How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
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
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?
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
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?
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?
Find out how we can describe the "symmetries" of this triangle and
investigate some combinations of rotating and flipping it.
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?
How many different rhythms can you make by putting two drums on the
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.
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?
Explore the different tunes you can make with these five gourds.
What are the similarities and differences between the two tunes you
Explore the different snakes that can be made using 5 cubes.
Investigate the different ways you could split up these rooms so
that you have double the number.
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
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?
My coat has three buttons. How many ways can you find to do up all
Can you find all the different ways of lining up these Cuisenaire
This activity investigates how you might make squares and pentominoes from Polydron.
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?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
How many ways can you find of tiling the square patio, using square
tiles of different sizes?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
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?
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 we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
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?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
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
The Red Express Train usually has five red carriages. How many ways
can you find to add two blue carriages?
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?
Investigate the different sounds you can make by putting the owls
and donkeys on the wheel.
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
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?
How many different shapes can you make by putting four right-
angled isosceles triangles together?
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?
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
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 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?
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?
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?
Terry and Ali are playing a game with three balls. Is it fair that
Terry wins when the middle ball is red?
Using all ten cards from 0 to 9, rearrange them to make five prime
numbers. Can you find any other ways of doing it?
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?
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
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
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?
Arrange 3 red, 3 blue and 3 yellow counters into a three-by-three square grid, so that there is only one of each colour in every row and every column
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.