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?

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?

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?

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?

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.

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?

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.

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?

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 ...?

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

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

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

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.

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?

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

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

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

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?

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

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

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

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

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.

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?

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?

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?

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?

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

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

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.

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

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?

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