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.

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

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?

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?

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

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

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

Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?

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

Can you use the information to find out which cards I have used?

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

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.

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?

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?

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?

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?

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?

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?

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

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?

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.

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

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?

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.

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.

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?

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

Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?

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

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?

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

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!

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

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

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

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

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

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

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?

If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?

Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.