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 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!

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

There were 22 legs creeping across the web. How many flies? How many spiders?

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

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

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

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. . . .

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 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!

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?

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?

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

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

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?

Number problems at primary level that require careful consideration.

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

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?

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?

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?

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

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

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?

Throw the dice and decide whether to double or halve the number. Will you be the first to reach the target?

Annie and Ben are playing a game with a calculator. What was Annie's secret number?

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

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

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

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

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 work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?

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

Use the information about Sally and her brother to find out how many children there are in the Brown family.

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 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?

Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?

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?

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?

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

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?

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?

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?

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

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

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?