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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?

Three Dice

Age 7 to 11
Challenge Level
Bomere Heath School in England obviously looked at more than just one of this month's problems, here is what Callen, Annalise,Eddi, Alex and Holly said,

We found out that $7+7+7=21$ so every time you roll a dice it will add up to
seven and when you roll three dice it will add up to $21$.

Noah and Guy wrote,

In three dice you roll three dice and add the top score up and the boottem score together and add it together we found out that the answer was always $21$ thats because three times seven makes $21$ and whatever you get on one side add to the other side always make $7$ like $6$ and $1$ and $2$ and $5$ they both make $7$ .

Sian, Mollie and Liam from Deansfield Community School sent in the following; 

The opposite sides always add up to $7$. When you have $3$ dice and you take the sum of the top and add the sum of the bottom the total equals $21$. This is because $3\times7$ is $21$.
If there are $4$ dice the sum of the top and bottom will always be $28$ because $4\times7=28$

Thank you all for these interesting findings.