problem
The best card trick?
Age
11 to 16
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?
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Tournament scheduling
Scheduling games is a little more challenging than one might desire. Here are some tournament formats that sport schedulers use.
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Divisibility tests
This article explains various divisibility rules and why they work. An article to read with pencil and paper handy.
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All about infinity
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.
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Ding dong bell
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.
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The random world
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.
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Mouhefanggai
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.
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Some circuits in graph or network theory
Eulerian and Hamiltonian circuits are defined with some simple examples and a couple of puzzles to illustrate Hamiltonian circuits.
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Whole number dynamics I
The first of five articles concentrating on whole number dynamics, ideas of general dynamical systems are introduced and seen in concrete cases.
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Sums of powers - a festive story
A story for students about adding powers of integers - with a festive twist.
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Links and knots
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.
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The Chinese remainder theorem
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."
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Keeping it safe and quiet
Simon Singh describes PKC, its origins, and why the science of code making and breaking is such a secret occupation.
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Approximations, Euclid's algorithm and continued fractions
This article sets some puzzles and describes how Euclid's algorithm and continued fractions are related.
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Mathematics in the financial markets
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.
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Infinite continued fractions
In this article we are going to look at infinite continued
fractions - continued fractions that do not terminate.
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Conic sections
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.
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Public key cryptography
An introduction to coding and decoding messages and the maths behind how to secretly share information.
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What are complex numbers?
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.
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Euler's formula
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.
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Where do we get our feet wet?
Professor Korner has generously supported school mathematics for more than 30 years and has been a good friend to NRICH since it started.
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Fractional calculus I
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.
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The use of mathematics in computer games
An account of how mathematics is used in computer games including
geometry, vectors, transformations, 3D graphics, graph theory and
simulations.
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The why and how of substitution
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.
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How many geometries are there?
An account of how axioms underpin geometry and how by changing one axiom we get an entirely different geometry.