A game in which players take it in turns to choose a number. Can you block your opponent?

You have 27 small cubes, 3 each of nine colours. Use the small cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of every colour.

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

A game for 2 people that everybody knows. You can play with a friend or online. If you play correctly you never lose!

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?

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?

Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.

Use the interactivities to complete these Venn diagrams.

Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?

Can you fit the tangram pieces into the outline of Little Ming?

Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

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.

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. . . .

A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.

Can you set the logic gates so that the number of bulbs which are on is the same as the number of switches which are on?

An interactive activity for one to experiment with a tricky tessellation

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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?

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!

Use the interactivity to create some steady rhythms. How could you create a rhythm which sounds the same forwards as it does backwards?

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?

If you have only four weights, where could you place them in order to balance this equaliser?

Can you complete this jigsaw of the multiplication square?

Train game for an adult and child. Who will be the first to make the train?

NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

Can you work out what is wrong with the cogs on a UK 2 pound coin?

Can you find all the different ways of lining up these Cuisenaire rods?

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?

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.

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 in them?

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 interactivity or play this dice game yourself. How could you make it fair?

Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?

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?

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.

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?

Six balls of various colours are randomly shaken into a trianglular arrangement. What is the probability of having at least one red in the corner?

Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.