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.

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?

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.

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

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?

The challenge here is to find as many routes as you can for a fence to go so that this town is divided up into two halves, each with 8 blocks.

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

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

This activity investigates how you might make squares and pentominoes from Polydron.

Can you draw a square in which the perimeter is numerically equal to the area?

Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?

A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

How many ways can you find of tiling the square patio, using square tiles of different sizes?

My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?

These practical challenges are all about making a 'tray' and covering it with paper.

What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?

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?

In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?

What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?

Find your way through the grid starting at 2 and following these operations. What number do you end on?

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?

What happens when you try and fit the triomino pieces into these two grids?

El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?

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

Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?

Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?

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?

Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?

My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8. How many possible combinations are there to try?

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.

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

Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?

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

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!

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?

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.

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.

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!

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

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

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

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

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

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

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

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