A game that tests your understanding of remainders.

Each clue in this Sudoku is the product of the two numbers in adjacent cells.

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

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

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

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?

6! = 6 x 5 x 4 x 3 x 2 x 1. The highest power of 2 that divides exactly into 6! is 4 since (6!) / (2^4 ) = 45. What is the highest power of two that divides exactly into 100!?

You can work out the number someone else is thinking of as follows. Ask a friend to think of any natural number less than 100. Then ask them to tell you the remainders when this number is divided by. . . .

Find the highest power of 11 that will divide into 1000! exactly.

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

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.

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

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?

Imagine you were given the chance to win some money... and imagine you had nothing to lose...

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?

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

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

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?

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.

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?

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

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?

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

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.

Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

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

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

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" .

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.

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

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

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

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?

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

On my calculator I divided one whole number by another whole number and got the answer 3.125. If the numbers are both under 50, what are they?

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. . . .

Number problems at primary level that may require resilience.

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

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?

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

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

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.

This task combines spatial awareness with addition and multiplication.

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?