Who is who?

Logic Level 3

On an island there are 3 types of people: knights that always tell the truth, knaves that always lie, and jesters that tell the truth only after a lie and vice versa.

While you are on the island, you come across an old man, a boy, and a girl.

Old man : "I am a jester." "The boy is a knight."
Boy : "I am a knight." "The girl is a jester."
Girl : "I am a knave." "The old man is a jester."

How many jesters are there among the three?

Cannot be determined 3 1 2 0

1 solution

Saya Suka
Jan 9, 2017

The girl must be a jester since neither a knight nor a knave will ever admit to be a knave. Thus her claim that the old man is a jester must be the truth, after the lie she told about herself. Thus the old man's second statement about the boy being a knight must be a lie, after the one truth about being a jester himself. Since the boy's first statement is a lie, he must be a knave or jester. The boy's true identity is revealed by his own second statement, which is true; since a knave can't make a true statement, the boy must be a jester. So all three are jesters.

Can anyone check the wiki, the part where there is an example for technique 1? It doesn't seem correct to me.

Saya Suka - 4 years, 5 months ago

Neither knights nor knaves can make the statement "I am a knave." You are correct there. I cleaned up your last sentence a little (the logic was fine but it was slightly hard to read).

Jason Dyer Staff - 4 years, 5 months ago

Thank you, my English needed any and all help to be understood. Actually, not just that, people don't quite get my meanings even when speaking in my native language.

Saya Suka - 4 years, 5 months ago

What doesn't seem correct? Can you elaborate on it?

Pi Han Goh - 4 years, 5 months ago

Rachel did not do it and Samantha did it, these two situations are not contradictory.

Saya Suka - 4 years, 5 months ago

{We claim that Teresa broke the vase, which will be proved by contradiction.

Suppose Teresa didn't break the vase. Then, she must be telling the truth and the other two girls must be lying. So Rachel didn't break the vase and Samantha broke the vase, which is a contradiction (since only one person broke the vase). In other words, Teresa must have broken the vase.}

If we suppose Teresa told the truth, Sam's "Rachel did it" and Rachel's " Sam did not do it" must be lies. Then, the 3 truths would be
1) Teresa did not do it (by Teresa's supposedly truthful words),
2) Rachel did not do it (if we say that Sam's lied to mother) and
3) Sam did it (if we say Rachel is another liar).
We can see that there's only one guilty party here in this case of 'supposing Teresa is an angel', and that is Sam, so I can't see any contradiction in this one example.

Saya Suka - 4 years, 4 months ago

No Knights will ever lie and say they're actually Jesters, so whether or not the old man is a real Jester, his second statement would always be a lie. Therefore, the boy could not have been a Knight as they both said. For his second statement, it's in opposition to what the girl's claiming herself to be, his Jester vs her knave. At most only one of the claims might be the truth, but by a similar argument in the first sentence that "No Knights will ever lie and say they're actually knaves (instead of Jesters)", we know the girl lied with her first statement, so she can neither be a Knight nor a knave. As a Jester, she can only tell the truth by her second statement for a Jester old man and the boy with mixed truth values must be the last of the Jester trio.

Saya Suka - 1 month ago

Who is who?

1 solution

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