Stage: Challenge Level: 
Many exceptional young mathematicians are involved with the Mathematical Olympiads and Maths Challenges, and there is a vibrant community on the Ask NRICH pages to discuss the issues that arise with these problems and the training for these events. For those unfamiliar with Ask NRICH, it is an online mathematics discussion board where school students can post questions and receive advice on how to solve their mathematical problems. The feel of the board is very much about helping students to learn how to work through the mathematics themselves, rather than giving out solutions. This style of learning is ideal for Olympiad Training, and there is usually a vibrant set of threads concerning BMO1 itself.
However, NRICH is more than an online discussion forum: the main NRICH website contains thousands of mathematical problems on all aspects of mathematics for ages 5 to 19. The NRICH staff spends a good deal of time inventing fascinating, engaging, rich mathematical tasks. The new problems appear on the website each month, and the older problems are all available through the search facilities.
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 our suggestions, along with some information about and guidance on NRICH problems.
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, so you can extend the type of thinking so enjoyable in Olympiad problems to other areas of mathematical activity which you might be 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. You might find that these are an
interesting source of discussion on Ask NRICH!
If you want to get straight into the three star material, you might want to look at some of these problems, 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
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. Where these
differ from typical articles on the web is that they include
activities and problems for you to try as you read through
them and 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.
Logic, Truth Tables and Switching Circuits Challenge
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 pages!
Learning mathematics. Questioning. Assessment. Rich Tasks. Problem solving. Pedagogy. Mathematical Thinking. Able learners. biology. Enrichment.
Published .
Copyright © 2007. University of Cambridge. All rights reserved.
NRICH is part of the family of activities in the Millennium Mathematics Project, which also includes the Plus and Motivate sites.
email: nrich@damtp.cam.ac.uk
