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 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 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!

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In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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

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?

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?

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

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

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

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?

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.

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?

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?

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?

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?

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

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

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

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?

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

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

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?

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?

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

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?

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?

Here is a chance to play a version of the classic Countdown Game.

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?

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

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

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

Number problems at primary level that require careful consideration.

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?

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

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.

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

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

Number problems at primary level that may require resilience.

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

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?

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?

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?