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 find all the different ways of lining up these Cuisenaire
How many different triangles can you make on a circular pegboard
that has nine pegs?
Use the clues to colour each square.
How many different rhythms can you make by putting two drums on the
Can you cover the camel with these pieces?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
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?
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....?
What happens when you try and fit the triomino pieces into these
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
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?
Find out how we can describe the "symmetries" of this triangle and
investigate some combinations of rotating and flipping it.
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
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?
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
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?
Sort the houses in my street into different groups. Can you do it in any other ways?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Place six toy ladybirds into the box so that there are two
ladybirds in every column and every row.
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.
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
Use the interactivity to find out how many quarter turns the man
must rotate through to look like each of the pictures.
Try out the lottery that is played in a far-away land. What is the
chance of winning?
If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?
Investigate the different sounds you can make by putting the owls
and donkeys on the wheel.
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?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Place the numbers 1 to 6 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.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
How many different ways can you find to join three equilateral
triangles together? Can you convince us that you have found them
This 100 square jigsaw is written in code. It starts with 1 and
ends with 100. Can you build it up?
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?
Use your mouse to move the red and green parts of this disc. Can
you make images which show the turnings described?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
How many trains can you make which are the same length as Matt's,
using rods that are identical?
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
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 outlines of these clocks?
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 people?
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.