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

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

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

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

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?

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.

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

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?

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!

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?

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

Can you complete this jigsaw of the multiplication square?

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.

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

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.

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?

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

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?

A game that tests your understanding of remainders.

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.

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?

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

You can work out the number someone else is thinking of as follows. Ask a friend to think of any natural number less than 100. Then ask them to tell you the remainders when this number is divided by. . . .

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

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

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

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 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?

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?

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?

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?

Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.

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

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

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?

Number problems at primary level that may require determination.

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

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

Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?

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,. . . .

A game for 2 or more players with a pack of cards. Practise your skills of addition, subtraction, multiplication and division to hit the target score.

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

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?

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

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?

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