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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?

Curious Number

Age 7 to 11 Challenge Level:

Do you know any divisibility rules?
A number is divisible by $3$ if its digits, when added together, are divisible by $3$. For example, take $174: 1 + 7 + 4 = 12$ which is divisible by $3$. You can add it as many times as you want. $12: 1 + 2 = 3$
A number is divisible by $6$ if it is an even number and it is divisible by $3$.
A number is divisible by $4$, if the tens and units form a number which is divisible by $4$, for example $732$ and $9048$ are divisible by $4$ (because $32$ and $48$ are divisible by $4$, but $338$ and $2342$ are not (because $38$ and $42$ are not divisible by $4$). (Why does this work?)
It could be a good idea to make a table to keep track of where the digits $1$ to $6$ could go. 
Where will the even numbers have to go?
So what about the odd numbers?
Where will the $5$ have to go?