In how many distinct ways can six islands be joined by bridges so that each island can be reached from every other island...
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
A game that demands a logical approach using systematic working to deduce a winning strategy
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?
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?
A toy has a regular tetrahedron, a cube and a base with triangular
and square hollows. If you fit a shape into the correct hollow a
bell rings. How many times does the bell ring in a complete game?
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
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?
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 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
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
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?
Ben has five coins in his pocket. How much money might he have?
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
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. . . .
Investigate the different ways you could split up these rooms so
that you have double the number.
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?
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
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?
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?
You have 5 darts and your target score is 44. How many different
ways could you score 44?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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?
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?
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?
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?
One face of a regular tetrahedron is painted blue and each of the
remaining faces are painted using one of the colours red, green or
yellow. How many different possibilities are there?
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
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?
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.
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?
Using all ten cards from 0 to 9, rearrange them to make five prime
numbers. Can you find any other ways of doing it?
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
Using only the red and white rods, how many different ways are
there to make up the other colours of rod?
Can you find all the different ways of lining up these Cuisenaire
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?
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 ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
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.
This challenge extends the Plants investigation so now four or more children are involved.
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.
Explore the different tunes you can make with these five gourds.
What are the similarities and differences between the two tunes you
Find out how we can describe the "symmetries" of this triangle and
investigate some combinations of rotating and flipping it.
An environment which simulates working with Cuisenaire rods.