Find the sum of all three-digit numbers each of whose digits is
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?
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?
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
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Can you substitute numbers for the letters in these sums?
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?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
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 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the
numbers on each circle add up to the same amount. Can you find the
rule for giving another set of six 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.
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
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
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.
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
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?
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
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?
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
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?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
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
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
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?
Use the 'double-3 down' dominoes to make a square so that each side
has eight dots.
This is an adding game for two players.
How could you arrange at least two dice in a stack so that the total of the visible spots is 18?
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?
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
Investigate the different distances of these car journeys and find out how long they take.
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
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?
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
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 make square numbers by adding two prime numbers together?
I throw three dice and get 5, 3 and 2. Add the scores on the three
dice. What do you get? Now multiply the scores. What do you notice?
Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?
Mr. Sunshine tells the children they will have 2 hours of homework.
After several calculations, Harry says he hasn't got time to do
this homework. Can you see where his reasoning is wrong?
I was looking at the number plate of a car parked outside. Using my special code S208VBJ adds to 65. Can you crack my code and use it to find out what both of these number plates add up to?
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.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.