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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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Six points are arranged in space so that no three are collinear. How many line segments can be formed by joining the points in pairs?

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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.

Domino Tetrads

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

There are 28 dominoes in a set, which can be arranged in seven sets of four making a complete link, like the one below.

Is it possible to use all 28 dominoes arranging them in this way?
What patterns can you see in the solution(s) and can you explain them?
How do you know that you have all the solutions?

You may find our Dominoes Environment useful for working on this problem.

Printable NRICH Roadshow resource.