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?
The highlight of Gill's fourth birthday party was a game of musical chairs. The game got down to herself, nurse and me. Only two chairs were left - the hard chair and the comfy chair, with a big gap between them. The music stopped and we all piled onto the nearest chair, some on top of one another. If Gill's bottom was firmly in contact with one of the two chairs, in how many different ways
could this have happened?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
This problem is taken from the UKMT Mathematical Challenges.