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

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?

What happens when you try and fit the triomino pieces into these two grids?

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

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

Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?

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

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

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

Can you hang weights in the right place to make the equaliser balance?

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....?

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

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?

How many different rhythms can you make by putting two drums on the wheel?

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

Use the information about Sally and her brother to find out how many children there are in the Brown family.

Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.

Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

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

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?

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

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

Investigate the different sounds you can make by putting the owls and donkeys on the wheel.

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

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

Can you make the green spot travel through the tube by moving the yellow spot? Could you draw a tube that both spots would follow?

In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?

Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?

Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?

Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

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

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

How many different triangles can you make on a circular pegboard that has nine pegs?

Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.

There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?

Sort the houses in my street into different groups. Can you do it in any other ways?

If you have only four weights, where could you place them in order to balance this equaliser?