Here's a puzzle/riddle from a book I came across: does anyone know how to solve it?
According to the book the solution is Greg but I can't figure out how to get that answer – quite stuck on how to even get started.
From Raymond Smullyan, The Gödelian Puzzle Book: Puzzles, Paradoxes & Proofs:
A logician once visited a very strange island in which not every inhabitant was either a knight (who always told the truth) or knave (who always lied). Those who were neither one were called outcasts.
An outcast would lie on some days and be truthful on others.
On any day, he would either lie the entire day, or be truthful the entire day, but his behavior could change from day to day.On a given day, to say that a person is currently truthful is to say that he is either a knight (who is truthful on all days) or that he is an outcast and that day is one of his truthful days.
The logician was captured by a tribe of bandits. Curiously enough, the chief bandit was a knight, and this fact was common knowledge. He had been interested in logic and loved to test his victims.
And so he led the logician into a room with nine natives and
explained that only one of them was a knight—each one of the other eight was either a knave or an outcast. The logician’s task was to determine which one was the knight. If he succeeded, he would be set free; otherwise, he would be executed. Here is what the
nine men said.Archie: The knight is either Cary, Elmak, Greg or myself. Barab: I am an outcast. Cary: Either Elmak is currently truthful or Greg is not. Dreg: Archie lied. Elmak: Barab and Dreg didn’t both lie. Frisch: Cary lied. Greg: Archie is not the knight. Hal: I am a knave and Ilak is an outcast. Ilak: I am a knave and Frisch lied.
The logician thought about this for while and finally said, "I don’t have enough information to solve the problem. I need to know whether or not Hal is an outcast. Then I might be able to solve it." The chief bandit was fair enough to tell him whether or not Hal was an outcast, and the logician could then figure out which one was the knight.
Which one was the knight?
Source: page 38 chapter 4 of the Puzzle Book
Best Answer
Let's go through some of the statements and see what we can figure out. (This ended up being a nearly complete solution, so try to read only one at a time to leave something for you to do!):
For each final case, you should write down a set of values for each of the people that are not self-contradictory to be sure that each case that we found is actually possible (i.e., that we didn't miss any logical connections).