Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
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 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?
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....?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Try out the lottery that is played in a far-away land. What is the
chance of winning?
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 triangles can you make on a circular pegboard that has nine pegs?
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
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 find all the different ways of lining up these Cuisenaire
Place the numbers 1 to 10 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.
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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?
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?
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
Explore the different tunes you can make with these five gourds.
What are the similarities and differences between the two tunes you
An environment which simulates working with Cuisenaire rods.
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.
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?
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?
Find out what a "fault-free" rectangle is and try to make some of
What shape is the overlap when you slide one of these shapes half
way across another? Can you picture it in your head? Use the
interactivity to check your visualisation.
Find out how we can describe the "symmetries" of this triangle and
investigate some combinations of rotating and flipping it.
Can you find all the different triangles on these peg boards, and
find their angles?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
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?
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!
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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.
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
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.
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. . . .
Can you fit the tangram pieces into the outline of this telephone?
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?
Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?
Can you fit the tangram pieces into the outline of Granma T?
Can you complete this jigsaw of the multiplication square?
Investigate how the four L-shapes fit together to make an enlarged
L-shape. You could explore this idea with other shapes too.
Exchange the positions of the two sets of counters in the least possible number of moves
How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?
A game for 2 people that everybody knows. You can play with a
friend or online. If you play correctly you never lose!
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?