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. . . .
A game that demands a logical approach using systematic working to deduce a winning strategy
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
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?
How many tricolour flags are possible with 5 available colours such
that two adjacent stripes must NOT be the same colour. What about
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 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
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?
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?
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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
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?
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?
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?
Eight children enter the autumn cross-country race at school. How
many possible ways could they come in at first, second and third
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?
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?
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?
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?
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 ...?
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.
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?
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 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?
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?
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?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
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?
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?
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?
Is it possible to use all 28 dominoes arranging them in squares of
four? What patterns can you see in the solution(s)?
You have 5 darts and your target score is 44. How many different
ways could you score 44?
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?
Ben has five coins in his pocket. How much money might he have?
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?
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?
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?
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
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
This challenge extends the Plants investigation so now four or more children are involved.
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.