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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?
Lesser Digits
How many positive integers less than or equal to 4000 can be written down without using the digits 7, 8 or 9?
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.)
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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.