Can you replace the letters with numbers? Is there only one
solution in each case?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
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?
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?
The value of the circle changes in each of the following problems.
Can you discover its value in each problem?
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
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
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?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
There are three buckets each of which holds a maximum of 5 litres.
Use the clues to work out how much liquid there is in each bucket.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
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.
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?
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!
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Use the information to work out how many gifts there are in each
What is the sum of all the three digit whole numbers?
Find out what a Deca Tree is and then work out how many leaves
there will be after the woodcutter has cut off a trunk, a branch, a
twig and a leaf.
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
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?
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.
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?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
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?
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?
There are over sixty different ways of making 24 by adding,
subtracting, multiplying and dividing all four numbers 4, 6, 6 and
8 (using each number only once). How many can you find?
Can you work out some different ways to balance this equation?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
Have a go at balancing this equation. Can you find different ways of doing it?
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?
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 challenge encourages you to explore dividing a three-digit number by a single-digit number.
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?
These sixteen children are standing in four lines of four, one
behind the other. They are each holding a card with a number on it.
Can you work out the missing numbers?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
All the girls would like a puzzle each for Christmas and all the
boys would like a book each. Solve the riddle to find out how many
puzzles and books Santa left.
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?
What is happening at each box in these machines?
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
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
This task combines spatial awareness with addition and multiplication.
Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?
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?