January 20–January 26, 2009

Problem

Let g(n) be the number of solutions (x, y, z) of x + 2y + 3z = n with x, y, and z all nonnegative integers. Show that

g(0) = 0, g(1) = 1, g(2) = 2, g(n) = g(n-3) + floor(n/2) + 1

where

floor(n/2) = n/2 when n is even and (n-1)/2 when n is odd

Solution

here

List of solvers

Michael Draper, Matt Inouye (undergrad); Koopa Koo, Jacob Lewis, Dustin Moody, Justin Shih (graduate); Gary Raymond (staff); Mike Goodman, Luan Nguyen, Lloyd Sakazaki, Peiyush Jain, Josh Lim, Lawrence Hon, Anand Rajagopalan (outside).

Michael Draper wins the prize!