First of all, pick the number of times a week that you would like to eat chocolate. Multiply this number by 2...

This is the section of stemNRICH devoted to the advanced applied mathematics underlying the study of the sciences at higher levels

bioNRICH is the area of the stemNRICH site devoted to the mathematics underlying the study of the biological sciences, designed to help develop the mathematics required to get the most from your. . . .

In this article for teachers, Alan Parr looks at ways that mathematics teaching and learning can start from the useful and interesting things can we do with the subject, including. . . .

PhysNRICH is the area of the StemNRICH site devoted to the mathematics underlying the study of physics

See how differential equations might be used to make a realistic model of a system containing predators and their prey.

Why MUST these statistical statements probably be at least a little bit wrong?

Two buses leave at the same time from two towns Shipton and Veston on the same long road, travelling towards each other. At each mile along the road are milestones. The buses' speeds are constant. . . .

In four years 2001 to 2004 Arsenal have been drawn against Chelsea in the FA cup and have beaten Chelsea every time. What was the probability of this? Lots of fractions in the calculations!

Chris is enjoying a swim but needs to get back for lunch. If she can swim at 3 m/s and run at 7m/sec, how far along the bank should she land in order to get back as quickly as possible?

A car is travelling along a dual carriageway at constant speed. Every 3 minutes a bus passes going in the opposite direction, while every 6 minutes a bus passes the car travelling in the same. . . .

How many eggs should a bird lay to maximise the number of chicks that will hatch? An introduction to optimisation.

Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.

Sixth in our series of problems on population dynamics for advanced students.

Fifth in our series of problems on population dynamics for advanced students.

An advanced mathematical exploration supporting our series of articles on population dynamics for advanced students.

This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.

Fourth in our series of problems on population dynamics for advanced students.

Third in our series of problems on population dynamics for advanced students.

This problem opens a major sequence of activities on the mathematics of population dynamics for advanced students.

Invent scenarios which would give rise to these probability density functions.

An advanced mathematical exploration supporting our series of articles on population dynamics for advanced students.

First in our series of problems on population dynamics for advanced students.

Second in our series of problems on population dynamics for advanced students.

Given the graph of a supply network and the maximum capacity for flow in each section find the maximum flow across the network.

How do you write a computer program that creates the illusion of stretching elastic bands between pegs of a Geoboard? The answer contains some surprising mathematics.

Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information.

A player has probability 0.4 of winning a single game. What is his probability of winning a 'best of 15 games' tournament?

Edward Wallace based his A Level Statistics Project on The Mean Game. Each picks 2 numbers. The winner is the player who picks a number closest to the mean of all the numbers picked.

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

At Holborn underground station there is a very long escalator. Two people are in a hurry and so climb the escalator as it is moving upwards, thus adding their speed to that of the moving steps. . . .

Bricks are 20cm long and 10cm high. How high could an arch be built without mortar on a flat horizontal surface, to overhang by 1 metre? How big an overhang is it possible to make like this?

The third installment in our series on the shape of astronomical systems, this article explores galaxies and the universe beyond our solar system.

The probability that a passenger books a flight and does not turn up is 0.05. For an aeroplane with 400 seats how many tickets can be sold so that only 1% of flights are over-booked?

The builders have dug a hole in the ground to be filled with concrete for the foundations of our garage. How many cubic metres of ready-mix concrete should the builders order to fill this hole to. . . .

The shortest path between any two points on a snooker table is the straight line between them but what if the ball must bounce off one wall, or 2 walls, or 3 walls?

This is about a fiendishly difficult jigsaw and how to solve it using a computer program.

This article for students introduces the idea of naming knots using numbers. You'll need some paper and something to write with handy!

At what positions and speeds can the bomb be dropped to destroy the dam?

A brief video explaining the idea of a mathematical knot.

Two cyclists, practising on a track, pass each other at the starting line and go at constant speeds... Can you find lap times that are such that the cyclists will meet exactly half way round the. . . .

If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.

Your school has been left a million pounds in the will of an ex- pupil. What model of investment and spending would you use in order to ensure the best return on the money?

Simple models which help us to investigate how epidemics grow and die out.

Formulate and investigate a simple mathematical model for the design of a table mat.

How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?

You have two bags, four red balls and four white balls. You must put all the balls in the bags although you are allowed to have one bag empty. How should you distribute the balls between the two. . . .

Explain why, when moving heavy objects on rollers, the object moves twice as fast as the rollers. Try a similar experiment yourself.