Let's suppose that you are going to have a magazine which has 16 pages of A5 size. Can you find some different ways to make these pages? Investigate the pattern for each if you number the pages.

Arrange 3 red, 3 blue and 3 yellow counters into a three-by-three square grid, so that there is only one of each colour in every row and every column

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.

Jack has nine tiles. He put them together to make a square so that two tiles of the same colour were not beside each other. Can you find another way to do it?

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?

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

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.

These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?

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?

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?

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?

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!

The pages of my calendar have got mixed up. Can you sort them out?

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?

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.

Use these head, body and leg pieces to make Robot Monsters which are different heights.

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

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?

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

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

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

There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

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

On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?

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.

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?

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

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

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

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

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?

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?

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

Find all the different shapes that can be made by joining five equilateral triangles edge to edge.

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

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

What is the smallest number of coins needed to make up 12 dollars and 83 cents?

Using all ten cards from 0 to 9, rearrange them to make five prime numbers. Can you find any other ways of doing it?

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.

Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?

In this matching game, you have to decide how long different events take.

What could the half time scores have been in these Olympic hockey matches?

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?

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?

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

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

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

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?