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?
Choose a symbol to put into the number sentence.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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!
If you have only four weights, where could you place them in order
to balance this equaliser?
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
Start by putting one million (1 000 000) into the display of your
calculator. Can you reduce this to 7 using just the 7 key and add,
subtract, multiply, divide and equals as many times as you like?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
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?
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?
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?
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
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?
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?
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?
A game for 2 people that everybody knows. You can play with a
friend or online. If you play correctly you never lose!
Use the Cuisenaire rods environment to investigate ratio. Can you
find pairs of rods in the ratio 3:2? How about 9:6?
Investigate how the four L-shapes fit together to make an enlarged
L-shape. You could explore this idea with other shapes too.
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!
A card pairing game involving knowledge of simple ratio.
A generic circular pegboard resource.
Find out how we can describe the "symmetries" of this triangle and
investigate some combinations of rotating and flipping it.
Choose the size of your pegboard and the shapes you can make. Can
you work out the strategies needed to block your opponent?
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.
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?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
A train building game for 2 players.
Can you find all the different ways of lining up these Cuisenaire
This 100 square jigsaw is written in code. It starts with 1 and
ends with 100. Can you build it up?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Using angular.js to bind inputs to outputs
Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?
How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?
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?
Can you complete this jigsaw of the multiplication square?
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
An interactive game to be played on your own or with friends.
Imagine you are having a party. Each person takes it in turns to
stand behind the chair where they will get the most chocolate.
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?
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
Work out the fractions to match the cards with the same amount of
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....?
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.
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?
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?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
Watch this film carefully. Can you find a general rule for
explaining when the dot will be this same distance from the