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 is the sum of all the three digit whole numbers?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
If the answer's 2010, what could the question be?
There are over sixty different ways of making 24 by adding,
subtracting, multiplying and dividing all four numbers 4, 6, 6 and
8 (using each number only once). How many can you find?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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.
Number problems at primary level that may require determination.
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?
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.
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
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.
Can you replace the letters with numbers? Is there only one
solution in each case?
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?
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?
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?
Can you work out some different ways to balance this equation?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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?
Have a go at balancing this equation. Can you find different ways of doing it?
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
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?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
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.
Use the information to work out how many gifts there are in each
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?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
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?
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?
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.
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
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?
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?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Can you arrange 5 different digits (from 0 - 9) in the cross in the
What is happening at each box in these machines?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
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 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?
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.
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?