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Scalene Polygon with sides 1<= S_i <= 2013

Source: Turkish NMO 1st Round - 2013 - Problem 15

April 19, 2013
algebra proposedalgebra

Problem Statement

No matter how nn real numbers on the interval [1,2013][1,2013] are selected, if it is possible to find a scalene polygon such that its sides are equal to some of the numbers selected, what is the least possible value of nn?
<spanclass=′latex−bold′>(A)</span> 14<spanclass=′latex−bold′>(B)</span> 13<spanclass=′latex−bold′>(C)</span> 12<spanclass=′latex−bold′>(D)</span> 11<spanclass=′latex−bold′>(E)</span> 10 <span class='latex-bold'>(A)</span>\ 14 \qquad<span class='latex-bold'>(B)</span>\ 13 \qquad<span class='latex-bold'>(C)</span>\ 12 \qquad<span class='latex-bold'>(D)</span>\ 11 \qquad<span class='latex-bold'>(E)</span>\ 10
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