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 was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?

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

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?

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

NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.

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

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 fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?

Can you fit the tangram pieces into the outline of Mai Ling?

Can you fit the tangram pieces into the outlines of these clocks?

Can you fit the tangram pieces into the outlines of the candle and sundial?

Ahmed has some wooden planks to use for three sides of a rabbit run against the shed. What quadrilaterals would he be able to make with the planks of different lengths?

Board Block game for two. Can you stop your partner from being able to make a shape on the board?

Can you fit the tangram pieces into the outline of this junk?

An interactive game for 1 person. You are given a rectangle with 50 squares on it. Roll the dice to get a percentage between 2 and 100. How many squares is this? Keep going until you get 100. . . .

A game for 2 people that can be played on line or with pens and paper. Combine your knowledege of coordinates with your skills of strategic thinking.

Can you fit the tangram pieces into the outline of the child walking home from school?

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

Work out the fractions to match the cards with the same amount of money.

Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?

A game to be played against the computer, or in groups. Pick a 7-digit number. A random digit is generated. What must you subract to remove the digit from your number? the first to zero wins.

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?

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

How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!

Use the interactivity or play this dice game yourself. How could you make it fair?

What shaped overlaps can you make with two circles which are the same size? What shapes are 'left over'? What shapes can you make when the circles are different sizes?

What are the coordinates of the coloured dots that mark out the tangram? Try changing the position of the origin. What happens to the coordinates now?

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

Can you fit the tangram pieces into the outlines of these people?

Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?

Exchange the positions of the two sets of counters in the least possible number of moves

An interactive activity for one to experiment with a tricky tessellation

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

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

Can you fit the tangram pieces into the outline of Granma T?

A game for 2 people that everybody knows. You can play with a friend or online. If you play correctly you never lose!

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?

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....?

An interactive game to be played on your own or with friends. Imagine you are having a party. Each person takes it in turns to stand behind the chair where they will get the most chocolate.

Can you fit the tangram pieces into the outline of this telephone?

Can you fit the tangram pieces into the outline of Little Fung at the table?

Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?

Can you fit the tangram pieces into the outline of Little Ming playing the board game?

Can you fit the tangram pieces into the outline of this shape. How would you describe it?