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
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:
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
If you are nearing university, you might look at the collections of problems in the Prepare for University
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
Chinese Remainder Theorem
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!