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?

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?

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.

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

Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.

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

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

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

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

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?

This number has 903 digits. What is the sum of all 903 digits?

Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?

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

Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?

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.

Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?

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

Shut the Box game for an adult and child. Can you turn over the cards which match the numbers on the dice?

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.

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?

Twizzle, a female giraffe, needs transporting to another zoo. Which route will give the fastest journey?

In this investigation, you are challenged to make mobile phone numbers which are easy to remember. What happens if you make a sequence adding 2 each time?

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?

If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?

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

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

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 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.

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

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

Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?

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?

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?

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

Can you complete this jigsaw of the multiplication square?

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?

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

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?

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 task combines spatial awareness with addition and multiplication.

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

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

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.

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

Can you work out some different ways to balance this equation?

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

Have a go at balancing this equation. Can you find different ways of doing it?

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

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?