Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?

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

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

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

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?

This task combines spatial awareness with addition and multiplication.

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

Benâ€™s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

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?

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

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

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?

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

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?

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!

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?

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

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

Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.

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

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

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 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?

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?

Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?

Number problems at primary level that may require resilience.

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

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

A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.

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?

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

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

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

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?

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

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.

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

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?

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

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?

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?

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.

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.

The triangles in these sets are similar - can you work out the lengths of the sides which have question marks?