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?

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

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

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. . . .

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

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?

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

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

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

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.

A tool for generating random integers.

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

An interactive activity for one to experiment with a tricky tessellation

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?

Explore this interactivity and see if you can work out what it does. Could you use it to estimate the area of a shape?

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

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. . . .

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

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

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

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.

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?

Use the Cuisenaire rods environment to investigate ratio. Can you find pairs of rods in the ratio 3:2? How about 9:6?

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?

Can you find all the different triangles on these peg boards, and find their angles?

How many different triangles can you make on a circular pegboard that has nine pegs?

Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.

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

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?

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

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?

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.

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?

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?

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

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

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!

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

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

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....?

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?

Complete the squares - but be warned some are trickier than they look!

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