Logic Contest, Question 5
English (A continuación texto en español)
Question 5:
We have three inhabitants in our island (Check the Setting in Question 1) Alice, Ben and Christine. Alice says, “All of us are knaves.” Ben replies, “Exactly one of us is a knight.
What type of inhabitants are Alice, Ben and Christine? (Give the right reason for why your answer is correct)
The firts person that write a comment with the correct answer wins a Little Bitty Baby Learns Hebrew.
Español:
Pregunta 5:
Tenemos tres habitantes en nuestra isla (vea el escenario de la Pregunta 1) Alice, Ben y Christine. Alice dice, “Todos somos truhanes.” Ben contesta, “Exactamente uno de nosotros es un caballero.”
Que tipo de habitantes son Alice, Ben y Christine? (Tienes que dar la razón correcta del porque tu respuesta es correcta.)
La primera persona que escriba un comentario con la respuesta correcta se gana un Little Bitty Baby Learns Hebrew.
It’s an impossible situation. Everyone on the island claims to be a knight. Knights are telling the truth when they so cliam, and knaves are lying. When Alice says they are all knaves, she is claiming to be a knave herself. If she really is a knave she would claim to be a knight. If she really is a knight, she wouldn’t claim to be a knave.
Yo creo que Alice es un truhan por que ella no puede ser un caballero (ellos siempre dicen la verdad asi que no se diria a si misma que es un truhan, esto ya se habia aclarado desde el principio del concurso), y aqui ya no estoy muy segura pero creo que Ben es un caballero por que ellos siempre dicen la verdad y si no fuese asi entonces el seria un truhan y tambien lo seria Christine (dado que supondriamos que Bill miente y no hay caballeros) por lo cual la aseveracion de Alice seria cierta (imposible por que los truhanes mienten no dicen la verdad). Asi que Alice es truhan, Ben es caballero y Christine es truhan.
Siii, Ivett, tienes la razon, razonamiento correcto! El Little Bitty Hebrew se va para Mexico.
Yess, Ivett, you are right, correct reasoning! The Little Bitty Hebrew goes to Mexico.
Here the analysis in english:
Assume Alice is a knight. This means that what she said is true – they are all knaves. However, this contradicts the assumption that she is a knight; therefore, Alice is a knave. Since what Alice said is false, namely, that all of them are knaves, we can conclude that not everyone is a knave. In other words, at least one of them is a knight. Now, assume Ben is a knave. We already know that at least one person is a knight from Alice’s statement; so, that means Christine must be the knight because we already know that Alice is a knave. In other words, the statement “exactly one of us is a knight” would be true. Since this is what Ben said, then Ben must be a knight; however, this contradicts the assumption that Ben is a knave. Therefore, Ben is a knight. This means what Ben said is true, and he is the only knight. This means that Christine is a knave.