Chocolate Bars

This game is based on the investigation Chocolate.

This is a game you can play on your own or with friends. You must imagine you are having a party!

You have put 1 chocolate bar on one chair, 2 bars on another chair and 3 chocolate bars on a third chair.

Each person arrives at the party takes it in turns to go and stand behind the chair where they will get the most chocolate if it is shared out straight away.

Which chair will this be for the first person?
Which chair will this be for the second person to arrive?
Which chair will this be for the third person to arrive?
The fourth? Fifth? Sixth, seventh, eighth...?

Can you work out what fraction of a bar of chocolate each person will get every time someone else arrives at the party?

We were reminded of this game in an article by Peter Critchley in TES Mathematics Curriculum Special, Spring 2002.