At a movie theater, the manager announces that they will give a free ticket to the first person in line whose birthday is the same as someone who has already bought a ticket. You have the option of getting in line at any time. Assuming that you don't know anyone else's birthday, that birthdays are distributed randomly throughout the year, etc., what position in line gives you the greatest chance of being the first duplicate birthday?

from http://www.ocf.berkeley.edu/~wwu/riddles/hard.shtml

(In reply to Function by Tristan)

Your formula must be the same as the one I got because they give the same numbers:

[(n-1)*365!]/[(365^n)*(366-n)!]

In general for an r day year

[(n-1)*r!]/[(r^n)*(r+1-n)!]

The best position for an r day year is to round up the positive root of the polynomial equation x(x-1)=r
If this root is a whole number, n, then n and n+1 are tied for the best.

-Jer

Posted by Jer on 2004-03-31 12:16:10