NRICH and Olympiads

Age 14 to 18

Many exceptional young mathematicians are involved with the Mathematical Olympiads and Maths Challenges. A successful mathematical Olympian will undoubtedly be an expert mathematical problem solver. We are often asked to suggest suitable problems for these students to try from the NRICH website: this page contains some suggestions.

The NRICH website contains thousands of mathematical problems on all aspects of mathematics for ages 5 to 19. The NRICH team spends a good deal of time inventing fascinating, engaging, rich mathematical tasks. A typical NRICH problem will provide scope for exploration, investigation and extension: in short, plenty of mathematical ideas for the gifted young mathematician to get stuck into.

Some of our material is very similar in content to Olympiad questions, but NRICH problems cover the whole range of mathematical activity. This means that you can extend the type of thinking you have found enjoyable in Olympiad problems to other areas of mathematical activity that you are interested in, or studying at school.

The best way to get a feel for the rich set of offerings from the main NRICH site is to try a few problems. Here is a list of great starting points.

Problems to try

There are many, many problems for you to try. One way forward is to type a topic into the 'Search NRICH' box at the top of the page and see what comes up. Our problems have a 'Stage' rating (stage 3 is about 11 to 14, stage 4 is about 14-16, stage 5 is about 16-18) and a 'Difficulty rating' from 1 to 3 stars. Although you might be interested in some of our most difficult problems, all of our problems can lead to fascinating and very deep mathematical thinking. (If you don't believe us, try out some of the stage 2 problems, and ask yourself the question 'What if?' from time to time!)

To begin with, you might try looking at our best selection of NRICH starter problems. It is good to be creative and thoughtful about these problems and follow the questions which naturally arise in their solution. 

If you want to get straight into the three star material, you might want to look at some of the following, which are in no particular order:

Modular Fractions

Twisty Logic

Ford Circles

Bicentric Quadrilaterals

Making More Tracks


Scale Invariance

Cheese Cutting


Drug Stabiliser


Don't forget that many of the problems lead to other problems. The 'Tag Clouds' at the foot of the page will be a useful guide.

Science and Applied Mathematics

There are dozens of fascinating areas of mathematics in the wider sense and many past Olympians have gone on to careers in applied mathematics, the sciences or computing. You could see what drew them by looking at the fascinating, and often very challenging, scientific and applied mathematics problems on the stemNRICH pages.

If you are nearing university, you might look at the collections of problems in the Prepare for University section.

Things to read

NRICH has plenty of articles on mathematics. These differ from typical articles on the web because they often include activities and problems for you to try as you read through them. They usually have associated problems on the NRICH website.

These 6 introductory articles are particularly well suited to the sort of mathematics encountered on Olympiad problems

Introduction to Number Theory

Modular Arithmetic

Chinese Remainder Theorem

Mathematical Induction

Euler's Formula

Euclid's Algorithm I

These articles offer some other fascinating insights into mathematics. They all contain mathematical things to try and naturally lead into problems on the main NRICH site.

Some circuits in graph or network theory

The four colour theorem

An Introduction to Complex Numbers

Approximations, Euclid's Algorithm & Continued Fractions

Whole Number Dynamics I

This page scratches the surface of the NRICH offering. We hope that you find many hours of stimulating mathematical activity on our site!