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'.

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

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.

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?

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

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?

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?

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.

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

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.

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

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.

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

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?

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

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

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?

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?

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?

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.

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?

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

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

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!

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

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

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

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

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?

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

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

I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

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?

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?

Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

An activity making various patterns with 2 x 1 rectangular tiles.

George and Jim want to buy a chocolate bar. George needs 2p more and Jim need 50p more to buy it. How much is the chocolate bar?

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.