Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Place the numbers 1 to 10 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?
What happens when you try and fit the triomino pieces into these
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
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?
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!
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?
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.
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?
Can you cover the camel with these pieces?
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?
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 find all the different ways of lining up these Cuisenaire
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
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?
This challenge is about finding the difference between numbers which have the same tens digit.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
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?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
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?
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.
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
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?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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
How many different rhythms can you make by putting two drums on the
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?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Use these head, body and leg pieces to make Robot Monsters which
are different heights.
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
I was in my car when I noticed a line of four cars on the lane next
to me with number plates starting and ending with J, K, L and M.
What order were they in?
An activity making various patterns with 2 x 1 rectangular tiles.
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
How many different triangles can you make on a circular pegboard that has nine pegs?