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?

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

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 were 22 legs creeping across the web. How many flies? How many spiders?

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.

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

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?

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

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

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?

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

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 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?

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.

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

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

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

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?

Number problems at primary level that require careful consideration.

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

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?

Number problems at primary level that may require resilience.

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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

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

Resources to support understanding of multiplication and division through playing with number.

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!

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?

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

This task combines spatial awareness with addition and multiplication.

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

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?

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

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?

Twizzle, a female giraffe, needs transporting to another zoo. Which route will give the fastest journey?

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

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

Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?

How would you count the number of fingers in these pictures?

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

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

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.

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?