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The Egyptians expressed all fractions as the sum of different unit fractions. The Greedy Algorithm might provide us with an efficient way of doing this.

Draw some stars and measure the angles at their points. Can you find and prove a result about their sum?

The farmers want to redraw their field boundary but keep the area the same. Can you advise them?

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

Investigate what happens if we create number patterns using some simple rules.

Jack has nine tiles. He put them together to make a square so that two tiles of the same colour were not beside each other. Can you find another way to do it?

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

Kimie and Sebastian were making sticks from interlocking cubes and lining them up. Can they make their lines the same length? Can they make any other lines?

This problem challenges you to find out how many odd numbers there are between pairs of numbers. Can you find a pair of numbers that has four odds between them?

Find at least one way to put in some operation signs to make these digits come to 100.