
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?
An introduction to Ian Stewart's RI Christmas Lectures on Mathematics and Nature with investigations and activities on mathematical patterns in cosmology, music, snowflakes, and flowers, animal. . . .
Investigations and activities for you to enjoy on pattern in nature.
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.
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.
Scheduling games is a little more challenging than one might desire. Here are some tournament formats that sport schedulers use.
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.
For teachers. Yet more school maths from long ago-interest and percentages.
Jenny Murray describes the mathematical processes behind making patchwork in this article for students.

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 efficiently can various flat shapes be fitted together?

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
This article explains how credit card numbers are defined and the check digit serves to verify their accuracy.

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?