Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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?
Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Katie had a pack of 20 cards numbered from 1 to 20. She arranged
the cards into 6 unequal piles where each pile added to the same
total. What was the total and how could this be done?
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!
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Can you replace the letters with numbers? Is there only one
solution in each case?
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!
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.
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
Can you complete this jigsaw of the multiplication square?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Can you work out the arrangement of the digits in the square so
that the given products are correct? The numbers 1 - 9 may be used
once and once only.
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?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Choose a symbol to put into the number sentence.
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and
lollypops for 7p in the sweet shop. What could each of the children
buy with their money?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
If you take a three by three square on a 1-10 addition square and
multiply the diagonally opposite numbers together, what is the
difference between these products. Why?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
This challenge is a game for two players. Choose two numbers from the grid and multiply or divide, then mark your answer on the number line. Can you get four in a row before your partner?
On the table there is a pile of oranges and lemons that weighs
exactly one kilogram. Using the information, can you work out how
many lemons there are?
Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?
Find the next number in this pattern: 3, 7, 19, 55 ...
Rocco ran in a 200 m race for his class. Use the information to
find out how many runners there were in the race and what Rocco's
finishing position was.
A game for 2 people using a pack of cards Turn over 2 cards and try
to make an odd number or a multiple of 3.
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
We can arrange dots in a similar way to the 5 on a dice and they
usually sit quite well into a rectangular shape. How many
altogether in this 3 by 5? What happens for other sizes?
The Scot, John Napier, invented these strips about 400 years ago to
help calculate multiplication and division. Can you work out how to
use Napier's bones to find the answer to these multiplications?
If you had any number of ordinary dice, what are the possible ways
of making their totals 6? What would the product of the dice be
This task combines spatial awareness with addition and multiplication.
What is happening at each box in these machines?
On my calculator I divided one whole number by another whole number and got the answer 3.125 If the numbers are both under 50, what are they?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
Try adding together the dates of all the days in one week. Now
multiply the first date by 7 and add 21. Can you explain what
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
Mr McGregor has a magic potting shed. Overnight, the number of
plants in it doubles. He'd like to put the same number of plants in
each of three gardens, planting one garden each day. Can he do it?
Use the information to work out how many gifts there are in each
Put a number at the top of the machine and collect a number at the
bottom. What do you get? Which numbers get back to themselves?