September 30–October 6, 2008

Problem

Find positive integers x1, x2, ..., xm so that

  1. the sum x1 + x2 + ... + xm = 2008.
  2. the product x1x2 ... xm is as large as possible.
What is the maximum possible value for their product? (For example, the maximum product is at least as large as 2006 since we can pick three numbers: x1 = x2 = 1 and x3 = 2006.)

Solution

here.

List of solvers

Patrick Tam (undergrad? Berkeley); Dustin Moody, (grad); Gary Raymond (staff); Jack Lee (faculty); Peiyush Jain, Mike Goodman, Lloyd Sakazaki, Steve Wilmarth, Lawrence Hon (outside).

Jack Lee wins the prize! (It's rare that faculty win the ice cream, but this week Jack's solution was one of the few fully-justified solutions, and he hasn't won ice cream yet.)