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?

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?

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?

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

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

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

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?

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

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?

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

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

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?

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

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

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. . . .

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?

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

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

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

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

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

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?

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

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

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?

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?

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

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

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?

Number problems at primary level that require careful consideration.

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

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

Number problems at primary level that may require determination.

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

Use your logical reasoning to work out how many cows and how many sheep there are in each field.

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.

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

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?

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?

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?

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

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

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?