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

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

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

The Zargoes use almost the same alphabet as English. What does this birthday message say?

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?

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

What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?

Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.

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.

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

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

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?

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.

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

Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?

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?

If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?

You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.

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

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?

When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?

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

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?

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?

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

Can you fill in the empty boxes in the grid with the right shape and colour?

Find all the numbers that can be made by adding the dots on two dice.

If you put three beads onto a tens/ones abacus you could make the numbers 3, 30, 12 or 21. What numbers can be made with six beads?

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?

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

Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?

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

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

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

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.

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

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

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?

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

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

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

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?

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

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?