Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?

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

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

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

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

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

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

What two-digit numbers can you make with these two dice? What can't you make?

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

What happens when you round these three-digit numbers to the nearest 100?

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 the chosen number from the grid using the clues?

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

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

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

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

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

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

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 replace the letters with numbers? Is there only one solution in each case?

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?

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

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

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

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?

How many solutions can you find to this sum? Each of the different letters stands for a different number.

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

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?

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

This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.

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?

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.

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

Number problems at primary level that require careful consideration.

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?

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

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?

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?

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?

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.

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.

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?

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?

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?

Let's suppose that you are going to have a magazine which has 16 pages of A5 size. Can you find some different ways to make these pages? Investigate the pattern for each if you number the pages.

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 can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

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?