56 406 is the product of two consecutive numbers. What are these two numbers?
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.
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?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
Here is a chance to play a version of the classic Countdown Game.
In this game, you can add, subtract, multiply or divide the numbers on the dice. Which will you do so that you get to the end of the number line first?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
How will you work out which numbers have been used to create this multiplication square?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?
Can you work out what a ziffle is on the planet Zargon?
Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?
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?
An old game but lots of arithmetic!
Ben’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?
Shut the Box game for an adult and child. Can you turn over the cards which match the numbers on the dice?
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?
This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!
Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?
Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.
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?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
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?
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!
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?
This task combines spatial awareness with addition and multiplication.
Play this game and see if you can figure out the computer's chosen number.
How many starfish could there be on the beach, and how many children, if I can see 28 arms?
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.
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
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?
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?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
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?
There are over sixty different ways of making 24 by adding, subtracting, multiplying and dividing all four numbers 4, 6, 6 and 8 (using each number only once). How many can you find?
What is the sum of all the three digit whole numbers?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
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?
Does this 'trick' for calculating multiples of 11 always work? Why or why not?
How would you count the number of fingers in these pictures?
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.
There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
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?
Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?
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?