What happens when you try and fit the triomino pieces into these
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?
Find out how we can describe the "symmetries" of this triangle and
investigate some combinations of rotating and flipping it.
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 cover the camel with these pieces?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
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?
Use the clues to colour each square.
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 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.
Can you find all the different ways of lining up these Cuisenaire
Use the interactivity to find out how many quarter turns the man must rotate through to look like each of the pictures.
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
How many trains can you make which are the same length as Matt's, using rods that are identical?
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 work out how to balance this equaliser? You can put more
than one weight on a hook.
Use your mouse to move the red and green parts of this disc. Can
you make images which show the turnings described?
Explore the different tunes you can make with these five gourds.
What are the similarities and differences between the two tunes you
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?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Sort the houses in my street into different groups. Can you do it in any other ways?
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.
How many different triangles can you make on a circular pegboard that has nine pegs?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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 this interactive strategy game for 2
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Investigate the different sounds you can make by putting the owls
and donkeys on the wheel.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?
How many different rhythms can you make by putting two drums on the
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
Can you fit the tangram pieces into the outline of this telephone?
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 brazier for roasting chestnuts?
Can you fit the tangram pieces into the outline of Little Fung at the table?
Can you fit the tangram pieces into the outlines of the chairs?
A game for 2 people that everybody knows. You can play with a
friend or online. If you play correctly you never lose!
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?
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?
An interactive activity for one to experiment with a tricky tessellation
A variant on the game Alquerque