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....?
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 find all the different ways of lining up these Cuisenaire rods?
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?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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?
Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.
How many different triangles can you make on a circular pegboard that has nine pegs?
Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.
Try out the lottery that is played in a far-away land. What is the chance of winning?
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?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Can you fit the tangram pieces into the outline of this junk?
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?
An interactive activity for one to experiment with a tricky tessellation
A game for 2 people that everybody knows. You can play with a friend or online. If you play correctly you never lose!
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?
Can you fit the tangram pieces into the outline of Granma T?
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
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?
Can you find all the different triangles on these peg boards, and find their angles?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Work out the fractions to match the cards with the same amount of money.
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?
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 card pairing game involving knowledge of simple ratio.
Find out what a "fault-free" rectangle is and try to make some of your own.
A train building game for 2 players.
Can you fit the tangram pieces into the outlines of the chairs?
A generic circular pegboard resource.
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?
If you have only four weights, where could you place them in order to balance this equaliser?
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. . . .
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
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 shape. How would you describe it?
Can you fit the tangram pieces into the outlines of the watering can and man in a boat?