Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
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
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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?
Try out the lottery that is played in a far-away land. What is the
chance of winning?
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?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
How many different triangles can you make on a circular pegboard that has nine pegs?
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?
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?
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?
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?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Can you find all the different triangles on these peg boards, and
find their angles?
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 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?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Find out how we can describe the "symmetries" of this triangle and
investigate some combinations of rotating and flipping it.
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.
A game for 2 players. Can be played online. One player has 1 red
counter, the other has 4 blue. The red counter needs to reach the
other side, and the blue needs to trap the red.
A game for 2 people that everybody knows. You can play with a
friend or online. If you play correctly you never lose!
Can you be the first to complete a row of three?
An environment which simulates working with Cuisenaire rods.
Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.
Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?
Explore the different tunes you can make with these five gourds.
What are the similarities and differences between the two tunes you
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
These formulae are often quoted, but rarely proved. In this article, we derive the formulae for the volumes of a square-based pyramid and a cone, using relatively simple mathematical concepts.
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!
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?
A simulation of target archery practice
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .
Use the Cuisenaire rods environment to investigate ratio. Can you
find pairs of rods in the ratio 3:2? How about 9:6?
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?
A generic circular pegboard resource.
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?
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?
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?
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.