Difference between revisions of "2011 AMC 10B Problems/Problem 11"
Epicfailiure (talk | contribs) (Created page with '==Problem== There are 52 people in a room. The statement " At least n people in the room have birthdays in the same month " is true for n. What is the largest possible value of …') |
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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 20:38, 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 
