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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?

Baby's Blocks

Stage: 3 Short Challenge Level: Challenge Level:1


Instead of confusing ourselves with the positions of the L's, we only need to look at where the G and I will go, and the L's will just go in the remaining positions. Starting with the G, we can put it in one of 4 places. Then there are 3 remaining places to put the I. So the number of words is $4 \times 3=12$.

This problem is taken from the UKMT Mathematical Challenges.