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

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

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.

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

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.

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?

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?

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

How many different shapes can you make by putting four right- angled isosceles triangles together?

Can you see who the gold medal winner is? What about the silver medal winner and the bronze medal winner?

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 focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.

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

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

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 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?

This task follows on from Build it Up and takes the ideas into three dimensions!

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

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?

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

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

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?

Can you find all the ways to get 15 at the top of this triangle of numbers?

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 ...?

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?

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.

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?

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

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

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

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

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?

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 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.

This train line has two tracks which cross at different points. Can you find all the routes that end at Cheston?

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

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 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?

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.

In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?

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

There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?

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?

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

Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?

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