You may also like
Painting Cubes
Imagine you have six different colours of paint. You paint a cube using a different colour for each of the six faces. How many different cubes can be painted using the same set of six colours?
How Many Dice?
A standard die has the numbers 1, 2 and 3 are opposite 6, 5 and 4 respectively so that opposite faces add to 7? If you make standard dice by writing 1, 2, 3, 4, 5, 6 on blank cubes you will find there are 2 and only 2 different standard dice. Can you prove this ?
Age 11 to 14
Challenge Level
The diagram shows a skeletal view of a 2 by 2 by 2 cube with one route 'down' the cube.
How many routes are there on the surface of the cube from A to
B?
(No `backtracking' allowed, i.e. each move must be away
from A towards B.)
Copyright © 1997 - 2021. University of Cambridge.
All rights reserved.
NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.