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.

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?

Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?

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?

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 arrange 5 different digits (from 0 - 9) in the cross in the way described?

Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?

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 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?

This challenge encourages you to explore dividing a three-digit number by a single-digit number.

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.

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?

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?

Using the statements, can you work out how many of each type of rabbit there are in these pens?

Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.

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?

Can you order the digits from 1-6 to make a number which is divisible by 6 so when the last digit is removed it becomes a 5-figure number divisible by 5, and so on?

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.

Have a go at balancing this equation. Can you find different ways of doing it?

Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?

Using the numbers 1, 2, 3, 4 and 5 once and only once, and the operations x and ÷ once and only once, what is the smallest whole number you can make?

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?

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.

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?

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

Can you work out some different ways to balance this equation?

The value of the circle changes in each of the following problems. Can you discover its value in each problem?

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!

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

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?

Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?

Use your logical reasoning to work out how many cows and how many sheep there are in each field.

This number has 903 digits. What is the sum of all 903 digits?

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.

Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?

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?

This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.

Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.

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?

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?

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

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?

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?

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?