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?
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?
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
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?
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
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?
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?
My coat has three buttons. How many ways can you find to do up all
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.
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?
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?
If each of these three shapes has a value, can you find the totals
of the combinations? Perhaps you can use the shapes to make the
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.
Explore the different snakes that can be made using 5 cubes.
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?
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 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?
Penta people, the Pentominoes, always build their houses from five
square rooms. I wonder how many different Penta homes you can
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
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
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?
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 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?
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
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.
This challenge extends the Plants investigation so now four or more children are involved.
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
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?
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.
Find all the numbers that can be made by adding the dots on two dice.
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
Can you fill in the empty boxes in the grid with the right shape
Use these head, body and leg pieces to make Robot Monsters which
are different heights.
Semaphore is a way to signal the alphabet using two flags. You
might want to send a message that contains more than just letters.
How many other symbols could you send using this code?
How many different ways can you find to join three equilateral
triangles together? Can you convince us that you have found 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
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?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
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?
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?
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?
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?
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?