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.

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.

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

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.

Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?

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?

A Sudoku with clues given as sums of entries.

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?

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.

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

Find out what a "fault-free" rectangle is and try to make some of your own.

There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.

Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.

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 work out how to balance this equaliser? You can put more than one weight on a hook.

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?

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

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

This challenge is about finding the difference between numbers which have the same tens digit.

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

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

What could the half time scores have been in these Olympic hockey matches?

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

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

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

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

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?

How many different triangles can you make on a circular pegboard that has nine pegs?

A package contains a set of resources designed to develop students’ mathematical thinking. This package places a particular emphasis on “being systematic” and is designed to meet. . . .

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

How many different rhythms can you make by putting two drums on the wheel?

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?

Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?

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!

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?

Can you find all the different ways of lining up these Cuisenaire rods?