Find out about Magic Squares in this article written for students. Why are they magic?!

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

Different combinations of the weights available allow you to make different totals. Which totals can you make?

Use the interactivity to play two of the bells in a pattern. How do you know when it is your turn to ring, and how do you know which bell to ring?

What happens when you round these numbers to the nearest whole number?

How many solutions can you find to this sum? Each of the different letters stands for a different number.

What happens when you round these three-digit numbers to the nearest 100?

Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.

Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?

You have been given nine weights, one of which is slightly heavier than the rest. Can you work out which weight is heavier in just two weighings of the balance?

Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.

An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.

This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.

An investigation that gives you the opportunity to make and justify predictions.

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?

Find the values of the nine letters in the sum: FOOT + BALL = GAME

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

Using the statements, can you work out how many of each type of rabbit there are in these pens?

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

Can you replace the letters with numbers? Is there only one solution in each case?

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

This Sudoku, based on differences. Using the one clue number can you find the solution?

Can you work out some different ways to balance this equation?

Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.

Have a go at balancing this equation. Can you find different ways of doing it?

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.

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?