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## 'Shuffle Shriek' printed from http://nrich.maths.org/

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 .

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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?