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 prize?

First of all, pick the number of times a week that you would like to eat chocolate. Multiply this number by 2...

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.

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?

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?

Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.

This article explains the concepts involved in scientific mathematical computing. It will be very useful and interesting to anyone interested in computer programming or mathematics.

Explain why, when moving heavy objects on rollers, the object moves twice as fast as the rollers. Try a similar experiment yourself.

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?

Can you find the lap times of the two cyclists travelling at constant speeds?

A ladder 3m long rests against a wall with one end a short distance from its base. Between the wall and the base of a ladder is a garden storage box 1m tall and 1m high. What is the maximum distance. . . .

Mike and Monisha meet at the race track, which is 400m round. Just to make a point, Mike runs anticlockwise whilst Monisha runs clockwise. Where will they meet on their way around and will they ever. . . .

Given the graph of a supply network and the maximum capacity for flow in each section find the maximum flow across the network.

This article explores ths history of theories about the shape of our planet. It is the first in a series of articles looking at the significance of geometric shapes in the history of astronomy.

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. . . .

Investigate circuits and record your findings in this simple introduction to truth tables and logic.

Explore the transformations and comment on what you find.

The second in a series of articles on visualising and modelling shapes in the history of astronomy.

How do scores on dice and factors of polynomials relate to each other?

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. . . .

An account of how mathematics is used in computer games including geometry, vectors, transformations, 3D graphics, graph theory and simulations.

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.

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. . . .

A player has probability 0.4 of winning a single game. What is his probability of winning a 'best of 15 games' tournament?

PhysNRICH is the area of the StemNRICH site devoted to the mathematics underlying the study of physics

This is the section of stemNRICH devoted to the advanced applied mathematics underlying the study of the sciences at higher levels

The third installment in our series on the shape of astronomical systems, this article explores galaxies and the universe beyond our solar system.

This article for students introduces the idea of naming knots using numbers. You'll need some paper and something to write with handy!

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. . . .

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. . . .

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?

This problem opens a major sequence of activities on the mathematics of population dynamics for advanced students.

How many eggs should a bird lay to maximise the number of chicks that will hatch? An introduction to optimisation.

Formulate and investigate a simple mathematical model for the design of a table mat.

Invent scenarios which would give rise to these probability density functions.

Simple models which help us to investigate how epidemics grow and die out.

This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.

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.

An advanced mathematical exploration supporting our series of articles on population dynamics for advanced students.

Third in our series of problems on population dynamics for advanced students.

Fourth in our series of problems on population dynamics for advanced students.

Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?

Fifth in our series of problems on population dynamics for advanced students.

Sixth in our series of problems on population dynamics for advanced students.

Second in our series of problems on population dynamics for advanced students.

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. . . .

See how the motion of the simple pendulum is not-so-simple after all.

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.