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?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
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?
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?
This challenge combines addition, multiplication, perseverance and even proof.
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
What is the sum of all the three digit whole numbers?
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.
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 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
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?
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?
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?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
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?
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?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
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.
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
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?
What is happening at each box in these machines?
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?
Use the information to work out how many gifts there are in each
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
The value of the circle changes in each of the following problems.
Can you discover its value in each problem?
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
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?
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.
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.
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?
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.
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
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 design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
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?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Got It game for an adult and child. How can you play so that you know you will always win?
This task combines spatial awareness with addition and multiplication.
This dice train has been made using specific rules. How many different trains can you make?
If you had any number of ordinary dice, what are the possible ways
of making their totals 6? What would the product of the dice be
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?
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?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
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?
This number has 903 digits. What is the sum of all 903 digits?