Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?
Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?
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?
The problem is 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.
Analysis of this problem is fascinating because it draws together a heady mix of theoretical and numerical probability along with estimates and approximations.
Go to last month's problems to see more solutions.
This article discusses what happens, and why, if you generate chains of sequences getting the next sequence from the differences between the adjacent terms in the sequence before it, eg (7, 2, 8, 3) maps to (5, 6, 5, 4).
These models have appeared around the Centre for Mathematical Sciences. Perhaps you would like to try to make some similar models of your own.