Difference between revisions of "2011 AMC 10B Problems/Problem 11"
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− | == Problem | + | == Problem== |
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? | 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? | ||
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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> | 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> | ||
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+ | == See Also== | ||
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+ | {{AMC10 box|year=2011|ab=B|num-b=10|num-a=12}} |
Revision as of 16:13, 4 June 2011
Problem
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
See Also
2011 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 10 |
Followed by Problem 12 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |