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.

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

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

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

Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?

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

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?

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

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

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

Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

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?

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

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.

Your challenge is to find the longest way through the network following this rule. You can start and finish anywhere, and with any shape, as long as you follow the correct order.

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

The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?

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.

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

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

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?

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

Find out what a "fault-free" rectangle is and try to make some of your own.

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

Sally and Ben were drawing shapes in chalk on the school playground. Can you work out what shapes each of them drew using the clues?

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

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?

What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?

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

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?

The Zargoes use almost the same alphabet as English. What does this birthday message say?

Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

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

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

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

Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?

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

If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?

If you have three circular objects, you could arrange them so that they are separate, touching, overlapping or inside each other. Can you investigate all the different possibilities?

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

What happens when you round these numbers to the nearest whole number?

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?

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

What happens when you round these three-digit numbers to the nearest 100?

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.