48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
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 replace the letters with numbers? Is there only one
solution in each case?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
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?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Have a go at balancing this equation. Can you find different ways of doing it?
Can you work out some different ways to balance this equation?
What is the sum of all the three digit whole numbers?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
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.
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.
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
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
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.
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?
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 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.
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?
Number problems at primary level that may require determination.
If the answer's 2010, what could the question be?
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?
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?
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.
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
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?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
This number has 903 digits. What is the sum of all 903 digits?
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
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?
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
Find the next number in this pattern: 3, 7, 19, 55 ...
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?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
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?
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.
Number problems at primary level that require careful consideration.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
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?
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.
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?