How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?
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
Your challenge is to find the longest way through the network
following this rule. You can start and finish anywhere, and with
any shape, as long as you follow the correct order.
A dog is looking for a good place to bury his bone. Can you work
out where he started and ended in each case? What possible routes
could he have taken?
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
The discs for this game are kept in a flat square box with a square
hole for each disc. Use the information to find out how many discs
of each colour there are in the box.
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Can you find which shapes you need to put into the grid to make the
totals at the end of each row and the bottom of each column?
Investigate the different ways you could split up these rooms so
that you have double the number.
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
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?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
This magic square has operations written in it, to make it into a
maze. Start wherever you like, go through every cell and go out a
total of 15!
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Ben has five coins in his pocket. How much money might he have?
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?
This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?
My cube has inky marks on each face. Can you find the route it has
taken? What does each face look like?
A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2
litres. Find a way to pour 9 litres of drink from one jug to
another until you are left with exactly 3 litres in three of the
Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.
Can you substitute numbers for the letters in these sums?
Alice's mum needs to go to each child's house just once and then
back home again. How many different routes are there? Use the
information to find out how long each road is on the route she
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?
This problem is based on a code using two different prime numbers
less than 10. You'll need to multiply them together and shift the
alphabet forwards by the result. Can you decipher the code?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Add the sum of the squares of four numbers between 10 and 20 to the
sum of the squares of three numbers less than 6 to make the square
of another, larger, number.
Can you make square numbers by adding two prime numbers together?
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
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?
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?
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 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?
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?
Arrange the digits 1, 1, 2, 2, 3 and 3 so that between the two 1's
there is one digit, between the two 2's there are two digits, and
between the two 3's there are three digits.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Find all the different shapes that can be made by joining five
equilateral triangles edge to edge.
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
Katie had a pack of 20 cards numbered from 1 to 20. She arranged
the cards into 6 unequal piles where each pile added to the same
total. What was the total and how could this be done?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Can you use the information to find out which cards I have used?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
There are 44 people coming to a dinner party. There are 15 square
tables that seat 4 people. Find a way to seat the 44 people using
all 15 tables, with no empty places.
You have 5 darts and your target score is 44. How many different
ways could you score 44?
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?
This dice train has been made using specific rules. How many different trains can you make?