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?

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?

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?

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

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?

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?

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

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?

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?

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

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 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.

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

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

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 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.

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

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?

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

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.

In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.

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.

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!

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

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?

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

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

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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?

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?

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

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?

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

Twizzle, a female giraffe, needs transporting to another zoo. Which route will give the fastest journey?

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

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?

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

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?

Find another number that is one short of a square number and when you double it and add 1, the result is also a square number.

At the beginning of May Tom put his tomato plant outside. On the same day he sowed a bean in another pot. When will the two be the same height?

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

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?

Claire thinks she has the most sports cards in her album. "I have 12 pages with 2 cards on each page", says Claire. Ross counts his cards. "No! I have 3 cards on each of my pages and there are. . . .

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?