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

Given the products of adjacent cells, can you complete this Sudoku?

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.

When I type a sequence of letters my calculator gives the product of all the numbers in the corresponding memories. What numbers should I store so that when I type 'ONE' it returns 1, and when I type. . . .

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?

The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?

Can you find what the last two digits of the number $4^{1999}$ are?

A 3 digit number is multiplied by a 2 digit number and the calculation is written out as shown with a digit in place of each of the *'s. Complete the whole multiplication sum.

Investigate $1^n + 19^n + 20^n + 51^n + 57^n + 80^n + 82^n $ and $2^n + 12^n + 31^n + 40^n + 69^n + 71^n + 85^n$ for different values of n.

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

Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.

The number 8888...88M9999...99 is divisible by 7 and it starts with the digit 8 repeated 50 times and ends with the digit 9 repeated 50 times. What is the value of the digit M?

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

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

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

What is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like? You can only use each digit once.

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.

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

In this game, you can add, subtract, multiply or divide the numbers on the dice. Which will you do so that you get to the end of the number line first?

I'm thinking of a number. When my number is divided by 5 the remainder is 4. When my number is divided by 3 the remainder is 2. Can you find my number?

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?

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

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?

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?

Find the number which has 8 divisors, such that the product of the divisors is 331776.

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?

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

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

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

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.

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?

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

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

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?

Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?

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?

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!

Can you complete this jigsaw of the multiplication square?

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?

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

Benâ€™s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

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

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?

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

A game that tests your understanding of remainders.

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

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?