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

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?

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.

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. . . .

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.

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

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.

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. . . .

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?

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. . . .

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?

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. . . .

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

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?

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

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

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

This task combines spatial awareness with addition and multiplication.

This challenge combines addition, multiplication, perseverance and even proof.

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. . . .

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

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

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?

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

In this article, Alf outlines six activities using the Gattegno chart, which help to develop understanding of place value, multiplication and division.

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?

Number problems at primary level that require careful consideration.

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

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

Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?

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!

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

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

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?

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

If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?

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.

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?

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

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?

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

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

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

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

Number problems at primary level that may require resilience.

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

Using the statements, can you work out how many of each type of rabbit there are in these pens?