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?

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?

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

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

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

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?

Using the digits 1, 2, 3, 4, 5, 6, 7 and 8, mulitply a two two digit numbers are multiplied to give a four digit number, so that the expression is correct. How many different solutions can you find?

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?

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.

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

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

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

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?

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?

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.

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. . . .

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

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.

Choose any four consecutive even numbers. Multiply the two middle numbers together. Multiply the first and last numbers. Now subtract your second answer from the first. Try it with your own. . . .

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

Alf describes how the Gattegno chart helped a class of 7-9 year olds gain an awareness of place value and of the inverse relationship between multiplication and division.

Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some. . . .

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.

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?

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

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

Does this 'trick' for calculating multiples of 11 always work? Why or why not?

Choose two digits and arrange them to make two double-digit numbers. Now add your double-digit numbers. Now add your single digit numbers. Divide your double-digit answer by your single-digit answer. . . .

This Sudoku requires you to do some working backwards before working forwards.

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?

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

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!?

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

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

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

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

What is the remainder when 2^{164}is divided by 7?

Take the number 6 469 693 230 and divide it by the first ten prime numbers and you'll find the most beautiful, most magic of all numbers. What is it?

Take any four digit number. Move the first digit to the end and move the rest along. Now add your two numbers. Did you get a multiple of 11?

Number problems at primary level that may require resilience.

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

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

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

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

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?

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. . . .

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