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Necklaces

Stage: 1 and 2 Challenge Level: Challenge Level:1

Does your school have a school fair? 
One of the classes in a school I often visit decided they'd have a stall where everything to be sold was as mathematical as possible!
The jewellery stall was going to carry necklaces, but mathematical ones.
Each would have four beads of one colour and four of another.
And they'd all be symmetrical like this:

  

How many different necklaces do you think could be made?
How do you know you've found them all?
What if there were nine beads, four of one colour and five of another?
Ten beads?
Eleven beads?
Twelve?  Thirteen ....?
What can you find out?

What other things do you think they could sell on their mathematical stall?

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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NRICH is part of the family of activities in the Millennium Mathematics Project.