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?

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?

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.

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

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

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?

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?

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?

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?

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?

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

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?

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

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

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 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?

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

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

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

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?

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

Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.

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

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 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?

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

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

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?

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

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

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?

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

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.

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

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

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

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

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?

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

Number problems at primary level that may require resilience.

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.

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