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!

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

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?

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?

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.

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!

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

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?

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

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.

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

Can you find all the ways to get 15 at the top of this triangle of numbers?

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

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

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

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?

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

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.

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

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

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?

When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?

Can you use this information to work out Charlie's house number?

Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?

Can you work out some different ways to balance this equation?

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

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?

Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.

Ana and Ross looked in a trunk in the attic. They found old cloaks and gowns, hats and masks. How many possible costumes could they make?

A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?

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

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

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

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

How could you arrange at least two dice in a stack so that the total of the visible spots is 18?

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

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

This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .

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

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

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?

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

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

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.