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.
First of all, pick the number of times a week that you would like
to eat chocolate. Multiply this number by 2...
Bricks are 20cm long and 10cm high. How high could an arch be built
without mortar on a flat horizontal surface, to overhang by 1
metre? How big an overhang is it possible to make like this?
If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Two cyclists, practising on a track, pass each other at the starting line and go at constant speeds... Can you find lap times that are such that the cyclists will meet exactly half way round the. . . .
Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and fill in the blanks in truth tables to record. . . .
Edward Wallace based his A Level Statistics Project on The Mean
Game. Each picks 2 numbers. The winner is the player who picks a
number closest to the mean of all the numbers picked.
Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.
Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and record your findings in truth tables.
This article for students introduces the idea of naming knots using numbers. You'll need some paper and something to write with handy!
A brief video explaining the idea of a mathematical knot.
Explain why, when moving heavy objects on rollers, the object moves
twice as fast as the rollers. Try a similar experiment yourself.
bioNRICH is the area of the stemNRICH site devoted to the
mathematics underlying the study of the biological sciences,
designed to help develop the mathematics required to get the most
from your. . . .
In this article for teachers, Alan Parr looks at ways that
mathematics teaching and learning can start from the useful and
interesting things can we do with the subject, including. . . .
PhysNRICH is the area of the StemNRICH site devoted to the mathematics underlying the study of physics
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
This is the section of stemNRICH devoted to the advanced applied
mathematics underlying the study of the sciences at higher levels
Use the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.
Explore the transformations and comment on what you find.
How do these modelling assumption affect the solutions?
Why MUST these statistical statements probably be at least a little
See how differential equations might be used to make a realistic
model of a system containing predators and their prey.
Invent scenarios which would give rise to these probability density functions.
An advanced mathematical exploration supporting our series of articles on population dynamics for advanced students.
First in our series of problems on population dynamics for advanced students.
Second in our series of problems on population dynamics for advanced students.
Third in our series of problems on population dynamics for advanced students.
This problem opens a major sequence of activities on the mathematics of population dynamics for advanced students.
A car is travelling along a dual carriageway at constant speed. Every 3 minutes a bus passes going in the opposite direction, while every 6 minutes a bus passes the car travelling in the same. . . .
Sixth in our series of problems on population dynamics for advanced students.
Fifth in our series of problems on population dynamics for advanced students.
Fourth in our series of problems on population dynamics for advanced students.
How do you write a computer program that creates the illusion of stretching elastic bands between pegs of a Geoboard? The answer contains some surprising mathematics.
The third installment in our series on the shape of astronomical systems, this article explores galaxies and the universe beyond our solar system.
The probability that a passenger books a flight and does not turn
up is 0.05. For an aeroplane with 400 seats how many tickets can be
sold so that only 1% of flights are over-booked?
To win on a scratch card you have to uncover three numbers that add
up to more than fifteen. What is the probability of winning a
An account of how mathematics is used in computer games including
geometry, vectors, transformations, 3D graphics, graph theory and
This is about a fiendishly difficult jigsaw and how to solve it
using a computer program.
The builders have dug a hole in the ground to be filled with concrete for the foundations of our garage. How many cubic metres of ready-mix concrete should the builders order to fill this hole to. . . .
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
The shortest path between any two points on a snooker table is the straight line between them but what if the ball must bounce off one wall, or 2 walls, or 3 walls?
Your school has been left a million pounds in the will of an ex-
pupil. What model of investment and spending would you use in order
to ensure the best return on the money?
A player has probability 0.4 of winning a single game. What is his
probability of winning a 'best of 15 games' tournament?
You have two bags, four red balls and four white balls. You must
put all the balls in the bags although you are allowed to have one
bag empty. How should you distribute the balls between the two. . . .
At Holborn underground station there is a very long escalator. Two
people are in a hurry and so climb the escalator as it is moving
upwards, thus adding their speed to that of the moving steps. . . .
It is possible to identify a particular card out of a pack of 15
with the use of some mathematical reasoning. What is this reasoning
and can it be applied to other numbers of cards?
At what positions and speeds can the bomb be dropped to destroy the
Chris is enjoying a swim but needs to get back for lunch. If she can swim at 3 m/s and run at 7m/sec, how far along the bank should she land in order to get back as quickly as possible?