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?

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?

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?

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.

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?

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

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?

Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?

Penta people, the Pentominoes, always build their houses from five square rooms. I wonder how many different Penta homes you can create?

If you had 36 cubes, what different cuboids could you make?

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?

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

Can you find all the different ways of lining up these Cuisenaire rods?

My coat has three buttons. How many ways can you find to do up all the buttons?

Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?

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

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

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?

When intergalactic Wag Worms are born they look just like a cube. Each year they grow another cube in any direction. Find all the shapes that five-year-old Wag Worms can be.

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?

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?

Lorenzie was packing his bag for a school trip. He packed four shirts and three pairs of pants. "I will be able to have a different outfit each day", he said. How many days will Lorenzie be away?

How many different shapes can you make by putting four right- angled isosceles triangles together?

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 Red Express Train usually has five red carriages. How many ways can you find to add two blue carriages?

There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?

In this investigation, you must try to make houses using cubes. If the base must not spill over 4 squares and you have 7 cubes which stand for 7 rooms, what different designs can you come up with?

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?

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?

Take three differently coloured blocks - maybe red, yellow and blue. Make a tower using one of each colour. How many different towers can you make?

How many different rhythms can you make by putting two drums on the wheel?

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?

Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?

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

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

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?

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

Investigate the different sounds you can make by putting the owls and donkeys on the wheel.

One face of a regular tetrahedron is painted blue and each of the remaining faces are painted using one of the colours red, green or yellow. How many different possibilities are there?

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?

In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?

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

Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way to share the sweets between the three children so they each get the kind they like. Is there more than one way to do it?

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