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 put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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!
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?
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.
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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?
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?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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.
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 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?
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 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?
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
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?
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?
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
Choose a symbol to put into the number sentence.
Have a go at balancing this equation. Can you find different ways of doing it?
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?
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?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Can you complete this jigsaw of the multiplication square?
Number problems at primary level that require careful consideration.
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
Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?
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
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?
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?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Can you work out some different ways to balance this equation?
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?
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
Start by putting one million (1 000 000) into the display of your
calculator. Can you reduce this to 7 using just the 7 key and add,
subtract, multiply, divide and equals as many times as you like?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Here is a chance to play a version of the classic Countdown Game.
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?
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?
This number has 903 digits. What is the sum of all 903 digits?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.