### Coin Tossing Games

You and I play a game involving successive throws of a fair coin. Suppose I pick HH and you pick TH. The coin is thrown repeatedly until we see either two heads in a row (I win) or a tail followed by a head (you win). What is the probability that you win?

### Scratch Cards

To win on a scratch card you have to uncover three numbers that add up to more than fifteen. What is the probability of winning a prize?

### Factoring a Million

In how many ways can the number 1 000 000 be expressed as the product of three positive integers?

# Last Biscuit

##### Stage: 4 Challenge Level:
This is a game for two players.

You could start with 12 biscuits (or buttons, or pebbles, or...) and put four biscuits (or buttons, or pebbles, or...) into one jar and eight into the other jar (you just need to make two groups).

Each player can take biscuits in one of two ways:
1. By taking any number they like from just one jar or
2. By taking the same amount from both jars.

The winner is the person who takes the last biscuit/s.

Play the interactive version here

Think carefully! See if you can discover a winning strategy before your friends do.