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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?


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?

Odd Squares

Age 7 to 11
Challenge Level
Can you describe what is happening in the images?
What can you say about the pattern of dots on each side of the red line in the third image?
If there was a fourth picture, what could it look like?
What is the starting number in the picture?
Can you draw a similar series of pictures for different starting numbers?