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

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

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

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

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?

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

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?

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?

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

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?

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

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 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?

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

Try out the lottery that is played in a far-away land. What is the chance of winning?

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

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.

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?

Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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 out what a "fault-free" rectangle is and try to make some of your own.

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?

Can you find all the different ways of lining up these Cuisenaire rods?

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

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?

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

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?

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

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?

Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?

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?

A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

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

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

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?

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?

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

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

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 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.

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

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

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?

These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?

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 this matching game, you have to decide how long different events take.