Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?
Have you ever tried to work out the largest number that your calculator can cope with? What about your computer? Perhaps you tried using powers to make really large numbers. In this problem you will. . . .
Find the smallest positive integer N such that N/2 is a perfect cube, N/3 is a perfect fifth power and N/5 is a perfect seventh power.
When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?
Can you work out how many apples there are in this fruit bowl if you know what fraction there are?
A bowl of fruit - March 2008
Noticing the regular movement of the Sun and the stars has led to a desire to measure time. This article for teachers and learners looks at the history of man's need to measure things.
In this problem, we define complex numbers and invite you to explore what happens when you add and multiply them.
Complex numbers can be represented graphically using an Argand diagram. This problem explains more...
July 1st 2001 was on a Sunday. July 1st 2002 was on a Monday. When did July 1st fall on a Monday again?
Find the missing coordinates which will form these eight quadrilaterals. These coordinates themselves will then form a shape with rotational and line symmetry.
Can you arrange the shapes in a chain so that each one shares a face (or faces) that are the same shape as the one that follows it?
Imagine you were given the chance to win some money... and imagine you had nothing to lose...
There are two sets of numbers. The second is the result of the first after an increase by a constant percentage. How can you find that percentage if one set of numbers is in code?
My cousin was 24 years old on Friday April 5th in 1974. On what day of the week was she born?
Find the area of the annulus in terms of the length of the chord which is tangent to the inner circle.
Explore the voltages and currents in this interesting circuit configuration.
In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?
There are six more girls than boys in Miss Spelling's class of 24 pupils. What is the ratio of girls to boys in the class?
Can you massage the parameters of these curves to make them match as closely as possible?
Discover how Heron of Alexandria missed his chance to explore the unknown mathematical land of complex numbers.
This follows up the 'magic Squares for Special Occasions' article which tells you you to create a 4by4 magicsquare with a special date on the top line using no negative numbers and no repeats.
Take the number 6 469 693 230 and divide it by the first ten prime numbers and you'll find the most beautiful, most magic of all numbers. What is it?
Read about the problem that tickled Euler's curiosity and led to a new branch of mathematics!
Anyone should be able to make a start on any of these resources. They are our favourites because they really get you thinking mathematically.
Grandpa was measuring a rug using yards, feet and inches. Can you help William to work out its area?
Four fair dice are marked differently on their six faces. Choose first ANY one of them. I can always choose another that will give me a better chance of winning. Investigate.
Explore the properties of this different sort of differential equation.
This task is looking at creating polygons with specific lengths. Also, there's a chance to explore symmetry.
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
Weekly Problem 43 - 2015
Rachel and Ross share a bottle of water. Can you work out how much water Rachel drinks?
Second challenge cipher
Given the products of adjacent cells, can you complete this Sudoku?
Follow the journey taken by this bird and let us know for how long and in what direction it must fly to return to its starting point.
Find curves which have gradients of +1 or -1 at various points
This article, written by Dr. Sue Gifford, evaluates the Early Learning Numbers Goal in England, in the light of research.
This article has lots of useful tips on becoming a skilful problem solver.
Astronomy grew out of problems that the early civilisations had. They needed to solve problems relating to time and distance - both mathematical topics.
Jenni Way describes her visit to a Japanese mathematics classroom.
Follow the mathematical journey of a sixth-former as she spent four weeks working on stemNRICH problems.
This article looks at knight's moves on a chess board and introduces you to the idea of vectors and vector addition.
Can you work out the number of chairs at a cafe from the number of legs?
Pure resources for A Level
Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?
Try to solve this very difficult problem and then study our two suggested solutions. How would you use your knowledge to try to solve variants on the original problem?
This article describes no ordinary maths lesson. There were 24 children, mostly Years 3 and 4, and there were 17 adults working with them - mothers, fathers, one grandmother and two grandfathers, a. . . .
Use the blue spot to help you move the yellow spot from one star to the other. How are the trails of the blue and yellow spots related?
What is the mean of this set of numbers?
Can you number the vertices, edges and faces of a tetrahedron so that the number on each edge is the mean of the numbers on the adjacent vertices and the mean of the numbers on the adjacent faces?
A simple method of defining the coefficients in the equations of chemical reactions with the help of a system of linear algebraic equations.