October 21–October 27, 2008
Problem
This is a classic logic puzzle with lots of variations; here's one version by Martin Gardner. (Note that there was a mistake in the problem when it was first given here; this is the corrected version.)
Two positive integers x and y are chosen with 2 ≤ x ≤ y and x + y ≤ 40. The sum of the two numbers is given to mathematician S; the product of the two is given to mathematician P. Assume that the mathematicians also know that 2 ≤ x ≤ y and that x + y ≤ 40.
On the telephone S says to P, "I see no way you can determine my sum." An hour later P calls him back to say, "I know your sum." Later S calls P again to report, "Now I know your product." What are the two numbers?
Solution
Here.
List of solvers
Mimi Fung (undergraduate); Dustin Moody (graduate); Lawrence Hon, Steve Wilmarth, Lloyd Sakazaki, Justin Shih (outside).
Justin Shih wins the prize!