How many tricolour flags are possible with 5 available colours such
that two adjacent stripes must NOT be the same colour. What about
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.
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)?
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?
In how many ways can a pound (value 100 pence) be changed into some combination of 1, 2, 5, 10, 20 and 50 pence coins?
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?
How many positive integers less than or equal to 4000 can be
written down without using the digits 7, 8 or 9?
Consider all of the five digit numbers which we can form using only
the digits 2, 4, 6 and 8. If these numbers are arranged in
ascending order, what is the 512th number?
If these elves wear a different outfit every day for as many days
as possible, how many days can their fun last?
In how many distinct ways can six islands be joined by bridges so that each island can be reached from every other island...
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?
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?
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
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
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
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. . . .
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
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.
A game that demands a logical approach using systematic working to deduce a winning strategy
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
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 six digit numbers are there which DO NOT contain a 5?
Four friends must cross a bridge. How can they all cross it in just 17 minutes?
Eight children enter the autumn cross-country race at school. How
many possible ways could they come in at first, second and third
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?
Penta people, the Pentominoes, always build their houses from five
square rooms. I wonder how many different Penta homes you can
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 do. . . .
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?
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.
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?
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
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?
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?
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?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
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
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?
A man has 5 coins in his pocket. Given the clues, can you work out
what the coins are?
In the planet system of Octa the planets are arranged in the shape
of an octahedron. How many different routes could be taken to get
from Planet A to Planet Zargon?
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?
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?
When you think of spies and secret agents, you probably wouldn’t think of mathematics. Some of the most famous code breakers in history have been mathematicians.
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?
How many ways can you find of tiling the square patio, using square
tiles of different sizes?
You have 5 darts and your target score is 44. How many different
ways could you score 44?
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
Explain why it is that when you throw two dice you are more likely to get a score of 9 than of 10. What about the case of 3 dice? Is a score of 9 more likely then a score of 10 with 3 dice?