Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?

This article takes the reader through divisibility tests and how they work. An article to read with pencil and paper to hand.

Scheduling games is a little more challenging than one might desire. Here are some tournament formats that sport schedulers use.

Think that a coin toss is 50-50 heads or tails? Read on to appreciate the ever-changing and random nature of the world in which we live.

The reader is invited to investigate changes (or permutations) in the ringing of church bells, illustrated by braid diagrams showing the order in which the bells are rung.

Infinity is not a number, and trying to treat it as one tends to be a pretty bad idea. At best you're likely to come away with a headache, at worse the firm belief that 1 = 0. This article discusses the different types of infinity.

Imagine two identical cylindrical pipes meeting at right angles and think about the shape of the space which belongs to both pipes. Early Chinese mathematicians call this shape the mouhefanggai.

A story for students about adding powers of integers - with a festive twist.

In this article we shall consider how to solve problems such as "Find all integers that leave a remainder of 1 when divided by 2, 3, and 5."

Some diagrammatic 'proofs' of algebraic identities and inequalities.

The first of five articles concentrating on whole number dynamics, ideas of general dynamical systems are introduced and seen in concrete cases.

Eulerian and Hamiltonian circuits are defined with some simple examples and a couple of puzzles to illustrate Hamiltonian circuits.

Simon Singh describes PKC, its origins, and why the science of code making and breaking is such a secret occupation.

Some puzzles requiring no knowledge of knot theory, just a careful inspection of the patterns. A glimpse of the classification of knots, prime knots, crossing numbers and knot arithmetic.

You can differentiate and integrate n times but what if n is not a whole number? This generalisation of calculus was introduced and discussed on askNRICH by some school students.

In this article we are going to look at infinite continued fractions - continued fractions that do not terminate.

An account of how mathematics is used in computer games including geometry, vectors, transformations, 3D graphics, graph theory and simulations.

The interplay between the two and three dimensional Euclidean geometry of conic sections is explored in this article. Suitable for students from 16+, teachers and parents.

An account of how axioms underpin geometry and how by changing one axiom we get an entirely different geometry.

An introduction to the ideas of public key cryptography using small numbers to explain the process. In practice the numbers used are too large to factorise in a reasonable time.

Step back and reflect! This article reviews techniques such as substitution and change of coordinates which enable us to exploit underlying structures to crack problems.

This article sets some puzzles and describes how Euclid's algorithm and continued fractions are related.

This article introduces complex numbers, brings together into one bigger 'picture' some closely related elementary ideas like vectors and the exponential and trigonometric functions and their derivatives and proves that e^(i pi)= -1.

Professor Korner has generously supported school mathematics for more than 30 years and has been a good friend to NRICH since it started.

Financial markets mean the business of trading risk. The article describes in simple terms what is involved in this trading, the work people do and the figures for starting salaries.

Some simple ideas about graph theory with a discussion of a proof of Euler's formula relating the numbers of vertces, edges and faces of a graph.