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Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects its speed at each stage.

Starting with two basic vector steps, which destinations can you reach on a vector walk?

Invent a scoring system for a 'guess the weight' competition.

When two closely matched teams play each other, what is the most likely result?

Which of these games would you play to give yourself the best possible chance of winning a prize?

Can you work out the means of these distributions using numerical methods?

What will happen when you switch on these circular circuits?

It is believed that weaker snooker players have a better chance of winning matches over eleven frames (i.e. first to win 6 frames) than they do over fifteen frames. Is this true?

A quadrilateral changes shape with the edge lengths constant. Show the scalar product of the diagonals is constant. If the diagonals are perpendicular in one position are they always perpendicular?

Which is the bigger, 9^10 or 10^9 ? Which is the bigger, 99^100 or 100^99 ?