This task encourages you to investigate the number of edging pieces and panes in different sized windows.

I added together some of my neighbours house numbers. Can you explain the patterns I noticed?

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

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

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

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

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

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 this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

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?

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

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?

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

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

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way to share the sweets between the three children so they each get the kind they like. Is there more than one way to do it?

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.

Stuart's watch loses two minutes every hour. Adam's watch gains one minute every hour. Use the information to work out what time (the real time) they arrived at the airport.

Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

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

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

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.

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?

This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?

In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?

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.

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

Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

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.

My dice has inky marks on each face. Can you find the route it has taken? What does each face look like?

There are lots of different methods to find out what the shapes are worth - how many can you find?

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

Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?

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

In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

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

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?

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 order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

This task depends on groups working collaboratively, discussing and reasoning to agree a final product.

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

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

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

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?