Photocopiers can reduce from A3 to A4 without distorting the image. Explore the relationships between different paper sizes that make this possible.
Take three whole numbers. The differences between them give you three new numbers. Find the differences between the new numbers and keep repeating this. What happens?
Can you devise a fair scoring system when dice land edge-up or corner-up?
How did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?
Use cunning to work out a strategy to win this game.