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

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

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?

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 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?

Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.

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

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.

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

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.

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

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

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

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

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?

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

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?

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?

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?

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

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

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

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?

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

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

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?

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

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?

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.

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?

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?

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?

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?

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

This challenge extends the Plants investigation so now four or more children are involved.

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.

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

In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?

You have 5 darts and your target score is 44. How many different ways could you score 44?

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

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?

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

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?

These two group activities use mathematical reasoning - one is numerical, one geometric.