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?!

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?

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.

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

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?

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.

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

A Sudoku with clues given as sums of entries.

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.

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

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?

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.

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?

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

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?

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

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?

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

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

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.

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

This challenge extends the Plants investigation so now four or more children are involved.

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

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

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

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

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

How many trains can you make which are the same length as Matt's, using rods that are identical?

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

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

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. . . .

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

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 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.

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

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?

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?

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

Try out the lottery that is played in a far-away land. What is the chance of winning?

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

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

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

Try this matching game which will help you recognise different ways of saying the same time interval.

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?