In planet Realmamber, 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 Rebels who do not abide by the planet's traditions.

How truthful a Rebel's statements are is unknown, except that they are not the same as those who are Knights, Liars, or Knaves. Thus, a rebel will never make just one or two statements; he will always make three or more.

The Realmamberians are favored by the God of Light, but he has not had any success in establishing meaningful dialogue with the inhabitants. He is aware that there are those among the Realmamberians who do not respect their traditional conventions regarding veracity. Perhaps, he might have better luck making contact with a Rebel.

The God of Light, in disguise, approaches four inhabitants, exactly one of whom is known to be a Rebel. As to the group or groups of other three speakers, little is known except that no more than one is a Knight.

The God of Light asks which one of the four is the Rebel. They each respond below:

Speaker A

1. Two of us are Rebels.
2. B is a Knight.
3. B was a Rebel, but he has reformed.
4. B’s third statement is true.

Speaker B

1. I am neither a Liar nor a Knave.
2. A’s first statement is true.
3. D is a Knight and C is the Rebel.
4. A is not the Rebel.

Speaker C

1. D is the Knight.
2. I am the Rebel.
3. B’s second statement is false.
4. D is neither a Knight nor a Knave.

Speaker D

1. B is either a Knave or the Rebel.
2. I am either a Knight or a Knave.
3. C falsely claims to be the Rebel.
4. A’s third statement is false.

The God of Light throws up his hands in frustration. It is time, he decides, for him to give up and return home to try to forget about the Realmamberians.

What group is represented by each of the four speakers?

(In reply to solution with explanation by Paul)

The phrase "exactly one of whom is known to be a Rebel" does not establish that there is one Rebel, but only that there is at least one Rebel.

Perhaps the phrase should have been "exactly one of whom is a Rebel", then "exactly one" would be congruent to "a Rebel" instead of what is "known".

The implication that there is but one Rebel in the request by the 'god of light' of "which one of the four is the Rebel" is again clouded when the 'god of light' "throws up his hands in frustration".   

Of course it can be deduced from what is known is that Speaker B is a Rebel.

Posted by Dej Mar on 2010-02-02 07:13:04