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Math Help - pigeonhole principle problem

  1. #1
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    Angry pigeonhole principle problem

    Hello!

    The following one is really bothering me:

    Suppose you live in a country with 9 000 000 inhabitants. At least how many people have their birthday on the same day?
    ---------------------------------------
    First I ignored the existence of the leap year, so I just simply computed 9 000 000/365 and got approx. 24657. But the answer is 24656 so I ralized that the leap year mattered. Then I assumed that 25% of the people in my country were born on a leap year and realized that at least 6147 were born on Feb. 29th by computing 9 000 000/(4*365). Then I computed (9000000-6147)/365 and got the wrong answer again. What am I doing wrong?
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  2. #2
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    Re: pigeonhole principle problem

    Quote Originally Posted by mgarson View Post
    Suppose you live in a country with 9 000 000 inhabitants. At least how many people have their birthday on the same day? I just simply computed 9 000 000/365 and got approx. 24657. But the answer is 24656 so I ralized that the leap year mattered.
    Leap year has nothing to do with it.
    Use the floor function
    \left\lfloor {\frac{{9 \cdot 10^6 }}{{365}}} \right\rfloor  = {\text{24657}}.
    Last edited by Plato; October 20th 2011 at 03:57 PM.
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  3. #3
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    Re: pigeonhole principle problem

    That's just it... The hint in the book says to think of Feb. 29:th. And the answer is 24656 and not 24657. The author even wants us to explain why 24657 is wrong.
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