## Problem of the Week 1156## A 3-Dimensional ChessboardThe normal chessboard coloring of the entire plane has the property that every square has four white and four black neighbors (neighbors include diagonal ones). Consider a 3-dimensional board made from cubes and colored in the usual alternating black-white pattern; each cube has 12 same-colored and 14 opposite-colored neighbors. Is it possible to assign white or black to each cube so that each has 13 white and 13 black neighbors?
Source: From the nice new problem book, © Copyright 2012 Stan Wagon. Reproduced with permission.
8 October 2012 |