not necessarily distinct) we have x+y+z∉Tx+y+z\not \in T. Find the maximum number of elements TT can have.
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