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?

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.

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?

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?

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?

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

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?

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?

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?

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?

Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?

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

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

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

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

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?

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

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?

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

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

Terry and Ali are playing a game with three balls. Is it fair that Terry wins when the middle ball is red?

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?

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

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?

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.

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?

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?

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

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?

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

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

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?

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?

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.

Jack has nine tiles. He put them together to make a square so that two tiles of the same colour were not beside each other. Can you find another way to do it?

Use these head, body and leg pieces to make Robot Monsters which are different heights.

Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?

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?

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?

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?

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

Arrange 3 red, 3 blue and 3 yellow counters into a three-by-three square grid, so that there is only one of each colour in every row and every column

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

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

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