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 .

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?