Use the clues to colour each square.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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?
What happens when you try and fit the triomino pieces into these
Can you cover the camel with these pieces?
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
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Place six toy ladybirds into the box so that there are two
ladybirds in every column and every row.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
How many different rhythms can you make by putting two drums on the
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
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?
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 see why 2 by 2 could be 5? Can you predict what 2 by 10
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
Use the information about Sally and her brother to find out how many children there are in the Brown family.
Choose a symbol to put into the number sentence.
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?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
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?
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
Can you hang weights in the right place to make the equaliser
This 100 square jigsaw is written in code. It starts with 1 and
ends with 100. Can you build it up?
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....?
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?
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?
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?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
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!
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.
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?
There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
Can you use the numbers on the dice to reach your end of the number line before your partner beats you?
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
If you have only four weights, where could you place them in order
to balance this equaliser?
Use your mouse to move the red and green parts of this disc. Can
you make images which show the turnings described?
Use the number weights to find different ways of balancing the equaliser.
Try out the lottery that is played in a far-away land. What is the
chance of winning?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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 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?
How many trains can you make which are the same length as Matt's,
using rods that are identical?
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
Can you make the green spot travel through the tube by moving the
yellow spot? Could you draw a tube that both spots would follow?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.