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

Your vessel, the Starship Diophantus, has become damaged in deep space. Can you use your knowledge of times tables and some lightning reflexes to survive?

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

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

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.

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.

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?

What is the least square number which commences with six two's?

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

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?

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?

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?

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

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

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.

Play this game and see if you can figure out the computer's chosen number.

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!?

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?

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.

This task offers an opportunity to explore all sorts of number relationships, but particularly multiplication.

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

I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?

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. . . .

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

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

The value of the circle changes in each of the following problems. Can you discover its value in each problem?

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

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" .

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?

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?

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.

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?

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

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

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?

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

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?

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?

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

Number problems at primary level that may require resilience.

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

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

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

Can you find different ways of creating paths using these paving slabs?

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!