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

Ryan,

Here's a method of getting the solution, you are more than welcome to adapt this to accommodate Feb. 29th:

One can set this up rather easily in a spreadsheet (Excel).

In B6 set up 1 (B7 = 2, B8 = 3, etc...)

In D6 set up 1.
In D7 set up "=D6*(365-B7+1)/365", and then copy that down

In F7 set up "=(B7-1)/365*D6", and then copy that down...

column B represents the position in line
column D represents the chance that no has YET had a duplicate, and
column F represents the chance that given that no one has had a duplicate already, that THIS position will create the duplicate.

Looking at column F, one will note that this chance increases until position 20, after which it decreases.

Posted by Thalamus on 2004-03-29 13:49:47