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
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.