MathDB
Turkey NMO 2006 1st Round - P32 (Combinatorics)

Source:

February 3, 2013
pigeonhole principle

Problem Statement

What is the greatest integer kk which makes the statement "When we take any 66 subsets with 55 elements of the set {1,2,,9}\{1,2,\dots, 9\}, there exist kk of them having at least one common element." true?
<spanclass=latexbold>(A)</span> 1<spanclass=latexbold>(B)</span> 2<spanclass=latexbold>(C)</span> 3<spanclass=latexbold>(D)</span> 4<spanclass=latexbold>(E)</span> 5 <span class='latex-bold'>(A)</span>\ 1 \qquad<span class='latex-bold'>(B)</span>\ 2 \qquad<span class='latex-bold'>(C)</span>\ 3 \qquad<span class='latex-bold'>(D)</span>\ 4 \qquad<span class='latex-bold'>(E)</span>\ 5