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.

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

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

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.

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 challenging activity focusing on finding all possible ways of stacking rods.

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.

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.

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?

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.

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

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 models can you find which obey these rules?

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?

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

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?

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

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

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

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

This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.

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.

Use the clues about the symmetrical properties of these letters to place them on the grid.

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

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

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

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....?

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

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.

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?

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.

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

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

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

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?

Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?

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?

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

Can you find all the different triangles on these peg boards, and find their angles?

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

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

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 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. . . .

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?

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

This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.

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