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P12 [Combinatorics] - Turkish NMO 1st Round - 2014

Source:

May 22, 2014

Problem Statement

If one can find a student with at least kk friends in any class which has 2121 students such that at least two of any three of these students are friends, what is the largest possible value of kk?
<spanclass=latexbold>(A)</span> 8<spanclass=latexbold>(B)</span> 9<spanclass=latexbold>(C)</span> 10<spanclass=latexbold>(D)</span> 11<spanclass=latexbold>(E)</span> 12 <span class='latex-bold'>(A)</span>\ 8 \qquad<span class='latex-bold'>(B)</span>\ 9 \qquad<span class='latex-bold'>(C)</span>\ 10 \qquad<span class='latex-bold'>(D)</span>\ 11 \qquad<span class='latex-bold'>(E)</span>\ 12