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Card Trick 2

Can you explain how this card trick works?

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?

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

Age 11 to 14
Challenge Level

When you carry out this trick, you make lots of piles on the table, but you only keep three.
Are the others important to the problem, or can you ignore them when you are trying to understand how the trick works?