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Card Trick 2

Can you explain how this card trick works?

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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?

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Cube Paths

Given a 2 by 2 by 2 skeletal cube with one route `down' the cube. How many routes are there from A to B?

Cunning Card Trick

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

We are often intrigued by card tricks.
Is it magic or is there an explanation?
Perhaps mathematics can come to the rescue!