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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?

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?

Route Product

Age 7 to 11 Challenge Level:

Neil from Kells Lande Primary School wrote to say:

The route with the largest product is going up from A along the $5$ line, and down along the $2$ line, and then along the $0.5$ line to B, which has a product of $5$.
The route with the smallest product is to go horizontally along the $3$ line from A, then down the first $0.5$ line, along the $1$ line going horizontally, and then up to B along the $0.1$ line, which has a product of $0.15$.

You're right, well done, Neil. Class K's Magic Mathematicians at Charter Primary School told us how they found out the solution:

We worked in a group of four and found out all the routes from A to B, then we did all the sums and worked out all the answers.

Many of you also said that to find the largest and smallest products, it helped to look for the largest and smallest numbers. That's a good strategy, well done.