INTRODUCING 5 - days-a-week problem solving session for Math Olympiad and ISI Entrance. Learn More 

February 17, 2020

Pigeon Hole Principle Problem-11 from 2011 AMC 10B

Content
 [hide]

    What is The Pigeon Hole Principle?


    The Pigeon Hole Principle (also known as the Dirichlet box principleDirichlet principle or box principle) states that if $ \textbf n+1 $ or more pigeons are placed in $ \textbf n $ holes, then one hole must contain two or more pigeons.

    The extended version of this Principle states that if $ \textbf k$ objects are placed in $ \textbf n$  boxes then at least one box must hold at least $ \frac {k} {n} $ objects.

    Try the problem


    There are $52$ people in a room. what is the largest value of $ \textbf n $ such that the statement "At least $ \textbf n $ people in this room have birthdays falling in the same month" is always true?
    $ \textbf {(A)} 2\quad \textbf {(B)} 3\quad \textbf {(C)} 4\quad \textbf {(D)} 5\quad \textbf {(E)} 12$

    2011 AMC 10B Problem 11

    The Pigeon Hole Principle

    6 out of 10

    Mathematics Circle

    Knowledge Graph


    Pigeon Hole-Knowledge Graph

    Use some hints


    You have $52$ people in a room. You have to place them in $12$ boxes.

    can you say why did i take $12$ boxes?

    Because there are $12$ months in year.

    One box must have at least $ \frac {52} {12} $

    Subscribe to Cheenta at Youtube


    Leave a Reply

    This site uses Akismet to reduce spam. Learn how your comment data is processed.

    Cheenta. Passion for Mathematics

    Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.
    JOIN TRIAL
    support@cheenta.com