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?