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

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

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?

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

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?

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.

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

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

This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?

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

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

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?

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?

In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.

Take the number 6 469 693 230 and divide it by the first ten prime numbers and you'll find the most beautiful, most magic of all numbers. What is it?

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?

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

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?

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

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?

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?

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

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?

This task combines spatial awareness with addition and multiplication.

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 challenge combines addition, multiplication, perseverance and even proof.

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!

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

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

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

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

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

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?

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

EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.

After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?

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

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

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

Number problems at primary level that may require resilience.

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