2011 AMC 10B Problems/Problem 11: Difference between revisions
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==Problem== | == Problem 11 == | ||
There are 52 people in a room. | There are <math>52</math> people in a room. what is the largest value of <math>n</math> such that the statement "At least <math>n</math> people in this room have birthdays falling in the same month" is always true? | ||
(A) 2 (B) 3 (C) 4 (D) 5 (E) | <math> \textbf{(A)}\ 2 \qquad\textbf{(B)}\ 3 \qquad\textbf{(C)}\ 4 \qquad\textbf{(D)}\ 5 \qquad\textbf{(E)}\ 12 </math> | ||
==Solution== | ==Solution== | ||
By the | Pretend you have <math>52</math> people you want to place in <math>12</math> boxes. By the [[Pigeonhole Principle]], one box must have at least <math>\left\lceil \frac{52}{12} \right\rceil</math> people <math>\longrightarrow \boxed{\textbf{(D)} 5}</math> | ||
Revision as of 19:38, 25 May 2011
Problem 11
There are 
people in a room. what is the largest value of 
such that the statement "At least people in this room have birthdays falling in the same month" is always true?
Solution
Pretend you have people you want to place in 
boxes. By the Pigeonhole Principle, one box must have at least 
people 
