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Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

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Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?


Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?


Age 7 to 11
Challenge Level

Pupils from Town Close House in Norwich sent in these pictures of the work done by many of the pupils working together. Well done, some lively ideas.

town 1
Town 2
town 3
twon 4

Just to finish and say that there were a lot of good solutions. I particularly liked the solution from Amy from Archbishop Beck's chool. She suggested that the odds and evens were separated so in a $3x3$ square the houses went $1 ,3, 5, 7, 9, 11, 12, 10, 8, 6, 4, 2$ clockwise around the tiny square!


James also solved the problem in very creative way.   He says:

Would $28$ be an acceptable answer if the terraces were $1-7$ and opposite $8-14$ then on the sides $15-21$ and opposite that $22-28$?
It doesn't say the house numbers have to run in order. 

You're right, James, we didn't say that the house numbers were in numerical order so I think your solution would definitely work.  Well done!