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?

Question

Ronan Donaldson

Mathematics

23 July, 17:16

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?

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Answers (1)

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PbJ · Answer 1

Troll 1: Knight

Troll 2: Knave

Troll 3: Knight

Step-by-step explanation:

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.