May 12–May 18, 2009

Problem

A man buys two boxes of matches and puts them in his pocket. Every time he has to light a match, he selects at random one box or the other. After some time, he takes one of the boxes from his pocket, and finds it is empty (after absentmindedly placing the box back in his pocket after using the last match). Supposing that each box originally had n matches, what is the probability that there are now k matches in the other box? (Here, 0 ≤ k ≤ n.)

Solution

here

List of solvers

Matt Inouye (undergrad); Koopa Koo (graduate); Justin Shih (UCLA grad); Lloyd Sakazaki, Mukund Tirumalai, Gaurav Chanda, Gary M. Raymond (outside).

Matt Inouye wins the prize!