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?
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?
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.
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
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.
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
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?
Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?
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?
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
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?
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?
If you had 36 cubes, what different cuboids could you make?
How many ways can you find of tiling the square patio, using square
tiles of different sizes?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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?
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
If these elves wear a different outfit every day for as many days
as possible, how many days can their fun last?
Investigate the different ways you could split up these rooms so
that you have double the number.
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?
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?
Explore the different snakes that can be made using 5 cubes.
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
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?
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 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?
Can you find all the different ways of lining up these Cuisenaire
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
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 three differently coloured blocks - maybe red, yellow and blue. Make a tower using one of each colour. How many different towers 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?
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
Penta people, the Pentominoes, always build their houses from five
square rooms. I wonder how many different Penta homes you can
You have 5 darts and your target score is 44. How many different
ways could you score 44?
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?
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?
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
In this investigation, you must try to make houses using cubes. If
the base must not spill over 4 squares and you have 7 cubes which
stand for 7 rooms, what different designs can you come up with?
How many different ways can you find to join three equilateral
triangles together? Can you convince us that you have found them
An environment which simulates working with Cuisenaire rods.
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.
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
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
Using 3 rods of integer lengths, none longer than 10 units and not
using any rod more than once, you can measure all the lengths in
whole units from 1 to 10 units. How many ways can you do this?
Sam sets up displays of cat food in his shop in triangular stacks.
If Felix buys some, then how can Sam arrange the remaining cans in
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?
Tim had nine cards each with a different number from 1 to 9 on it.
How could he have put them into three piles so that the total in
each pile was 15?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?