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

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

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

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

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.

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

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

Investigate circuits and record your findings in this simple introduction to truth tables and logic.

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

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!

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. . . .

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

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

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

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

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. . . .

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

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

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

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

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

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

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

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

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.

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. . . .

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

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

A brief video explaining the idea of a mathematical knot.

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.

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. . . .

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

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.

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

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. . . .

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

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

Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and fill in the blanks in truth tables to record. . . .

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

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

See how the motion of the simple pendulum is not-so-simple after all.

Work in groups to try to create the best approximations to these physical quantities.

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

Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?

How do scores on dice and factors of polynomials relate to each other?