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?
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 put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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?
Can you find all the different ways of lining up these Cuisenaire
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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 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?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
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?
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?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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?
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
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?
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.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
If you have only four weights, where could you place them in order
to balance this equaliser?
Find out what a "fault-free" rectangle is and try to make some of
Explore the different tunes you can make with these five gourds.
What are the similarities and differences between the two tunes you
How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?
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!
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?
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
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?
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
Can you complete this jigsaw of the multiplication square?
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?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
Use the blue spot to help you move the yellow spot from one star to
the other. How are the trails of the blue and yellow spots related?
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.
A generic circular pegboard resource.
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
Can you fit the tangram pieces into the outline of this telephone?
Use the interactivities to complete these Venn diagrams.
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
Can you fit the tangram pieces into the outlines of the watering can and man in a boat?
Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?