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 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 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.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
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?
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 do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
In the multiplication sum, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
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 replace the letters with numbers? Is there only one solution in each case?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
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?
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 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?
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
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?
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?
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!
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 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?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
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?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?
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?
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?
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 information?
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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?
What is happening at each box in these machines?
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
Use the information to work out how many gifts there are in each pile.
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?
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.
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?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
How would you count the number of fingers in these pictures?
If the answer's 2010, what could the question be?
Find the next number in this pattern: 3, 7, 19, 55 ...
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
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.
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?
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.
Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?
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?
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?