Find the numbers in this sum
Whenever two chameleons of different colours meet they change
colour to the third colour. Describe the shortest sequence of
meetings in which all the chameleons change to green if you start
with 12. . . .
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?
This article suggests some ways of making sense of calculations involving positive and negative numbers.
What is the sum of all the digits in all the integers from one to
In this game the winner is the first to complete a row of three. Are some squares easier to land on than others?
A combination mechanism for a safe comprises thirty-two tumblers
numbered from one to thirty-two in such a way that the numbers in
each wheel total 132... Could you open the safe?
How can we help students make sense of addition and subtraction of negative numbers?
Find a great variety of ways of asking questions which make 8.
Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.
What is the sum of all the three digit whole numbers?
This challenge is to make up YOUR OWN alphanumeric. Each letter
represents a digit and where the same letter appears more than once
it must represent the same digit each time.
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?
There are exactly 3 ways to add 4 odd numbers to get 10. Find all
the ways of adding 8 odd numbers to get 20. To be sure of getting
all the solutions you will need to be systematic. What about. . . .
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?
Investigate $1^n + 19^n + 20^n + 51^n + 57^n + 80^n + 82^n $ and $2^n + 12^n + 31^n + 40^n + 69^n + 71^n + 85^n$ for different values of n.
When I type a sequence of letters my calculator gives the product
of all the numbers in the corresponding memories. What numbers
should I store so that when I type 'ONE' it returns 1, and when I
type. . . .
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.
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
This article explains how to make your own magic square to mark a special occasion with the special date of your choice on the top line.
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?
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 your logical reasoning to work out how many cows and how many
sheep there are in each field.
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
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.
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.
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
Replace each letter with a digit to make this addition correct.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
This addition sum uses all ten digits 0, 1, 2...9 exactly once.
Find the sum and show that the one you give is the only
Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit
numbers such that their total is close to 1500?
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 number has 903 digits. What is the sum of all 903 digits?
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?
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?
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?
Arrange three 1s, three 2s and three 3s in this square so that
every row, column and diagonal adds to the same total.
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?
Can you make square numbers by adding two prime numbers together?
These two group activities use mathematical reasoning - one is
numerical, one geometric.
Well now, what would happen if we lost all the nines in our number
system? Have a go at writing the numbers out in this way and have a
look at the multiplications table.
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.
Find the next number in this pattern: 3, 7, 19, 55 ...
Use the 'double-3 down' dominoes to make a square so that each side
has eight dots.
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant