In the planet Realmivory, all the inhabitants are either Knights, who always speak truthfully; Liars, who always speak falsely; Knaves, who make statements that are alternately true and false, but in which order is unknown; or those few Revoltosos who do not abide by the planet's traditions.

A Revoltoso is an eccentric person who can choose to speak truthfully like Knights, or speak falsely like Liars or, alternate between true and false statements (not necessarily in that order) like Knaves.

Four inhabitants: Atys, Euryalus, Lausus and Turnus were busy in a conversation. In response to a query posited by an inquisitive visitor from a neighboring planet regarding their identity, they say:

Atys:
1. I am a Knight. 
2. Euryalus is not a Knave.

Euryalus: 
1. I am a Knave. 
2. Lausus  is not a Liar.

Lausus:  
1. I am a Liar. 
2. Turnus is not a Revoltoso.

Turnus: 
1. I am a Revoltoso. 
2. Atys is not a Knight.

(i) Determine the probability that:
(Atys, Euryalus, Lausus, Turnus) = (Knight, Revoltoso, Knave, Liar) given that the types of the four inhabitants are distinct.

(ii) What is the answer to (i) if the types of the four inhabitants may or may not be distinct?

(In reply to Solution for part (i) by Dustin)

Experimenting in a spreadsheet has yielded an answer of 1/9.

Posted by Dustin on 2012-07-16 06:01:52