Can you find the hidden factors which multiply together to produce each quadratic expression?

Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?

Charlie likes to go for walks around a square park, while Alison likes to cut across diagonally. Can you find relationships between the vectors they walk along?

Play the game of Poison, Antidote, Water to start to understand the mathematics of associativity and groups.

A weekly challenge: these are shorter problems aimed at Post-16 students or enthusiastic younger students.

Can you work out the irrational numbers that belong in the circles to make the multiplication arithmagon correct?

Explore the properties of some groups such as: The set of all real numbers excluding -1 together with the operation x*y = xy + x + y. Find the identity and the inverse of the element x.

Can you work out what simple structures have been dressed up in these advanced mathematical representations?

We received both numerical and algebraic solutions to this problem. Lots of you made a generalisation and there were some clear proofs too.

John Mason describes the thinking behind this month's tasks.

An introduction to the sort of algebra studied at university, focussing on groups.

We think this 3x3 version of the game is often harder than the 5x5 version. Do you agree? If so, why do you think that might be?