Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Place six toy ladybirds into the box so that there are two
ladybirds in every column and every row.
A game for 2 people. Take turns placing a counter on the star. You
win when you have completed a line of 3 in your colour.
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
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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?
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?
You have 5 darts and your target score is 44. How many different
ways could you score 44?
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?
Use the clues to colour each square.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
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!
In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?
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?
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
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?
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.
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?
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?
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
Can you make a train the same length as Laura's but using three
differently coloured rods? Is there only one way of doing 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?
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?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Can you put the 25 coloured tiles into the 5 x 5 square so that no
column, no row and no diagonal line have tiles of the same colour
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!
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?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
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?
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?
What happens when you try and fit the triomino pieces into these
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 cover the camel with these pieces?
Use these head, body and leg pieces to make Robot Monsters which
are different heights.
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
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?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
These are the faces of Will, Lil, Bill, Phil and Jill. Use the
clues to work out which name goes with each face.
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?
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?
This 100 square jigsaw is written in code. It starts with 1 and
ends with 100. Can you build it up?
Can you fill in this table square? The numbers 2 -12 were used to
generate it with just one number used twice.
Find all the numbers that can be made by adding the dots on two dice.
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
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?
You cannot choose a selection of ice cream flavours that includes
totally what someone has already chosen. Have a go and find all the
different ways in which seven children can have ice cream.
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?
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?