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

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

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

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

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

Can you find the chosen number from the grid using the clues?

What happens when you round these numbers to the nearest whole number?

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 ...?

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

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

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?

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?

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

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

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.

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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.

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

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

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?

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.

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

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?

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.

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?

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

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

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

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

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.

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

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

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?

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

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

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

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.

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

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?

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

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

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

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?

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