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?

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.

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

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

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

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

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 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?

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

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?

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.

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.

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

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!

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

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. . . .

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

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 is a game for two players. Choose two numbers from the grid and multiply or divide, then mark your answer on the number line. Can you get four in a row before your partner?

Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

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.

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?

Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?

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

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?

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?

A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.

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?

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?

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

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?

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?

Number problems at primary level that require careful consideration.

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

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

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

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

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

There are over sixty different ways of making 24 by adding, subtracting, multiplying and dividing all four numbers 4, 6, 6 and 8 (using each number only once). How many can you find?

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?

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?

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?