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
(No `backtracking' allowed, i.e. each move must be away
from A towards B.)
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice.