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.

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

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. . . .

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. . . .

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

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

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

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.

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

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.

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

It is possible to identify a particular card out of a pack of 15 with the use of some mathematical reasoning. What is this reasoning and can it be applied to other numbers of cards?

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

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

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

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.

Second 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.

A brief video explaining the idea of a mathematical knot.

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

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. . . .

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

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

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

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

engNRICH is the area of the stemNRICH Advanced site devoted to the mathematics underlying the study of engineering

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

Look at the calculus behind the simple act of a car going over a step.

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

This article explains the concepts involved in scientific mathematical computing. It will be very useful and interesting to anyone interested in computer programming or mathematics.

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

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

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. . . .

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

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

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

This problem opens a major sequence of activities on the mathematics of 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.

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. . . .

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

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

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.

To win on a scratch card you have to uncover three numbers that add up to more than fifteen. What is the probability of winning a prize?

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

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?

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

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

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?