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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?

Loose Change

Stage: 3 Short Challenge Level: Challenge Level:1

If there are two $5$p pieces, this gives one way.

If there is one $5$p piece, then there are two $2$p coins, one $2$p coin or no $2$p coins, with all the other coins as $1$p coins.

If there are no $5$p coins, there are between $0$ and $5$ coins that are $2$p, and all the rest are $1$p.

Therefore there are $1+3+6=10$ ways to give change.

This problem is taken from the UKMT Mathematical Challenges.
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