Can you explain how this card trick works?
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?
Given a 2 by 2 by 2 skeletal cube with one route `down' the cube.
How many routes are there from A to B?
Suppose that Gill's bottom was firmly in contact with the Hard Chair. Then the possible combinations would be:
This problem is taken from the UKMT Mathematical Challenges.