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?

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?

Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?

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

My cousin was 24 years old on Friday April 5th in 1974. On what day of the week was she born?

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.

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?

Alice's mum needs to go to each child's house just once and then back home again. How many different routes are there? Use the information to find out how long each road is on the route she took.

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?

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.

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

On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?

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

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

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?

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

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?

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?

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

Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?

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

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

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

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?

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?

Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

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.

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

Stuart's watch loses two minutes every hour. Adam's watch gains one minute every hour. Use the information to work out what time (the real time) they arrived at the airport.

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?

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?

Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.

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

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

Can you fill in the empty boxes in the grid with the right shape and colour?

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.