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?

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?

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?

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

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?

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

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?

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

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.

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

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.

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

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?

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

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

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?

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?

Number problems at primary level that may require determination.

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

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

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?

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

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

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!

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?

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

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.

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

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?

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

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

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

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?

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?

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

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?

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

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

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

Number problems at primary level that require careful consideration.

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

Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?

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?

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