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10/16/2007

July 8–July 14, 2008

Problem

A local movie theater has a contest each day. The way the contest works is each customer writes down their birthday as they buy a ticket; the first customer whose birthday matches that of an earlier customer gets a free ticket. Suppose that I can get in line wherever I want, but I don't know anyone else's birthday. What position in line should I take to maximize my odds of getting a free ticket?

Solution

I didn't specifically mention assumptions about the distribution of birthdays or about handling leap days in this problem. Several people mentioned that birthdays are not uniformly distributed across a year, and a few tackled the problem taking leap days into account. I incorporated all this cool stuff into the solution here.

List of solvers

Steve Wilmarth (undergrad); Dustin Moody (graduate); Roman Holenstein, Kate Smith, Rajneesh Hegde, Lloyd Sakazaki, Mike Goodman, Stefan Sharkansky, Konrad Schroder (outside).

Rajneesh Hegde wins the prize!