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?

Number problems at primary level that may require resilience.

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.

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.

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

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?

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?

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

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.

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.

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

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

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

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?

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

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

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

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

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

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

Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?

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

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

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

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

This task combines spatial awareness with addition and multiplication.

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

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.

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. . . .

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.

Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.

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

The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?

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?

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

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

A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

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

Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?

Amy has a box containing domino pieces but she does not think it is a complete set. Which of her domino pieces are missing?

Number problems at primary level that require careful consideration.

Annie cut this numbered cake into 3 pieces with 3 cuts so that the numbers on each piece added to the same total. Where were the cuts and what fraction of the whole cake was each piece?

Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?

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

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