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

There are three buckets each of which holds a maximum of 5 litres. Use the clues to work out how much liquid there is in each bucket.

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!

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

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

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

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

The value of the circle changes in each of the following problems. Can you discover its value in each problem?

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.

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

Can you replace the letters with numbers? Is there only one solution in each case?

Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.

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

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

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

These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing 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?

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?

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?

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?

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?

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

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

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!

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

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?

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.

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

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

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?

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?

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

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?

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?

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?

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

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

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?

Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?

What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.

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.

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

How would you count the number of fingers in these pictures?

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

Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?

This task combines spatial awareness with addition and multiplication.

This challenge combines addition, multiplication, perseverance and even proof.

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?

Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?