Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
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 fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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?
Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
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?
56 406 is the product of two consecutive numbers. What are these two numbers?
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.
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?
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 happens?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
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?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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?
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!
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 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!
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?
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
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 each time?
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
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.
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?
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Use the information to work out how many gifts there are in each pile.
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?
This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
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?
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
What is happening at each box in these machines?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
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.
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
How would you count the number of fingers in these pictures?
If the answer's 2010, what could the question be?
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.
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?
Can you work out what a ziffle is on the planet Zargon?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?