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.

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

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

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

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!

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

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

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 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?

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?

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

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?

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

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

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

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?

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

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

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. . . .

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 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?

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

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

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

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?

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?

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

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

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

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

Number problems at primary level that require careful consideration.

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?

Put a number at the top of the machine and collect a number at the bottom. What do you get? Which numbers get back to themselves?

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

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?

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?

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?

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?

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.

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

This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.

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?