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

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.

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

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

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

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

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?

If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?

A Sudoku with clues given as sums of entries.

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

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?

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

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

Investigate the different ways you could split up these rooms so that you have double the number.

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

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

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?

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

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.

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. . . .

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?

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

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

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?

How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?

In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

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?

A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?

Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

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

Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?

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?

I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?

An activity making various patterns with 2 x 1 rectangular tiles.

Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.

George and Jim want to buy a chocolate bar. George needs 2p more and Jim need 50p more to buy it. How much is the chocolate bar?

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

Use these head, body and leg pieces to make Robot Monsters which are different heights.

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

In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?

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

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.