MathDB
P03 [Combinatorics] - Turkish NMO 1st Round - 2004

Source:

November 15, 2013
pigeonhole principle

Problem Statement

At most how many elements does a set have such that all elements are less than 102102 and it doesn't contain the sum of any two elements?
<spanclass=latexbold>(A)</span> 49<spanclass=latexbold>(B)</span> 50<spanclass=latexbold>(C)</span> 51<spanclass=latexbold>(D)</span> 54<spanclass=latexbold>(E)</span> 62 <span class='latex-bold'>(A)</span>\ 49 \qquad<span class='latex-bold'>(B)</span>\ 50 \qquad<span class='latex-bold'>(C)</span>\ 51 \qquad<span class='latex-bold'>(D)</span>\ 54 \qquad<span class='latex-bold'>(E)</span>\ 62