May 20–May 26, 2008
Problem
Suppose we have a room with infinitely many boxes, and a child, Joe, who likes to shuffle his toys among these boxes. Initially, there is one box containing AB toys, while the rest are empty. Every hour Joe takes one toy from each non-empty box and put these toys (together) in an empty box. At some time there are A boxes each holding B toys.
For which A and B is this possible?
Solution
here.
List of solvers
Steve Wilmarth (undergrad); Robert Bradshaw, Dustin Moody (graduate); Lloyd Sakazaki, Konrad Schroder, Kate Smith, Yo Tu, Mike Goodman (outside).
The winner this week is Robert Bradshaw, who was the only one who found all the solutions (though some of them were trivial).