Can you find all the different ways of lining up these Cuisenaire
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?
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?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
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?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
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....?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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?
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?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Find out what a "fault-free" rectangle is and try to make some of
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
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?
Train game for an adult and child. Who will be the first to make the train?
Find out how we can describe the "symmetries" of this triangle and
investigate some combinations of rotating and flipping it.
An environment which simulates working with Cuisenaire rods.
Can you find all the different triangles on these peg boards, and
find their angles?
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?
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
A train building game for 2 players.
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
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?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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 see why 2 by 2 could be 5? Can you predict what 2 by 10
Choose a symbol to put into the number sentence.
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?
Use the Cuisenaire rods environment to investigate ratio. Can you
find pairs of rods in the ratio 3:2? How about 9:6?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
Can you fit the tangram pieces into the outline of Little Fung at the table?
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.
Can you fit the tangram pieces into the outline of this telephone?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
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 clocks?
Can you fit the tangram pieces into the outlines of these people?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
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?
Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?
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?
Work out the fractions to match the cards with the same amount of
Can you fit the tangram pieces into the outlines of the workmen?
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?