Take the number 6 469 693 230 and divide it by the first ten prime numbers and you'll find the most beautiful, most magic of all numbers. What is it?

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

Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.

56 406 is the product of two consecutive numbers. What are these two numbers?

All the girls would like a puzzle each for Christmas and all the boys would like a book each. Solve the riddle to find out how many puzzles and books Santa left.

On a calculator, make 15 by using only the 2 key and any of the four operations keys. How many ways can you find to do it?

Using the numbers 1, 2, 3, 4 and 5 once and only once, and the operations x and ÷ once and only once, what is the smallest whole number you can make?

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

Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?

Resources to support understanding of multiplication and division through playing with number.

Chandrika was practising a long distance run. Can you work out how long the race was from the information?

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

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?

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

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

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!

There are four equal weights on one side of the scale and an apple on the other side. What can you say that is true about the apple and the weights from the picture?

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

Use the information to work out how many gifts there are in each pile.

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.

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

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?

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!

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

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?

This task combines spatial awareness with addition and multiplication.

Where can you draw a line on a clock face so that the numbers on both sides have the same total?

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 big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?

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

This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.

Number problems at primary level that require careful consideration.

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?

Number problems at primary level that may require determination.

In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.

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

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

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

This problem is designed to help children to learn, and to use, the two and three times tables.

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?

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

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

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

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

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?

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?

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?