Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
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?
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
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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!
A tetromino is made up of four squares joined edge to edge. Can
this tetromino, together with 15 copies of itself, be used to cover
an eight by eight chessboard?
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?
Use the clues to colour each square.
What happens when you try and fit the triomino pieces into these
You have 4 red and 5 blue counters. How many ways can they be
placed on a 3 by 3 grid so that all the rows columns and diagonals
have an even number of red counters?
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
Can you find all the different ways of lining up these Cuisenaire
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
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?
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
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?
Is it possible to place 2 counters on the 3 by 3 grid so that there
is an even number of counters in every row and every column? How
about if you have 3 counters or 4 counters or....?
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 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?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
Hover your mouse over the counters to see which ones will be
removed. Click to remover them. The winner is the last one to
remove a counter. How you can make sure you win?
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?
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?
Can you cover the camel with these pieces?
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.
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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?
If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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?
Let's say you can only use two different lengths - 2 units and 4
units. Using just these 2 lengths as the edges how many different
cuboids can you make?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
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?
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?
Using different numbers of sticks, how many different triangles are
you able to make? Can you make any rules about the numbers of
sticks that make the most triangles?
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
Alice and Brian are snails who live on a wall and can only travel
along the cracks. Alice wants to go to see Brian. How far is the
shortest route along the cracks? Is there more than one way to go?
How many different ways can you find to join three equilateral
triangles together? Can you convince us that you have found them
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.