Can you order the digits from 1-6 to make a number which is divisible by 6 so when the last digit is removed it becomes a 5-figure number divisible by 5, and so on?

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

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?

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

Can you replace the letters with numbers? Is there only one solution in each case?

Can you work out some different ways to balance this equation?

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?

Have a go at balancing this equation. Can you find different ways of doing it?

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

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!

Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?

In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?

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

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?

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.

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!

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

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

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?

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

This challenge encourages you to explore dividing a three-digit number by a single-digit number.

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

We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?

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

This problem is designed to help children to learn, and to use, the two and three times tables.

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

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?

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

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?

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

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

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?

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?

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

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?

Chandrika was practising a long distance run. Can you work out how long the race was from the information?

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?

Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.

There are four equal weights on one side of the scale and an apple on the other side. What can you say that is true about the apple and the weights from the picture?

EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.

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?

Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.

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