In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?

This challenge is about finding the difference between numbers which have the same tens digit.

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?

In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

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 cards 2, 4, 6, 8, +, - and =, what number statements can you make?

You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?

There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?

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?

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

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

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

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?

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?

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

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?

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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

Find your way through the grid starting at 2 and following these operations. What number do you end on?

Find all the numbers that can be made by adding the dots on two dice.

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!

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

Your challenge is to find the longest way through the network following this rule. You can start and finish anywhere, and with any shape, as long as you follow the correct order.

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?

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?

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

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

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?

What happens when you round these three-digit numbers to the nearest 100?

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.