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?

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?

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

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?

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?

Are these statements always true, sometimes true or never true?

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.

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!

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

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.

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

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?

This challenge encourages you to explore dividing a three-digit number by a single-digit 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?

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

Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?

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

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.

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.

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 work out some different ways to balance this equation?

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

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

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?

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

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

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 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?

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.

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?

Each clue in this Sudoku is the product of the two numbers in adjacent cells.

Number problems at primary level that may require resilience.

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

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

If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?

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

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?

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

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

This article for teachers describes how modelling number properties involving multiplication using an array of objects not only allows children to represent their thinking with concrete materials,. . . .

Can you complete this jigsaw of the multiplication square?

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?

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?

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?

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.

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

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