If you wrote all the possible four digit numbers made by using each
of the digits 2, 4, 5, 7 once, what would they add up to?
You have four jugs of 9, 7, 4 and 2 litres capacity. The 9 litre
jug is full of wine, the others are empty. Can you divide the wine
into three equal quantities?
Using 3 rods of integer lengths, none longer than 10 units and not
using any rod more than once, you can measure all the lengths in
whole units from 1 to 10 units. How many ways can you do this?
Find the numbers in this sum
The picture shows a lighthouse and many underwater creatures. If
you know the markings on the lighthouse are 1m apart, can you work
out the distances between some of the different creatures?
If each of these three shapes has a value, can you find the totals
of the combinations? Perhaps you can use the shapes to make the
This article suggests some ways of making sense of calculations involving positive and negative numbers.
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.
Susie took cherries out of a bowl by following a certain pattern.
How many cherries had there been in the bowl to start with if she
was left with 14 single ones?
In this game the winner is the first to complete a row of three. Are some squares easier to land on than others?
In this problem you have to place four by four magic squares on the
faces of a cube so that along each edge of the cube the numbers
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?
What is the sum of all the three digit whole numbers?
Find the sum of all three-digit numbers each of whose digits is
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
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?
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
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Investigate the different distances of these car journeys and find out how long they take.
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
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?
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.
Arrange three 1s, three 2s and three 3s in this square so that
every row, column and diagonal adds to the same total.
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Tell your friends that you have a strange calculator that turns
numbers backwards. What secret number do you have to enter to make
141 414 turn around?
Use the 'double-3 down' dominoes to make a square so that each side
has eight dots.
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 sheep talk the only letters used are B and A. A sequence of
words is formed by following certain rules. What do you notice when
you count the letters in each word?
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?
These alphabet bricks are painted in a special way. A is on one
brick, B on two bricks, and so on. How many bricks will be painted
by the time they have got to other letters of the alphabet?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
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.
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.
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.
Investigate the different distances of these car journeys and find
out how long they take.
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Max and Mandy put their number lines together to make a graph. How
far had each of them moved along and up from 0 to get the counter
to the place marked?
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?
Vera is shopping at a market with these coins in her purse. Which
things could she give exactly the right amount for?
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?
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?
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
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?
What is happening at each box in these machines?
This number has 903 digits. What is the sum of all 903 digits?
Is it possible to rearrange the numbers 1,2......12 around a clock
face in such a way that every two numbers in adjacent positions
differ by any of 3, 4 or 5 hours?