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. . . .

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?

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

Terry and Ali are playing a game with three balls. Is it fair that Terry wins when the middle ball is red?

There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?

Can you use the numbers on the dice to reach your end of the number line before your partner beats you?

A tool for generating random integers.

Play this well-known game against the computer where each player is equally likely to choose scissors, paper or rock. Why not try the variations too?

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.

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 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.

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.

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

Use the information about Sally and her brother to find out how many children there are in the Brown family.

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?

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....?

If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

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?

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

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 activity for one to experiment with a tricky tessellation

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!

In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?

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?

Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.

Move just three of the circles so that the triangle faces in the opposite direction.

Take it in turns to make a triangle on the pegboard. Can you block your opponent?

Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?

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?

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?

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?

Work out the fractions to match the cards with the same amount of money.

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.

How many different rhythms can you make by putting two drums on the wheel?

Exchange the positions of the two sets of counters in the least possible number of moves

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

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?

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.

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

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?

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

Here is a chance to play a version of the classic Countdown Game.