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Birthdays falling in the same month

Source: AMC 10 2011 b Problem 11

February 24, 2011
pigeonhole principleAMC

Problem Statement

There are 5252 people in a room. What is the largest value of nn such that the statement "At least nn people in this room have birthdays falling in the same month" is always true?
<spanclass=′latex−bold′>(A)</span> 2<spanclass=′latex−bold′>(B)</span> 3<spanclass=′latex−bold′>(C)</span> 4<spanclass=′latex−bold′>(D)</span> 5<spanclass=′latex−bold′>(E)</span> 12 <span class='latex-bold'>(A)</span>\ 2 \qquad <span class='latex-bold'>(B)</span>\ 3 \qquad <span class='latex-bold'>(C)</span>\ 4 \qquad <span class='latex-bold'>(D)</span>\ 5 \qquad <span class='latex-bold'>(E)</span>\ 12
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