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?

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?

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.

Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.

A game that tests your understanding of remainders.

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.

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

In this game, you can add, subtract, multiply or divide the numbers on the dice. Which will you do so that you get to the end of the number line first?

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

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?

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

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

Given the products of adjacent cells, can you complete this Sudoku?

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. . . .

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?

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.

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

Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.

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?

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

What is the smallest number of answers you need to reveal in order to work out the missing headers?

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

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

Can you complete this jigsaw of the multiplication square?

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.

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

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

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?

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 task combines spatial awareness with addition and multiplication.

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?

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

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.

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

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

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

Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.

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

This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

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?

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

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?

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

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

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

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?