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?

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

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

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?

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?

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?

Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?

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?

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

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.

Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

Can you replace the letters with numbers? Is there only one solution in each case?

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 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?

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?

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.

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

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

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!

Number problems at primary level that require careful consideration.

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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?

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

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?

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!

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?

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?

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?

These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?

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?

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

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

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

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?

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

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

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

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?

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

This challenge combines addition, multiplication, perseverance and even proof.

During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?

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?

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

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

Chandrika was practising a long distance run. Can you work out how long the race was from the information?

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

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