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Bracelets

Stage: 2 Challenge Level: Challenge Level:1
We had some good ideas for Bracelets, here is a selection of ideas that were sent in.
First this was sent in by Fatima at the British School Al Khubairat in U.A.E.
:

24 beads make an octagonal bracelet.
3 beads should be used on each side.

Alia and Fatima also from BSAK in U.A.E. sent in this good explanation of their ideas:

1.  Yes because it has the same difference
2.  24 because it’s even and in lots of times table like 8,3,4,6,2,12. You can make more irregular and regular shapes.
3.  With 12 beads split up equally to make 6 for each bracelet. Make a triangle (2 on each side). And if we have 18 we can make 3 (still
triangular and still 2 on each side).
4. You make a square have 12 beads to use for the outside (3 on each side) then use 6 beads to fill the middle.
5. You can a square bead it will be a bit the same but straighter. A square-based pyramid bead; it would make it much more spikier.
6. What about a different bracelet? What about necklaces and rings? Using square-based pyramid beads you can have a spiky ring, necklace and
bracelet. And also we can make irregular bracelets.

Annabel and Anna from Norfolk House School said that to find out how many objects you'll need you take the amount of sides double it and add it on.  So a square would go from 12 to 20 to 28.

Betsy from Mayfield Primary School wrote;

The smallest number of beads you can have for two bracelets is 10 unless you count the fact that with 8, 4 in each one there might be a space in the middle might not be depends on the way you draw it.
Another question I ask myself is what will happen if I’d have to make three bracelets.  The smallest is 15 because with the numbers 14,13,12 and 11 you can not make three identical bracelets.
Other Questions: what will happen if you need to have the same amount of beads in 10 bracelets, what will be the smallest number?
What is the smallest number of beads you can have on one bracelet (with a hole in the middle)?
How many shapes can you make with 1-18,19-24, 25-48. 49-96, 97-etc.?

Thank you Betsy for those questions and thank you to the others from British School Al Khubairat for your work. We hope you had fun doing this.