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.

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.

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.

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?

Can you find what the last two digits of the number $4^{1999}$ are?

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?

Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

Where will the point stop after it has turned through 30 000 degrees? I took out my calculator and typed 30 000 ÷ 360. How did this help?

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

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

Find a great variety of ways of asking questions which make 8.

A 3 digit number is multiplied by a 2 digit number and the calculation is written out as shown with a digit in place of each of the *'s. Complete the whole multiplication sum.

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

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. . . .

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

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?

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

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?

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

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

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

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

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

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

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 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?

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?

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?

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" .

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

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

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

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?

Number problems at primary level that require careful consideration.

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

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

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

Number problems at primary level that may require determination.

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

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?

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?

These pictures and answers leave the viewer with the problem "What is the Question". Can you give the question and how the answer follows?