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?

7 balls are shaken in a container. You win if the two blue balls touch. What is the probability of winning?

This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.

Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?

Identical discs are flipped in the air. You win if all of the faces show the same colour. Can you calculate the probability of winning with n discs?

Use this animation to experiment with lotteries. Choose how many balls to match, how many are in the carousel, and how many draws to make at once.

Imagine picking up a bow and some arrows and attempting to hit the target a few times. Can you work out the settings for the sight that give you the best chance of gaining a high score?

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

Can you beat Piggy in this simple dice game? Can you figure out Piggy's strategy, and is there a better one?

Can you work out which spinners were used to generate the frequency charts?

Carry out some time trials and gather some data to help you decide on the best training regime for your rowing crew.

Try out the lottery that is played in a far-away land. What is the chance of winning?

A simple spinner that is equally likely to land on Red or Black. Useful if tossing a coin, dropping it, and rummaging about on the floor have lost their appeal. Needs a modern browser; if IE then at. . . .

Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.

This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.

Can you locate the lost giraffe? Input coordinates to help you search and find the giraffe in the fewest guesses.

What is the relationship between the angle at the centre and the angles at the circumference, for angles which stand on the same arc? Can you prove it?

How many different triangles can you make which consist of the centre point and two of the points on the edge? Can you work out each of their angles?

Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.

An activity based on the game 'Pelmanism'. Set your own level of challenge and beat your own previous best score.

Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.

Meg and Mo need to hang their marbles so that they balance. Use the interactivity to experiment and find out what they need to do.

Practise your diamond mining skills and your x,y coordination in this homage to Pacman.

Meg and Mo still need to hang their marbles so that they balance, but this time the constraints are different. Use the interactivity to experiment and find out what they need to do.

Mo has left, but Meg is still experimenting. Use the interactivity to help you find out how she can alter her pouch of marbles and still keep the two pouches balanced.

A game for 1 person to play on screen. Practise your number bonds whilst improving your memory

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

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 Little Fung at the table?

Use the interactivity to make this Islamic star and cross design. Can you produce a tessellation of regular octagons with two different types of triangle?

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

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

Two circles of equal radius touch at P. One circle is fixed whilst the other moves, rolling without slipping, all the way round. How many times does the moving coin revolve before returning to P?

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?

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 circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?

Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.

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.

Show how this pentagonal tile can be used to tile the plane and describe the transformations which map this pentagon to its images in the tiling.

Can you fit the tangram pieces into the outline of this telephone?

The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.

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 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 to be played against the computer, or in groups. Pick a 7-digit number. A random digit is generated. What must you subract to remove the digit from your number? the first to zero wins.

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.

A game for 1 person. Can you work out how the dice must be rolled from the start position to the finish? Play on line.

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