April 22–April 28, 2008

Problem

Andrew has n3 white cubes of the size 1 x 1 x 1. He wants to construct an n x n x n cube with all its faces being completely white. Find the minimal number of the faces of small cubes that Basil must paint black in order to prevent Andrew from completing his task. Consider the cases:

  1. n = 3
  2. n = 1000

Solution

here.

List of solvers

Steve Wilmarth, Doug Sherbon (undergrad); Dustin Moody (graduate); Marina Meila (faculty); Stefan Sharkansky, Kate Smith, Lloyd Sakazaki (outside).

Konrad Schroder, Doug Faust, Steven Behrend, and Eric Brodeur got half the problem correct.

Dustin Moody wins the prize!