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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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Permute It

Take the numbers 1, 2, 3, 4 and 5 and imagine them written down in every possible order to give 5 digit numbers. Find the sum of the resulting numbers.

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Flagging

How many tricolour flags are possible with 5 available colours such that two adjacent stripes must NOT be the same colour. What about 256 colours?

Shuffle Shriek

Stage: 3 Challenge Level: Challenge Level:1
Shuffles are more formally known as permutations. The first person to study permutations in any depth was Gauss. At the age of 19 he used them to prove that it was possible to construct a regular 17 sided polygon by ruler and compass. In the19th century Galois developed the theory of permutations into abstract group theory in order to prove that there is no formula to solve fifth order equations..