If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?

Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.

Four children were sharing a set of twenty-four butterfly cards. Are there any cards they all want? Are there any that none of them want?

There are ten children in Becky's group. Can you find a set of numbers for each of them? Are there any other sets?

Can you arrange these numbers into 7 subsets, each of three numbers, so that when the numbers in each are added together, they make seven consecutive numbers?

Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?

Can you find the values at the vertices when you know the values on the edges?

It is possible to identify a particular card out of a pack of 15 with the use of some mathematical reasoning. What is this reasoning and can it be applied to other numbers of cards?

Discover a handy way to describe reorderings and solve our anagram in the process.

The binary operation * for combining sets is defined as the union of two sets minus their intersection. Prove the set of all subsets of a set S together with the binary operation * forms a group.

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.

Show that the infinite set of finite (or terminating) binary sequences can be written as an ordered list whereas the infinite set of all infinite binary sequences cannot.

Sydney discovered that this problem was really about factors and multiples. Perhaps you can help find the last solutions?

Pupils in Mrs Simmons' Maths class drew some very clear diagrams to help them find the solution to this problem.

Yanqing from Devonport High School for Girls sent us a very clear explanation of her solution to this problem.

Curt from Reigate College explains very well why this graph has a symmetrical pitchfork shape.

Take it in turns to place a domino on the grid. One to be placed horizontally and the other vertically. Can you make it impossible for your opponent to play?

Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.

Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?

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