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?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
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?
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?
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....?
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?
How many different triangles can you make on a circular pegboard that has nine pegs?
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?
Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.
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.
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
A generic circular pegboard resource.
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?
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?
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?
Choose a symbol to put into the number sentence.
Use the interactivity or play this dice game yourself. How could you make it fair?
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?
Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?
Can you fit the tangram pieces into the outlines of the chairs?
A card pairing game involving knowledge of simple ratio.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!
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?
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 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.
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
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. . . .
An interactive activity for one to experiment with a tricky tessellation
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 outlines of these people?
A train building game for 2 players.
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?
Can you fit the tangram pieces into the outlines of these clocks?
Exchange the positions of the two sets of counters in the least possible number of moves
A game for 2 people that everybody knows. You can play with a friend or online. If you play correctly you never lose!
Find out what a "fault-free" rectangle is and try to make some of your own.
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?
Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?