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?

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?

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

Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?

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?

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

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

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

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

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

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

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

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

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,. . . .

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?

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

Claire thinks she has the most sports cards in her album. "I have 12 pages with 2 cards on each page", says Claire. Ross counts his cards. "No! I have 3 cards on each of my pages and there are. . . .

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

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?

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

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?

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

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

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

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.

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?

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?

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?

Can you complete this jigsaw of the multiplication square?

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.

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

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

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.

Number problems at primary level that may require determination.

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?

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

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?

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?

How will you decide which way of flipping over and/or turning the grid will give you the highest total?

Resources to support understanding of multiplication and division through playing with number.

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

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

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

This task combines spatial awareness with addition and multiplication.

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