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Here are two pictures of children and parents in Africa making bracelets. They have lots of colourful beads to choose from.

Let's think about making a bracelet using two different colours of beads.

The smallest bracelet will have two of each colour and the largest five of each colour.

The challenge

Find all the ways of arranging four beads and then five beads on the bracelets, each time using just the two colours. Be careful not to have any arrangements the same! These two will be counted the same, as they are both 3 of one colour and 2 of the other colour.

Can you convince others that you have found them all?

Try this next for six, seven, eight, nine and ten beads.

Try this next for six, seven, eight, nine and ten beads.

A new person joins your group and wants to make bracelets.

Can you put on paper for them some guidance so that they have a system to make sure that they find them all and know how to avoid repeats?

Can you put on paper for them some guidance so that they have a system to make sure that they find them all and know how to avoid repeats?