### 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?

### Permute It

Take the numbers 1, 2, 3, 4 and 5 and imagine them written down in every possible order to give 5 digit numbers. Find the sum of the resulting numbers.

### Flagging

How many tricolour flags are possible with 5 available colours such that two adjacent stripes must NOT be the same colour. What about 256 colours?

# Shuffle Shriek

##### Stage: 3 Challenge Level:

Learn how to use the Shuffle Interactivity using the tutorials movies before trying this question.

You also need to know about the identity shuffle and the order of a shuffle .

This text is usually replaced by the Flash movie.

Convince yourself there are no other 3-ball shuffles than the 6 pictured above.

Now for the 4-ball shuffles.

Your task will be to find all the 4-ball shuffles and work out their orders.

There is only 1 order 1 shuffle, the identity.

Next consider the order 2 shuffles.
How many are there of these? Can you list them all?

Use the labels that the interactivity supplies when you are listing the different shuffles .

Now consider the order 3 and the order 4 shuffles.
How many are there of these? Can you list them all?

Convince yourself that there are no order 5 shuffles.

Can you prove that you have found all the 4-ball shuffles?