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?
Can you order the digits from 1-6 to make a number which is
divisible by 6 so when the last digit is removed it becomes a
5-figure number divisible by 5, and so on?
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?
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?
56 406 is the product of two consecutive numbers. What are these
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Can you work out some different ways to balance this equation?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
This challenge encourages you to explore dividing a three-digit number by a single-digit 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?
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?
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Find the next number in this pattern: 3, 7, 19, 55 ...
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?
Can you fill in this table square? The numbers 2 -12 were used to
generate it with just one number used twice.
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.
Have a go at balancing this equation. Can you find different ways of doing it?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
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.
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?
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?
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?
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?
This number has 903 digits. What is the sum of all 903 digits?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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.
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?
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
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!
All the girls would like a puzzle each for Christmas and all the
boys would like a book each. Solve the riddle to find out how many
puzzles and books Santa left.
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
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?
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
Can you see how these factor-multiple chains work? Find the chain
which contains the smallest possible numbers. How about the largest
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?
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?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
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!
There are four equal weights on one side of the scale and an apple
on the other side. What can you say that is true about the apple
and the weights from the picture?
On my calculator I divided one whole number by another whole number and got the answer 3.125 If the numbers are both under 50, what are they?
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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.