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?
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 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?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
How many six digit numbers are there which DO NOT contain a 5?
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. . . .
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
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?
Is it possible to use all 28 dominoes arranging them in squares of
four? What patterns can you see in the solution(s)?
In how many distinct ways can six islands be joined by bridges so that each island can be reached from every other island...
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?
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?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
Three dice are placed in a row. Find a way to turn each one so that
the three numbers on top of the dice total the same as the three
numbers on the front of the dice. Can you find all the ways to. . . .
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?
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.
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?
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?
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
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
Using only the red and white rods, how many different ways are
there to make up the other colours of rod?
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.
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?
How many tricolour flags are possible with 5 available colours such
that two adjacent stripes must NOT be the same colour. What about
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?
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
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.
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
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?
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?
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?
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.
An environment which simulates working with Cuisenaire rods.
This challenge extends the Plants investigation so now four or more children are involved.
Using all ten cards from 0 to 9, rearrange them to make five prime
numbers. Can you find any other ways of doing it?
Four friends must cross a bridge. How can they all cross it in just 17 minutes?
In a league of 5 football teams which play in a round robin
tournament show that it is possible for all five teams to be league
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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
How many ways can you find of tiling the square patio, using square
tiles of different sizes?
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 can you put five cereal packets together to make different
shapes if you must put them face-to-face?
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?
Can you find all the different ways of lining up these Cuisenaire
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?