### Keeping it Safe and Quiet

##### Stage: 2, 3, 4 and 5

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

### Sums of Powers - A Festive Story

##### Stage: 3 and 4

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

### The Best Card Trick?

##### Stage: 3 and 4 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?

### Ding Dong Bell

##### Stage: 3, 4 and 5

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.

### Tournament Scheduling

##### Stage: 3, 4 and 5

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

### The Random World

##### Stage: 3, 4 and 5

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.

##### Stage: 3, 4 and 5

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.

### Mouhefanggai

##### Stage: 4

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.

### Whole Number Dynamics I

##### Stage: 4 and 5

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

### The Chinese Remainder Theorem

##### Stage: 4 and 5

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."

##### Stage: 4 and 5

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.

### Some Circuits in Graph or Network Theory

##### Stage: 4 and 5

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

### Euler's Formula

##### Stage: 5

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.

### Mathematics in the Financial Markets

##### Stage: 5

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.

### Where Do We Get Our Feet Wet?

##### Stage: 5

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

### Infinite Continued Fractions

##### Stage: 5

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

### The Use of Mathematics in Computer Games

##### Stage: 5

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

### Proofs with Pictures

##### Stage: 5

Some diagrammatic 'proofs' of algebraic identities and inequalities.

### Conic Sections

##### Stage: 5

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.

### How Many Geometries Are There?

##### Stage: 5

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

### Approximations, Euclid's Algorithm & Continued Fractions

##### Stage: 5

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