8th Swedish 1968 Problem 2 How many different ways (up to rotation) are there of labeling the faces of a cube with the numbers 1, 2, ... , 6?
30 Solution Rotate the cube so that 1 is uppermost. There are then 5 choices for the opposite face. There are then 4! = 24 ways of arranging the other 4 faces, but groups of 4 are related by rotation, so 5·6 = 30 ways in all. 8th Swedish 1968 © John Scholes jscholes@kalva.demon.co.uk 30 December 2003 Last corrected/updated 30 Dec 03