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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?

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Square Areas

Can you work out the area of the inner square and give an explanation of how you did it?

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Kissing Triangles

Determine the total shaded area of the 'kissing triangles'.

Packing Small Boxes

Age 11 to 14 Short Challenge Level:

A large box measures 1.7 m by 1.2 m by 1.5 m.

It is to be packed with smaller boxes each measuring 15 cm by 20 cm by 20 cm.

What is the greatest number of small boxes that can be fitted into the larger box, assuming that they are all placed in the same orientation?

This problem is taken from the World Mathematics Championships
You can find more short problems, arranged by curriculum topic, in our short problems collection.