# pigeonhole principle problem

• Oct 20th 2011, 02:24 PM
mgarson
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? (Headbang)
• Oct 20th 2011, 03:00 PM
Plato
Re: pigeonhole principle problem
Quote:

Originally Posted by mgarson
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
$\left\lfloor {\frac{{9 \cdot 10^6 }}{{365}}} \right\rfloor = {\text{24657}}$.
• Oct 20th 2011, 04:46 PM
mgarson
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.