While walking through a fictional forest, you encounter three trolls guarding a bridge. Each is either a knight, who always tells the truth, or a knave, who always lies. The trolls will not let you pass until you correctly identify each as either a knight or a knave. Each troll makes a single statement:

Troll 1: If I am a knave, then there are exactly two knights here.
Troll 2: Troll 1 is lying.
Troll 3: Either we are all knaves or at least one of us is a knight.

Which troll is which?

Troll 3's statement must be true because if they can only be knights or knaves, unless all of them are knaves, at least one must be a knight. Thus, Troll 3 is a knight.

If Troll 2 is a knight, then Troll 1 is knave, but if that were the case Troll 1's statement would be true, and since knaves do not tell the truth, this assumption is incorrect.

If Troll 2 is a knave, Troll 1 is a knight and his statement can be disregarded since it is conditioned to the possibility of him being a knave.

Therefore, Trolls 1 and 3 are knights and Troll 2 is a knave.

andromache andromache · Answer 2 · 2022-01-27T11:45:08+01:00

Troll 1: Knight

Troll 2: Knave

Troll 3: Knight

The following information should be considered:

Troll 3's statement should be true since they can only be knights or knaves, till all of them are knaves, at least one must be a knight.
In the case when Troll 2 is a knight, so Troll 1 is knave, but if that were the case Troll 1's statement should be true, and since knaves do not tell the truth, this assumption is incorrect.
In the case when Troll 2 is a knave, Troll 1 is a knight and his statement can be disregarded.

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