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 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?
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
In how many different ways can you break up a stick of 7 interlocking cubes? Now try with a stick of 8 cubes and a stick of 6 cubes.
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
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 we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
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?
This activity investigates how you might make squares and pentominoes from Polydron.
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?
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
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 many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
If these elves wear a different outfit every day for as many days
as possible, how many days can their fun last?
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?
Investigate the different ways you could split up these rooms so
that you have double the number.
I start my journey in Rio de Janeiro and visit all the cities as Hamilton described, passing through Canberra before Madrid, and then returning to Rio. What route could I have taken?
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?
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
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
Explore the different tunes you can make with these five gourds.
What are the similarities and differences between the two tunes you
Can you find all the different ways of lining up these Cuisenaire
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.
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 ways can you find of tiling the square patio, using square
tiles of different sizes?
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
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 can you put five cereal packets together to make different
shapes if you must put them face-to-face?
Is it possible to rearrange the numbers 1,2......12 around a clock
face in such a way that every two numbers in adjacent positions
differ by any of 3, 4 or 5 hours?
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?
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 5 darts and your target score is 44. How many different
ways could you score 44?
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?
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?
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
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?
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
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 children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
In how many distinct ways can six islands be joined by bridges so that each island can be reached from every other island...
Blue Flibbins are so jealous of their red partners that they will
not leave them on their own with any other bue Flibbin. What is the
quickest way of getting the five pairs of Flibbins safely to. . . .
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
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 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?
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?
Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?
A lady has a steel rod and a wooden pole and she knows the length
of each. How can she measure out an 8 unit piece of pole?
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?
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?