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The Rebel III (Posted on 2010-01-05) Difficulty: 3 of 5
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.

A, B, C and D are four inhabitants of the planet, who are busy in a conversation when a visitor from a neighboring planet stops by and asks each of them their identity. They say:

Inhabitant A:
  1. My statements are not all truthful.
  2. We are overworked.
  3. We are all lucky to be here.
  4. We Realmamberians are favored by the gods.

Inhabitant B:
  1. I agree with A's third statement.
  2. Every time I see a visitor, I think maybe it is one of the gods, in disguise.
  3. I am doing more than my share of the work.
  4. My statements are all truthful.

Inhabitant C:
  1. My statements are all truthful.
  2. D's second statement is false.
  3. The gods do not visit us in disguise.
  4. We are all overworked.

Inhabitant D:
  1. C's first statement is truthful.
  2. B's third statement is truthful.
  3. My statements are all truthful.
  4. The gods frequently visit us in disguise.
Which one is the Knight, which one is the Liar, which one is the Knave, and which one is the Rebel?

No Solution Yet Submitted by K Sengupta    
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Solution Solution | Comment 1 of 4

A's first statement must be true, thus A cannot be a Knight or a Liar.

Looking at D's first statement, if it is true, then C = Knight, D = Rebel, leaving B = Liar and A = Knave.  But this cannot be because A's third statement would conflict with B's first statement.  So C cannot be the Knight, and D's first statement is False.  Thus B = Knight.

This makes D's second statement true, and C's second statement false.  Thus C = Liar.

D's third statement is False, while D's fourth statement is true (conflict with C's third), making D the Knave.

A = Rebel
B = Knight
C = Liar
D = Knave

(Disclaimer:  It could be argued that C's false statement 3 and D's statement 4 do not conflict because of the qualifier 'frequently'.  That is, the gods could visit in disguise, but not frequently, making both statements false.)

  Posted by hoodat on 2010-01-05 12:53:50
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