The number 10112359550561797752808988764044943820224719 is called a 'slippy number' because, when the last digit 9 is moved to the front, the new number produced is the slippy number multiplied by 9.

When I type a sequence of letters my calculator gives the product of all the numbers in the corresponding memories. What numbers should I store so that when I type 'ONE' it returns 1, and when I type. . . .

Visitors to Earth from the distant planet of Zub-Zorna were amazed when they found out that when the digits in this multiplication were reversed, the answer was the same! Find a way to explain. . . .

Investigate $1^n + 19^n + 20^n + 51^n + 57^n + 80^n + 82^n $ and $2^n + 12^n + 31^n + 40^n + 69^n + 71^n + 85^n$ for different values of n.

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

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?

Amazing as it may seem the three fives remaining in the following `skeleton' are sufficient to reconstruct the entire long division sum.

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

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

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

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?

The number 8888...88M9999...99 is divisible by 7 and it starts with the digit 8 repeated 50 times and ends with the digit 9 repeated 50 times. What is the value of the digit M?

The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?

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

When the number x 1 x x x is multiplied by 417 this gives the answer 9 x x x 0 5 7. Find the missing digits, each of which is represented by an "x" .

Find the number which has 8 divisors, such that the product of the divisors is 331776.

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

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.

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

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

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?

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

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

Can you score 100 by throwing rings on this board? Is there more than way to do it?

Rocco ran in a 200 m race for his class. Use the information to find out how many runners there were in the race and what Rocco's finishing position was.

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

On the table there is a pile of oranges and lemons that weighs exactly one kilogram. Using the information, can you work out how many lemons there are?

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.

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 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?

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

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?

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?

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?

Number problems at primary level that may require determination.

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

Number problems at primary level that require careful consideration.

Use this information to work out whether the front or back wheel of this bicycle gets more wear and tear.

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?

Chandrika was practising a long distance run. Can you work out how long the race was from the information?

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?

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

Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?

Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?

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