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.

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.

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

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

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

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.

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 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?

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.

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?

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

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?

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?

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

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

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.

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

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

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

How many models can you find which obey these rules?

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

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?

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

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?

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. . . .

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?

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?

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

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

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?

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

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

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.

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.

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

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?

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

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.

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