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?

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!

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

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

Given the products of adjacent cells, can you complete this Sudoku?

Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.

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

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

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!

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?

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

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

Each clue in this Sudoku is the product of the two numbers in adjacent cells.

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

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.

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?

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

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

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 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?

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?

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

Does this 'trick' for calculating multiples of 11 always work? Why or why not?

Your vessel, the Starship Diophantus, has become damaged in deep space. Can you use your knowledge of times tables and some lightning reflexes to survive?

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.

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 you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

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?

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?

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?

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

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

Can you find different ways of creating paths using these paving slabs?

This article for teachers describes how modelling number properties involving multiplication using an array of objects not only allows children to represent their thinking with concrete materials,. . . .

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

Number problems at primary level that may require resilience.

Number problems at primary level that require careful consideration.

Here is a chance to play a version of the classic Countdown Game.

Can you each work out the number on your card? What do you notice? How could you sort the cards?

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

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'.

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

56 406 is the product of two consecutive numbers. What are these two numbers?

We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?

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.