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?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
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?
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?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
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?
Noah saw 12 legs walk by into the Ark. How many creatures did he see?
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?
A toy has a regular tetrahedron, a cube and a base with triangular and square hollows. If you fit a shape into the correct hollow a bell rings. How many times does the bell ring in a complete game?
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
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?
Explore the different snakes that can be made using 5 cubes.
Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.
Find all the numbers that can be made by adding the dots on two dice.
Here are some rods that are different colours. How could I make a yellow rod using white and red rods?
If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?
If you had 36 cubes, what different cuboids could you make?
My coat has three buttons. How many ways can you find to do up all the buttons?
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?
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?
Terry and Ali are playing a game with three balls. Is it fair that Terry wins when the middle ball is red?
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?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Can you fill in the empty boxes in the grid with the right shape and colour?
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
How can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?
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?
How many ways can you find of tiling the square patio, using square tiles of different sizes?
This activity investigates how you might make squares and pentominoes from Polydron.
Penta people, the Pentominoes, always build their houses from five square rooms. I wonder how many different Penta homes you can create?
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?
The Red Express Train usually has five red carriages. How many ways can you find to add two blue carriages?
How many different shapes can you make by putting four right- angled isosceles triangles together?
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.
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?
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?
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?
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 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?
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?
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
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?
This challenge extends the Plants investigation so now four or more children are involved.
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.
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.
You have 5 darts and your target score is 44. How many different ways could you score 44?
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.
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?