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?

Benâ€™s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

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?

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.

If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?

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?

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?

This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?

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

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

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

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?

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.

EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.

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?

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.

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 at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.

A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

Put a number at the top of the machine and collect a number at the bottom. What do you get? Which numbers get back to themselves?

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

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

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.

Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.

Use the information to work out how many gifts there are in each pile.

How would you count the number of fingers in these pictures?

Annie cut this numbered cake into 3 pieces with 3 cuts so that the numbers on each piece added to the same total. Where were the cuts and what fraction of the whole cake was each piece?

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.

This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?

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

Where can you draw a line on a clock face so that the numbers on both sides have the same total?

The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?

In this investigation, you are challenged to make mobile phone numbers which are easy to remember. What happens if you make a sequence adding 2 each time?

What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?

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

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

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

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?

A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.