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.

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

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

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

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

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

This task looks at the different turns involved in different Olympic sports as a way of exploring the mathematics of turns and angles.

What is the same and what is different about these tiling patterns and how do they contribute to the floor as a whole?

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?

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?

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.

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

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

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

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.

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

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

Design your own scoring system and play Trumps with these Olympic Sport cards.

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

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.

This is a collection of mathematical activities linked to the Football World Cup 2006. These activities can easily be updated for another football event or could be the inspiration for. . . .

This activity challenges you to decide on the 'best' number to use in each statement. You may need to do some estimating, some calculating and some research.

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

Can you put these times on the clocks in order? You might like to arrange them in a circle.

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

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