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### Number and algebra

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# Cycling Squares

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### Pebbles

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### Sweets in a Box

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Age 7 to 11

Challenge Level

In the circle of numbers below each adjoining pair adds to make a square number:

For example,

$14 + 2 = 16, 2 + 7 = 9, 7 + 9 = 16$

and so on.

Can you make a similar - but larger - cycle of pairs that each add to make a square number, using all the numbers in the box below, once and once only?

You might find it helpful to print off and cut up these cards of the numbers so you can move them around to try out your ideas.

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?