March 13, 2012
Problem of the Week
for Tuesday, March 13, 2012
(Contibuted by former Saint Ann's student- Will Lockhart)
A path can be found through a 3 by 3 square that starts at the center and passes through each square one and only one time. The path pictured below can be labeled 5,4,1,2,3,6,9,8,7 as this is the sequence of squares visited along the path. Can a similar path be found through the 3 by 3 by 3 cube that starts at the center, passes through the faces of neighboring cubes, and visits all 27 cubes one and only one time? For the purpose of describing your path, use the labels T, M, and B for any cube the the top, middle, or bottom layers respectively, and the numbers 1 through 9 for distinguishing between cubes in each layer. Your path, therefore, begins with M5. Your challenge is to find such a path and record it, or explain why no such path exists.
