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

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.

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.

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?

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?

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. . . .

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

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

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

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

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

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

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. . . .

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

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

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.

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

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

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

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.

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

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.

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?

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

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

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

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.

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