How will you work out which numbers have been used to create this multiplication square?

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?

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?

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.

Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?

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

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

Where can you draw a line on a clock face so that the numbers on both sides have the same total?

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

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?

Number problems at primary level that may require resilience.

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?

Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?

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!

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

Number problems at primary level that require careful consideration.

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.

Rocco ran in a 200 m race for his class. Use the information to find out how many runners there were in the race and what Rocco's finishing position was.

Use the information to work out how many gifts there are in each pile.

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?

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

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

How many starfish could there be on the beach, and how many children, if I can see 28 arms?

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!

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

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?

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

Can you score 100 by throwing rings on this board? Is there more than way to do it?

On the table there is a pile of oranges and lemons that weighs exactly one kilogram. Using the information, can you work out how many lemons there are?

Find the next number in this pattern: 3, 7, 19, 55 ...

Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.

This task combines spatial awareness with addition and multiplication.

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

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?

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?

Put a number at the top of the machine and collect a number at the bottom. What do you get? Which numbers get back to themselves?

Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?

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

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?

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?

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?

On a calculator, make 15 by using only the 2 key and any of the four operations keys. How many ways can you find to do it?

Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?

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

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.

There are three buckets each of which holds a maximum of 5 litres. Use the clues to work out how much liquid there is in each bucket.