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### Number and algebra

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# Reach 100

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### Pebbles

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### Sweets in a Box

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Age 7 to 11

Challenge Level

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Simply writing out the numbers $1 - 9$ along the top of your paper can be a great help.

Imagine arranging your four two-digit numbers in columns to do the addition sum, like this:

$5 \: 2$

$1 \; 9$

$5 \; 1$

$2 \; 9$

If the total has to be $100$, think about how the four digits you choose could add to make the $0$ in the units column, then look at the tens column.

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?

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?