Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
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?
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 triangles can you make using sticks that are 3cm, 4cm and 5cm long?
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
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
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
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
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?
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?
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?
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?
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?
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?
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.
Can you find all the different ways of lining up these Cuisenaire
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
My coat has three buttons. How many ways can you find to do up all
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.
Investigate the different sounds you can make by putting the owls
and donkeys on the wheel.
How many different rhythms can you make by putting two drums on the
Explore the different tunes you can make with these five gourds.
What are the similarities and differences between the two tunes you
The Red Express Train usually has five red carriages. How many ways
can you find to add two blue carriages?
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.
This challenge extends the Plants investigation so now four or more children are involved.
Penta people, the Pentominoes, always build their houses from five
square rooms. I wonder how many different Penta homes you can
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.
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?
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?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
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?
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.
Can you fill in the empty boxes in the grid with the right shape
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?
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?
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
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?
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?
Use these head, body and leg pieces to make Robot Monsters which are different heights.
Four children were sharing a set of twenty-four butterfly cards.
Are there any cards they all want? Are there any that none of them
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 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
If these elves wear a different outfit every day for as many days
as possible, how many days can their fun last?
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?
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 shapes can you make by putting four right-
angled isosceles triangles together?