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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?

One Wasn't Square

Age 7 to 11 Challenge Level:

What can you deduce from what Jamie says?
Making a list of square numbers might help.
You could try finding pairs of numbers that make squares.
All the numbers, including the squares, are less than $40$.