Logic Contest, Question 3
English (A continuación texto en español)
Question 3:
We continue in the same island (Question 1). As in Question 2, we have only two inhabitants Perla and Todd. This time Perla says, “Both of us are knaves.”
What type of inhabitants are Perla and Todd? (Give the right reason for why your answer is correct)
The first person that write a comment with the correct answer win a copy of Handy English Encoder Decoder
Español:
Pregunta 3:
Continuamos en la misma isla de la Pregunta 1, y como en la pregunta 2, solo tenemos dos habitantes Perla y Todd. Esta vez Perla dice, “Ambos somos truhanes.”
Que tipo de habitantes son Perla y Todd? (Tienes que dar la razón correcta del porque tu respuesta es correcta.)
La primera persona que escriba un comentario con las respuesta correcta gana una copia de Handy English Encoder Decoder
Perla is a knave, Todd is a knight.
Sorry I forgot to put the reason:
Perla says “Both of us are knaves”. If she is a knave, she lied and both are not knaves. If she is a
knight, she told the truth, in which case both are knaves (which can’t be if she told the truth).
Congratulations Dan, you are correct, and win the Handy English Encoder Decoder..
See you in the Question 10, the challenge!
Next another way to say solution, just for didactic purposes:
Analysis:
This almost sounds like Perla is claiming to be a knave, which we earlier said cannot happen on the island of knights and knaves. In point of fact, she is making this claim, but indirectly. An inhabitant cannot directly claim to be a knave, but as we will see they can do so indirectly.
Assume Perla is a knight. Then what she said is true, and this leads to a contradiction. Therefore, Perla is a knave and what she said is false. So, how can the statement “Both of us are knaves” be false? It is false if at least one of them is a knight. Since we know Perla is a knave, then this means Todd is a knight. This is a very good example of how a knave can indirectly claim they are a knave.