Imagine you have six different colours of paint. You paint a cube
using a different colour for each of the six faces. How many
different cubes can be painted using the same set of six colours?
Is it possible to use all 28 dominoes arranging them in squares of
four? What patterns can you see in the solution(s)?
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.
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
A man has 5 coins in his pocket. Given the clues, can you work out
what the coins are?
This challenge extends the Plants investigation so now four or more children are involved.
How many tricolour flags are possible with 5 available colours such
that two adjacent stripes must NOT be the same colour. What about
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?
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.
Can you find all the different ways of lining up these Cuisenaire
Four friends must cross a bridge. How can they all cross it in just 17 minutes?
Find out how we can describe the "symmetries" of this triangle and
investigate some combinations of rotating and flipping it.
The machine I use to produce Braille messages is faulty and one of the pins that makes a raised dot is not working. I typed a short message in Braille. Can you work out what it really says?
Eight children enter the autumn cross-country race at school. How
many possible ways could they come in at first, second and third
An environment which simulates working with Cuisenaire rods.
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?
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
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?
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?
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?
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
Penta people, the Pentominoes, always build their houses from five
square rooms. I wonder how many different Penta homes you can
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?
This activity investigates how you might make squares and pentominoes from Polydron.
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 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
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
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?
Explore the different tunes you can make with these five gourds.
What are the similarities and differences between the two tunes you
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?
A game that demands a logical approach using systematic working to deduce a winning strategy
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?
Sam displays cans in 3 triangular stacks. With the same number he
could make one large triangular stack or stack them all in a square
based pyramid. How many cans are there how were they arranged?
Here is a collection of puzzles about Sam's shop sent in by club
members. Perhaps you can make up more puzzles, find formulas or
find general methods.
How many ways can you find of tiling the square patio, using square
tiles of different sizes?
George and Jim want to buy a chocolate bar. George needs 2p more
and Jim need 50p more to buy it. How much is the chocolate bar?
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
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
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.
Have a go at this game which involves throwing two dice and adding
their totals. Where should you place your counters to be more
likely to win?
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
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 shaped boxes can you design for 36 sweets in one
layer? Can you arrange the sweets so that no sweets of the same
colour are next to each other in any direction?
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.
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?
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?
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
How many positive integers less than or equal to 4000 can be
written down without using the digits 7, 8 or 9?