How much do you have to turn these dials by in order to unlock the safes?

Can you describe the journey to each of the six places on these maps? How would you turn at each junction?

The triangles in these sets are similar - can you work out the lengths of the sides which have question marks?

Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?

Where will the point stop after it has turned through 30 000 degrees? I took out my calculator and typed 30 000 ÷ 360. How did this help?

Can you explain why it is impossible to construct this triangle?

A dot starts at the point (1,0) and turns anticlockwise. Can you estimate the height of the dot after it has turned through 45 degrees? Can you calculate its height?

Dante, Jack and Jemma all solved this problem. Jamie even sent in a challenge of his own!

A description of how to make the five Platonic solids out of paper.