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.
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 find all the different ways of lining up these Cuisenaire
Use the clues to colour each square.
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Can you cover the camel with these pieces?
What happens when you try and fit the triomino pieces into these
How many different rhythms can you make by putting two drums on the
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?
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?
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....?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
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 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
Terry and Ali are playing a game with three balls. Is it fair that
Terry wins when the middle ball is red?
How many trains can you make which are the same length as Matt's,
using rods that are identical?
Use your mouse to move the red and green parts of this disc. Can
you make images which show the turnings described?
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
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?
Sort the houses in my street into different groups. Can you do it in any other ways?
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
Explore the different tunes you can make with these five gourds.
What are the similarities and differences between the two tunes you
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
Place six toy ladybirds into the box so that there are two
ladybirds in every column and every row.
Investigate the different sounds you can make by putting the owls
and donkeys on the wheel.
How many different ways can you find to join three equilateral
triangles together? Can you convince us that you have found them
How many different triangles can you make on a circular pegboard
that has nine pegs?
Try out the lottery that is played in a far-away land. What is the
chance of winning?
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.
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
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.
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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 people?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Can you fit the tangram pieces into the outlines of these clocks?
A variant on the game Alquerque
A game for 2 people that everybody knows. You can play with a
friend or online. If you play correctly you never lose!
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?