Four jewellers share their stock. Can you work out the relative values of their gems?

Is there an efficient way to work out how many factors a large number has?

Take an equilateral triangle and cut it into smaller pieces. What can you do with them?

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

Drawing the right diagram can help you to prove a result about the angles in a line of squares.

Can you work out how these polygon pictures were drawn, and use that to figure out their angles?

Which countries have the most naturally athletic populations?

Can you make sense of the charts and diagrams that are created and used by sports competitors, trainers and statisticians?

99% of people who have measles have spots. Ben has spots. Do you think he has measles?

I'd be very surprised if I had three children all with the same birthday, but I read in the paper that it happened to one family...

In 1% of cases, an HIV test gives a positive result for someone who is HIV negative. How likely is it that someone who tests positive has HIV?

Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?

Are you at risk of being a victim of crime? How does your perception of that risk compare with the facts and figures?

Can you match the cards and figure out whether the tabloid headlines can be trusted?

Can you explain what is going on in these puzzling number tricks?

Where should you start, if you want to finish back where you started?

DNA profiling is an invaluable tool for the police. However, when it comes to probability, things aren't always as straightforward as they seem.