Ben’s class were making cutting up number tracks. First they
cut them into twos and added up the numbers on each piece. What
patterns could they see?
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. . . .
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?
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?
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. . . .
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?
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?
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?
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?
What is the sum of all the digits in all the integers from one to
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.
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?
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 the sum of all the three digit whole numbers?
Find a great variety of ways of asking questions which make 8.
Got It game for an adult and child. How can you play so that you know you will always win?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
This challenge combines addition, multiplication, perseverance and even proof.
This task combines spatial awareness with addition and multiplication.
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 is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
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?
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
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?
Bernard Bagnall recommends some primary school problems which use
numbers from the environment around us, from clocks to house
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.
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
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 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.
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?
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
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?
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?
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
A game for 2 people using a pack of cards Turn over 2 cards and try
to make an odd number or a multiple of 3.
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
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.
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?
Use the information to work out how many gifts there are in each
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
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.