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Find $S_r = 1^r + 2^r + 3^r + ... + n^r$ where r is any fixed positive integer in terms of $S_1, S_2, ... S_{r-1}$.

A circle is inscribed in an equilateral triangle. Smaller circles touch it and the sides of the triangle, the process continuing indefinitely. What is the sum of the areas of all the circles?

This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.

I start my journey in Rio de Janeiro and visit all the cities as Hamilton described, passing through Canberra before Madrid, and then returning to Rio. What route could I have taken?

Can you sort numbers into sets? Can you give each set a name?

This train line has two tracks which cross at different points. Can you find all the routes that end at Cheston?

Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?

Can you fill in the empty boxes in the grid with the right shape and colour?

Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?

During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?