Can you find all the different ways of lining up these Cuisenaire rods?
How many different rhythms can you make by putting two drums on the wheel?
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?
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?
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?
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
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?
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?
Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.
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 can you put five cereal packets together to make different shapes if you must put them face-to-face?
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?
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
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.
Investigate the different ways you could split up these rooms so that you have double the number.
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?
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
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.
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?
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?
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.
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
My coat has three buttons. How many ways can you find to do up all the buttons?
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?
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?
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?
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
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.
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?
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?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
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?
Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.
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?
Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?
If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?
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?
Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.
Using 3 rods of integer lengths, none longer than 10 units and not using any rod more than once, you can measure all the lengths in whole units from 1 to 10 units. How many ways can you do this?
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?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
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?
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?
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.
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.