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
Explore the different snakes that can be made using 5 cubes.
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?
Move from the START to the FINISH by moving across or down to the
next square. Can you find a route to make these totals?
Penta people, the Pentominoes, always build their houses from five
square rooms. I wonder how many different Penta homes you can
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?
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?
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?
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 Red Express Train usually has five red carriages. How many ways
can you find to add two blue carriages?
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?
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 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?
My coat has three buttons. How many ways can you find to do up 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?
Find all the numbers that can be made by adding the dots on two dice.
Use these head, body and leg pieces to make Robot Monsters which
are different heights.
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?
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?
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?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
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?
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 you had 36 cubes, what different cuboids could you make?
In how many ways could Mrs Beeswax put ten coins into her three
puddings so that each pudding ended up with at least two coins?
Lolla bought a balloon at the circus. She gave the clown six coins
to pay for it. What could Lolla have paid for the balloon?
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?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
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
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?
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?
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?
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.
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 fill in the empty boxes in the grid with the right shape
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
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
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?
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
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?
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?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
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
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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
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
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
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?