This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.

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

Unmultiply is a game of quick estimation. You need to find two numbers that multiply together to something close to the given target - fast! 10 levels with a high scores table.

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.

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?

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 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?

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

Can you complete this jigsaw of the multiplication square?

Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.

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?

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?

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

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?

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 a great variety of ways of asking questions which make 8.

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

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

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

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

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?

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 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?

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

A game that tests your understanding of remainders.

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?

Explore Alex's number plumber. What questions would you like to ask? Don't forget to keep visiting NRICH projects site for the latest developments and questions.

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 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.

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 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!

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.

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?

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

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

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

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 each work out the number on your card? What do you notice? How could you sort the cards?

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

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!

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?

6! = 6 x 5 x 4 x 3 x 2 x 1. The highest power of 2 that divides exactly into 6! is 4 since (6!) / (2^4 ) = 45. What is the highest power of two that divides exactly into 100!?

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

Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?

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?

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?

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 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.