In how many distinct ways can six islands be joined by bridges so that each island can be reached from every other island...
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. . . .
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?
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 leaders.
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 route again?
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?
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
Using only the red and white rods, how many different ways are there to make up the other colours of rod?
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?
Eight children enter the autumn cross-country race at school. How many possible ways could they come in at first, second and third places?
Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?
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.
How can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?
If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?
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 make?
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?
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 want?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
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 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?
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.
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
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 blocks.
How many tricolour flags are possible with 5 available colours such that two adjacent stripes must NOT be the same colour. What about 256 colours?
Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.
When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?
If you have three circular objects, you could arrange them so that they are separate, touching, overlapping or inside each other. Can you investigate all the different possibilities?
In how many ways can you arrange three dice side by side on a surface so that the sum of the numbers on each of the four faces (top, bottom, front and back) is equal?
Is it possible to use all 28 dominoes arranging them in squares of four? What patterns can you see in the solution(s)?
Four friends must cross a bridge. How can they all cross it in just 17 minutes?
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?
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?
How many six digit numbers are there which DO NOT contain a 5?
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
You have 5 darts and your target score is 44. How many different ways could you score 44?
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?
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?
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 man has 5 coins in his pocket. Given the clues, can you work out what the coins are?
Using all ten cards from 0 to 9, rearrange them to make five prime numbers. Can you find any other ways of doing it?
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 can you put five cereal packets together to make different shapes if you must put them face-to-face?
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.
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.
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?
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?
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?