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?
Can you put the 25 coloured tiles into the 5 x 5 square so that no
column, no row and no diagonal line have tiles of the same colour
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?
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....?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
Can you find all the different ways of lining up these Cuisenaire
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?
Find out how we can describe the "symmetries" of this triangle and
investigate some combinations of rotating and flipping it.
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
Our 2008 Advent Calendar has a 'Making Maths' activity for every
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?
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?
Explore the different tunes you can make with these five gourds.
What are the similarities and differences between the two tunes you
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
A simulation of target archery practice
Can you fit the tangram pieces into the outline of this junk?
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.
Find out what a "fault-free" rectangle is and try to make some of
Can you fit the tangram pieces into the outline of Mai Ling?
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 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?
A card pairing game involving knowledge of simple ratio.
Can you fit the tangram pieces into the outlines of these people?
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 these clocks?
Can you fit the tangram pieces into the outline of the child walking home from school?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
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.
A train building game for 2 players.
Use the Cuisenaire rods environment to investigate ratio. Can you
find pairs of rods in the ratio 3:2? How about 9:6?
Work out the fractions to match the cards with the same amount of
Can you find all the different triangles on these peg boards, and
find their angles?
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
Can you fit the tangram pieces into the outlines of the chairs?
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?
Can you fit the tangram pieces into the outline of Granma T?
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. . . .