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.

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

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.

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.

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.

A Sudoku with clues given as sums of entries.

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?

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

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

In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

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?

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

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

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?

Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

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?

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

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.

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

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

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

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?

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

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?

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

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

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

In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.

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

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?

In this matching game, you have to decide how long different events take.

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

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

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

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

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

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

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?

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?

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

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. . . .