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?

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

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

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

Our 2008 Advent Calendar has a 'Making Maths' activity for every 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.

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....?

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

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?

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?

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?

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

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

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

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

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.

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 outlines of the candle and sundial?

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.

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

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

Use the Cuisenaire rods environment to investigate ratio. Can you find pairs of rods in the ratio 3:2? How about 9:6?

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

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

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 Granma T?

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

Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

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

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

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?

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

An interactive activity for one to experiment with a tricky tessellation

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. . . .

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

Train game for an adult and child. Who will be the first to make the train?

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

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?

Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?

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

Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?

Use the blue spot to help you move the yellow spot from one star to the other. How are the trails of the blue and yellow spots related?

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