Two children made up a game as they walked along the garden paths.
Can you find out their scores? Can you find some paths of your own?
In how many ways could Mrs Beeswax put ten coins into her three
puddings so that each pudding ended up with at least two coins?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99
How many ways can you do it?
Move from the START to the FINISH by moving across or down to the
next square. Can you find a route to make these totals?
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!
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
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 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!
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
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
This task follows on from Build it Up and takes the ideas into three dimensions!
Can you find all the ways to get 15 at the top of this triangle of numbers?
This challenge is about finding the difference between numbers which have the same tens digit.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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?
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?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.
Can you arrange 5 different digits (from 0 - 9) in the cross in 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.
There are to be 6 homes built on a new development site. They could
be semi-detached, detached or terraced houses. How many different
combinations of these can you find?
In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?
Moira is late for school. What is the shortest route she can take from the school gates to the entrance?
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Can you substitute numbers for the letters in these sums?
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?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
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?
My coat has three buttons. How many ways can you find to do up all
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
Can you use the information to find out which cards I have used?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
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?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Use these head, body and leg pieces to make Robot Monsters which
are different heights.
El Crico the cricket has to cross a square patio to get home. He
can jump the length of one tile, two tiles and three tiles. Can you
find a path that would get El Crico home in three jumps?
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?
My cube has inky marks on each face. Can you find the route it has
taken? What does each face look like?
Start with three pairs of socks. Now mix them up so that no
mismatched pair is the same as another mismatched pair. Is there
more than one 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?
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.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?