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
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?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
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 score 100 by throwing rings on this board? Is there more
than way to do it?
A church hymn book contains 700 hymns. The numbers of the hymns are
displayed by combining special small single-digit boards. What is
the minimum number of small boards that is needed?
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?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?
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.
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?
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?
If these elves wear a different outfit every day for as many days
as possible, how many days can their fun last?
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?
If you had any number of ordinary dice, what are the possible ways
of making their totals 6? What would the product of the dice be
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Ben has five coins in his pocket. How much money might he have?
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
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?
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 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
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?
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 many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
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?
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?
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?
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
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?
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?
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?
You have 5 darts and your target score is 44. How many different
ways could you score 44?
Jack has nine tiles. He put them together to make a square so that two tiles of the same colour were not beside each other. Can you find another way to do it?
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
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?
Can you find all the different ways of lining up these Cuisenaire
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
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
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
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
How many ways can you find of tiling the square patio, using square
tiles of different sizes?
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?
A game that demands a logical approach using systematic working to deduce a winning strategy
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?
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?