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

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?

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

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?

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 nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

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?

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?

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?

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

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

In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?

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?

In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?

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

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

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

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?

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?

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?

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.

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?

In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?

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?

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?

A little mouse called Delia lives in a hole in the bottom of a tree.....How many days will it be before Delia has to take the same route again?

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

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

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

Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?

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

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

In how many different ways can you break up a stick of 7 interlocking cubes? Now try with a stick of 8 cubes and a stick of 6 cubes.

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

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 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?

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?

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

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

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

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

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?

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.

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

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

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?

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?

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.

Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?