Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
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.
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?
Claire thinks she has the most sports cards in her album. "I have
12 pages with 2 cards on each page", says Claire. Ross counts his
cards. "No! I have 3 cards on each of my pages and there are. . . .
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the 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.
There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. Can you use the information given to find out how many eggs are in each basket?
There were 22 legs creeping across the web. How many flies? How many spiders?
Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Can you draw a continuous line through 16 numbers on this grid so
that the total of the numbers you pass through is as high as
Woof is a big dog. Yap is a little dog.
Emma has 16 dog biscuits to give to the two dogs.
She gave Woof 4 more biscuits than Yap.
How many biscuits did each dog get?
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?
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
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?
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?
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.
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
Sam got into an elevator. He went down five floors, up six floors, down seven floors, then got out on the second floor. On what floor did he get on?
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?
Number problems at primary level that require careful consideration.
Fill in the numbers to make the sum of each row, column and
diagonal equal to 15.
Can you score 100 by throwing rings on this board? Is there more
than way 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.
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 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.
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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 task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
Cassandra, David and Lachlan are brothers and sisters. They range
in age between 1 year and 14 years. Can you figure out their exact
ages from the clues?
Noah saw 12 legs walk by into the Ark. How many creatures did he see?
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2
litres. Find a way to pour 9 litres of drink from one jug to
another until you are left with exactly 3 litres in three of the
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
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?
Find the next number in this pattern: 3, 7, 19, 55 ...
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
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!
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?
Move from the START to the FINISH by moving across or down to the
next square. Can you find a route to make these totals?
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?