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!

Throughout these challenges, the touching faces of any adjacent dice must have the same number. Can you find a way of making the total on the top come to each number from 11 to 18 inclusive?

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.

Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?

Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?

Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?

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

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

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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.

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

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.

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?

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?

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 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.

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

This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?

You have 5 darts and your target score is 44. How many different ways could you score 44?

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 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?

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

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?

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?

Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

Can you substitute numbers for the letters in these sums?

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

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

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

Place eight dots on this diagram, so that there are only two dots on each straight line and only two dots on each circle.

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?

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

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.

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?

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?

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

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 make square numbers by adding two prime numbers together?

When intergalactic Wag Worms are born they look just like a cube. Each year they grow another cube in any direction. Find all the shapes that five-year-old Wag Worms can be.

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.

Ben has five coins in his pocket. How much money might he have?

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 find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?

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

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?

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.