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1,2,..n divided into 2 groups

Source: P24 [Combinatorics] - Turkish NMO 1st Round - 2014

May 23, 2014
symmetrycombinatorics proposedcombinatorics

Problem Statement

If the integers 1,2,…,n1,2,\dots,n can be divided into two sets such that each of the two sets does not contain the arithmetic mean of its any two elements, what is the largest possible value of nn?
<spanclass=′latex−bold′>(A)</span> 7<spanclass=′latex−bold′>(B)</span> 8<spanclass=′latex−bold′>(C)</span> 9<spanclass=′latex−bold′>(D)</span> 10<spanclass=′latex−bold′>(E)</span> None of the preceding <span class='latex-bold'>(A)</span>\ 7 \qquad<span class='latex-bold'>(B)</span>\ 8 \qquad<span class='latex-bold'>(C)</span>\ 9 \qquad<span class='latex-bold'>(D)</span>\ 10 \qquad<span class='latex-bold'>(E)</span>\ \text{None of the preceding}
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