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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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It is possible to dissect any square into smaller squares. What is the minimum number of squares a 13 by 13 square can be dissected into?

Colourful Cube

Stage: 3 Challenge Level: Challenge Level:1

This cube is made up from $3\times 3\times 3$ little cubes whose faces are either all red or all yellow. 


The views from all sides of the cube look like this, and the little cube in the centre is red.

How many little red cubes are used in total? How many little yellow cubes are used?

Suppose the other views of the cube do not necessarily look like this, and the little cube in the centre is not necessarily red.

What is the most and least number of little red cubes that could be used? 

With thanks to Don Steward, whose ideas formed the basis of this problem.