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Pebbles

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?

Bracelets

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

Sweets in a Box

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

Which Is Quicker?

Age 7 to 11 Challenge Level:

If you are trying to count in something unfamiliar such as hundred thousands it might be useful to write down and read the first two (or more) numbers in the list.
How will you make a prediction?  What sorts of things do you need to take into account?