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

first of all we have to include feb 29. the reason to that that maybe you are the person who his birthday is on feb 29 or some one in line was born on feb 29 so we must include it

this means that the most possible different birthdays is 366

so if 367 people get line that means that there has to be at least two people that have the same birthday( supposing ofcourse that one of these people was born on feb 29) (and also supposing that the movie theater can hold more than 366 people)

so if i you get inline after 366 people have gone than you will have a chance of 0%  also if you were first in line.

if you were the 366th person inline you would have chance of 1 out of 366 that no body had the same birthday as some one else ofcourse same thing if you were second in line

with this we get the equation that if you were either (367-N) or (1+n)  in line you would have  N/366 chance of being the first duplicate birhtday

som the most possible chance is 50% wich is 183 in line

ofcourse all of this depends on luck but being the 183 in line you would have a 50% chance.

Posted by hunter on 2004-03-30 06:23:29