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?
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?
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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?
Find the sum of all three-digit numbers each of whose digits is
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 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.
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
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
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?
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?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
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?
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.
Investigate the different distances of these car journeys and find out how long they take.
Use the 'double-3 down' dominoes to make a square so that each side
has eight dots.
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
Vera is shopping at a market with these coins in her purse. Which
things could she give exactly the right amount for?
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Find the next number in this pattern: 3, 7, 19, 55 ...
Use the information to work out how many gifts there are in each
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
What is happening at each box in these machines?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Start with four numbers at the corners of a square and put the
total of two corners in the middle of that side. Keep going... Can
you estimate what the size of the last four numbers will be?
The value of the circle changes in each of the following problems.
Can you discover its value in each problem?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
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?
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?
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Find another number that is one short of a square number and when
you double it and add 1, the result is also a square number.
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?
Find out why these matrices are magic. Can you work out how they were made? Can you make your own Magic Matrix?
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?
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?
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.
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common?
Investigate the different distances of these car journeys and find
out how long they take.
In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.
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?