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?

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

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

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

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?

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?

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?

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

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

Find another number that is one short of a square number and when you double it and add 1, the result is also a square number.

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.

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?

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?

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?

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

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

Number problems at primary level that require careful consideration.

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

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.

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?

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?

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

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!

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

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!

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?

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

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

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

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

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?

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?

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

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?

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

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

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?

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

This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.

Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?

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

What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

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

Explore Alex's number plumber. What questions would you like to ask? Don't forget to keep visiting NRICH projects site for the latest developments and questions.

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

This task combines spatial awareness with addition and multiplication.