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?!

A Sudoku with clues given as sums of entries.

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?

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

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.

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.

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.

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

A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.

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?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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?

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

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....?

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

60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?

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?

Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?

Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?

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

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

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

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.

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 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?

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

What happens when you try and fit the triomino pieces into these two grids?

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. . . .

When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

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.

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

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

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

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

How many models can you find which obey these rules?

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

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

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

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?

This dice train has been made using specific rules. How many different trains can you make?

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

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

In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?