Make Those Bracelets

'Make Those Bracelets' printed from https://nrich.maths.org/

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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 four beads and the largest will have ten beads.

The Challenge

Find some ways of arranging four beads and then five beads on the bracelets, each time using 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.

If two arrangements would make the same bracelet when they are turned around or flipped over, these count as the same arrangement as well.

Try to find all the ways. Can you convince others that you have found them all?

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

Final Challenge

A new person joins your group and wants to make bracelets.
Can you write down some guidance for them so that they have a system to make sure they find all the different arrangements and avoid repeats?