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 rhythms can you make by putting two drums on the
What happens when you try and fit the triomino pieces into these
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
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 work out how to balance this equaliser? You can put more
than one weight on a hook.
How many different triangles can you make on a circular pegboard that has nine pegs?
How many trains can you make which are the same length as Matt's, using rods that are identical?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
Use the clues to colour each square.
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 cover the camel with these pieces?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
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?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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?
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?
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?
Use your mouse to move the red and green parts of this disc. Can
you make images which show the turnings described?
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?
Terry and Ali are playing a game with three balls. Is it fair that
Terry wins when the middle ball is red?
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?
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....?
Use the information about Sally and her brother to find out how many children there are in the Brown family.
Can you hang weights in the right place to make the equaliser
Explore the different tunes you can make with these five gourds.
What are the similarities and differences between the two tunes you
Can you find all the different ways of lining up these Cuisenaire
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help 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?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
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?
In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?
Investigate the different sounds you can make by putting the owls
and donkeys on the wheel.
If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Sort the houses in my street into different groups. Can you do it in any other ways?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
Find out what a "fault-free" rectangle is and try to make some of
Can you find all the different triangles on these peg boards, and
find their angles?
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.