Problem of the Week 1156A 3Dimensional 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 3dimensional board made from cubes and colored in the usual alternating blackwhite pattern; each cube has 12 samecolored and 14 oppositecolored 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, A Mathematical Orchard, Problems and Solutions, by Mark Krusemeyer, George Gilbert, and Loren Larson, MAA Problem Book Series, 2012. © Copyright 2012 Stan Wagon. Reproduced with permission.
