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

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

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

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

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

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?

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?

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?

How many trains can you make which are the same length as Matt's, using rods that are identical?

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

Use the interactivity to find out how many quarter turns the man must rotate through to look like each of the pictures.

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

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

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

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

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

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

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

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

If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?

A shape and space game for 2,3 or 4 players. Be the last person to be able to place a pentomino piece on the playing board. Play with card, or on the computer.

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....?

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?

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

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

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

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

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

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

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?

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?

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.

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

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

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.

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

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?

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?

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.

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?

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

An interactive activity for one to experiment with a tricky tessellation

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

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

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