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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?
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.
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.
If the answer's 2010, what could the question be?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the 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.
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.
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?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Use the information to work out how many gifts there are in each pile.
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
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 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.
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?
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?
Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?
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?
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!
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.
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
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?
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?
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
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 the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?
What is happening at each box in these machines?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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.
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.
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
How would you count the number of fingers in these pictures?
Find the next number in this pattern: 3, 7, 19, 55 ...
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
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?
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.
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?
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?
This number has 903 digits. What is the sum of all 903 digits?
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
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?
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?
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?