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 1 to 8 into the circles so that the four
calculations are correct?
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!
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 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!
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?
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?
You have 5 darts and your target score is 44. How many different
ways could you score 44?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using 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?
Use the clues to colour each square.
What happens when you try and fit the triomino pieces into these
Can you cover the camel with these pieces?
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?
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....?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
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?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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?
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.
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?
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
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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?
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?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
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.
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?
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 order the digits from 1-6 to make a number which is
divisible by 6 so when the last digit is removed it becomes a
5-figure number divisible by 5, and so on?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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?
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?
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?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Tim's class collected data about all their pets. Can you put the
animal names under each column in the block graph using the
Find all the numbers that can be made by adding the dots on two dice.
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
How many different ways can you find to join three equilateral
triangles together? Can you convince us that you have found them