What happens when you add the digits of a number then multiply the
result by 2 and you keep doing this? You could try for different
numbers and different rules.
If the answer's 2010, what could the question be?
This magic square has operations written in it, to make it into a
maze. Start wherever you like, go through every cell and go out a
total of 15!
Find the next number in this pattern: 3, 7, 19, 55 ...
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
There are 44 people coming to a dinner party. There are 15 square
tables that seat 4 people. Find a way to seat the 44 people using
all 15 tables, with no empty places.
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
These sixteen children are standing in four lines of four, one
behind the other. They are each holding a card with a number on it.
Can you work out the missing numbers?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
At the beginning of May Tom put his tomato plant outside. On the
same day he sowed a bean in another pot. When will the two be the
Zumf makes spectacles for the residents of the planet Zargon, who
have either 3 eyes or 4 eyes. How many lenses will Zumf need to
make all the different orders for 9 families?
Explore Alex's number plumber. What questions would you like to
ask? Don't forget to keep visiting NRICH projects site for the
latest developments and questions.
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
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.
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
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?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
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?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
There were 22 legs creeping across the web. How many flies? How many spiders?
Can you work out the arrangement of the digits in the square so
that the given products are correct? The numbers 1 - 9 may be used
once and once only.
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?
Twizzle, a female giraffe, needs transporting to another zoo. Which
route will give the fastest journey?
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
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?
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
What is happening at each box in these machines?
This number has 903 digits. What is the sum of all 903 digits?
Can you work out some different ways to balance this equation?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?
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?
Have a go at balancing this equation. Can you find different ways of doing it?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
This task combines spatial awareness with addition and multiplication.
This challenge combines addition, multiplication, perseverance and even proof.
Shut the Box game for an adult and child. Can you turn over the cards which match the numbers on the dice?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
Can you find which shapes you need to put into the grid to make the
totals at the end of each row and the bottom of each column?
An old game but lots of arithmetic!