Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
How many different rhythms can you make by putting two drums on the wheel?
Can you find all the different ways of lining up these Cuisenaire rods?
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?
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?
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?
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?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
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?
Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.
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?
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?
Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?
You have 5 darts and your target score is 44. How many different ways could you score 44?
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
How can you put five cereal packets together to make different shapes if you must put them face-to-face?
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?
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?
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?
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?
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.
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?
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
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?
Investigate the different ways you could split up these rooms so that you have double the number.
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
Use these head, body and leg pieces to make Robot Monsters which are different heights.
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?
If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
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?
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?
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?
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?
Terry and Ali are playing a game with three balls. Is it fair that Terry wins when the middle ball is red?
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?
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?
Ben has five coins in his pocket. How much money might he have?
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?
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?
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?
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 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?
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.
My coat has three buttons. How many ways can you find to do up all the buttons?
The Red Express Train usually has five red carriages. How many ways can you find to add two blue carriages?