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?
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?
Investigate the different sounds you can make by putting the owls and donkeys on the wheel.
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?
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.
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?
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
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 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?
Terry and Ali are playing a game with three balls. Is it fair that Terry wins when the middle ball is red?
How can you put five cereal packets together to make different shapes if you must put them face-to-face?
Find all the numbers that can be made by adding the dots on two dice.
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?
How many different rhythms can you make by putting two drums on the wheel?
Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?
Can you find all the different ways of lining up these Cuisenaire rods?
If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
Investigate the different ways you could split up these rooms so that you have double the number.
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
An environment which simulates working with Cuisenaire rods.
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?
Noah saw 12 legs walk by into the Ark. How many creatures did he see?
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?
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.
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.
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?
Imagine that the puzzle pieces of a jigsaw are roughly a rectangular shape and all the same size. How many different puzzle pieces could there be?
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 how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?
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 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?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
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?
The Red Express Train usually has five red carriages. How many ways can you find to add two blue carriages?
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
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?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
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.
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?
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?
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?
Try grouping the dominoes in the ways described. Are there any left over each time? Can you explain why?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
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?