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?

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. . . .

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

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

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

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

How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?

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

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

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

Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

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 the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

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?

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

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

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?

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 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?

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

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?

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?

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

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

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?

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....?

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

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.

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

A tool for generating random integers.

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?

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

If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?

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

Use the number weights to find different ways of balancing the equaliser.

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

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

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?

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

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

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