MathDB
Turkey NMO 2010 1st Round - P32 (Combinatorics)

Source:

July 26, 2012

Problem Statement

At least two of any three students of a school with 10011001 students are friends. How many of the numbers 334,412,450,499334,412,450,499 can be the number of friends of the one with the highest number of friends?
<spanclass=latexbold>(A)</span> 4<spanclass=latexbold>(B)</span> 3<spanclass=latexbold>(C)</span> 2<spanclass=latexbold>(D)</span> 1<spanclass=latexbold>(E)</span> None <span class='latex-bold'>(A)</span>\ 4 \qquad<span class='latex-bold'>(B)</span>\ 3 \qquad<span class='latex-bold'>(C)</span>\ 2 \qquad<span class='latex-bold'>(D)</span>\ 1 \qquad<span class='latex-bold'>(E)</span>\ \text{None}