This article explains various divisibility rules and why they work. An article to read with pencil and paper handy.

Challenge Level

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?

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

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.

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.

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.

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."

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

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.

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.

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

Some diagrammatic 'proofs' of algebraic identities and inequalities.

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

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

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.

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

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.

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

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.

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