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.

Bilbo goes on an adventure, before arriving back home. Using the information given about his journey, can you work out where Bilbo lives?

A simple method of defining the coefficients in the equations of chemical reactions with the help of a system of linear algebraic equations.

There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.

How can people be divided into groups fairly for events in the Paralympics, for school sports days, or for subject sets?

Scientist Bryan Rickett has a vision of the future - and it is one in which self-parking cars prowl the tarmac plains, hunting down suitable parking spots and manoeuvring elegantly into them.

How do decisions about scoring affect who wins a combined event such as the decathlon?

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

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

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. . . .

Jenny Murray describes the mathematical processes behind making patchwork in this article for students.

Noticing the regular movement of the Sun and the stars has led to a desire to measure time. This article for teachers and learners looks at the history of man's need to measure things.

Use the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.

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

From the information you are asked to work out where the picture was taken. Is there too much information? How accurate can your answer be?

Is it really greener to go on the bus, or to buy local?

Can Jo make a gym bag for her trainers from the piece of fabric she has?

What shape would fit your pens and pencils best? How can you make it?

Design and construct a prototype intercooler which will satisfy agreed quality control constraints.

For teachers. Yet more school maths from long ago-interest and percentages.

Build a scaffold out of drinking-straws to support a cup of water

This article explains how credit card numbers are defined and the check digit serves to verify their accuracy.

Can you deduce which Olympic athletics events are represented by the graphs?

Can you sketch graphs to show how the height of water changes in different containers as they are filled?

In this article, Alan Parr shares his experiences of the motivating effect sport can have on the learning of mathematics.

As part of Liverpool08 European Capital of Culture there were a huge number of events and displays. One of the art installations was called "Turning the Place Over". Can you find our how it works?

How does the time of dawn and dusk vary? What about the Moon, how does that change from night to night? Is the Sun always the same? Gather data to help you explore these questions.

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?