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?
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 to work on with others.
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Fill in the numbers to make the sum of each row, column and
diagonal equal to 34. For an extra challenge try the huge American
Flag magic square.
Number problems at primary level that may require determination.
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?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
What is the sum of all the three digit whole numbers?
Got It game for an adult and child. How can you play so that you know you will always win?
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.
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?
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
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?
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
Bernard Bagnall recommends some primary school problems which use
numbers from the environment around us, from clocks to house
Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
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!
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
Use the information to work out how many gifts there are in each
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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?
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.
Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Add the sum of the squares of four numbers between 10 and 20 to the
sum of the squares of three numbers less than 6 to make the square
of another, larger, number.
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!
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?
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?
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?
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
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?
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?
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
What is the largest number you can make using the three digits 2, 3
and 4 in any way you like, using any operations you like? You can
only use each digit once.
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
This is an adding game for two players.
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.
On a calculator, make 15 by using only the 2 key and any of the
four operations keys. How many ways can you find to do it?
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.