Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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?
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
Use the information about Sally and her brother to find out how many children there are in the Brown family.
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?
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?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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
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 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 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!
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
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?
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?
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
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?
Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.
How would you count the number of fingers in these pictures?
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
Number problems at primary level that require careful consideration.
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Choose a symbol to put into the number sentence.
If the answer's 2010, what could the question be?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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!
Well now, what would happen if we lost all the nines in our number
system? Have a go at writing the numbers out in this way and have a
look at the multiplications table.
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?
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
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
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?
Bernard Bagnall recommends some primary school problems which use
numbers from the environment around us, from clocks to house
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.
48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Number problems at primary level that may require determination.
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
An old game but lots of arithmetic!
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.
Annie cut this numbered cake into 3 pieces with 3 cuts so that the
numbers on each piece added to the same total. Where were the cuts
and what fraction of the whole cake was each piece?
Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?