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
Go to last month's problems to see more solutions.
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?