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

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

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.

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

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

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

Imagine that the puzzle pieces of a jigsaw are roughly a rectangular shape and all the same size. How many different puzzle pieces could there be?

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.

You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?

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

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?

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?

My coat has three buttons. How many ways can you find to do up all the buttons?

Lorenzie was packing his bag for a school trip. He packed four shirts and three pairs of pants. "I will be able to have a different outfit each day", he said. How many days will Lorenzie be away?

These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.

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?

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

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.

Can you find out in which order the children are standing in this line?

Moira is late for school. What is the shortest route she can take from the school gates to the entrance?

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

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.

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?

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.

El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?

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?

Using the statements, can you work out how many of each type of rabbit there are in these pens?

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?

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

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

Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.

My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8. How many possible combinations are there to try?

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

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?

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?

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?

This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?

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?

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

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

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?

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

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.

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

These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.