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

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

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

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?

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?

What happens when you try and fit the triomino pieces into these two grids?

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

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?

Can you hang weights in the right place to make the equaliser balance?

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

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

Investigate the different sounds you can make by putting the owls and donkeys 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.

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

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

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

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

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

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?

How many trains can you make which are the same length as Matt's, using rods that are identical?

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

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

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

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

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

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

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

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

Take it in turns to place a domino on the grid. One to be placed horizontally and the other vertically. Can you make it impossible for your opponent to play?

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?

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

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

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

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

Use the interactivity to find out how many quarter turns the man must rotate through to look like each of the pictures.

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!

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. . . .

An interactive activity for one to experiment with a tricky tessellation

Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?

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

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.

If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?