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

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?

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

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

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

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

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

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?

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....?

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

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

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

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

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

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

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?

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?

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

Can you fit the tangram pieces into the outlines of the chairs?

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

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

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

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

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?

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

An interactive activity for one to experiment with a tricky tessellation

Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?

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

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?

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

Move just three of the circles so that the triangle faces in the opposite direction.

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. . . .

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?

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.

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

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

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

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

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?

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

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

How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?