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

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

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

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

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?

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In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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

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

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

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?

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?

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.

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?

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

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.

How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?

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

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

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

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

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

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

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.

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.

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

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.

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.

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?

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?

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

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?

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.

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?

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?

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

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

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?

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?

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

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.

Number problems at primary level that require careful consideration.

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?