Xan #2

Logic Level 1

In the country of Xan there are three classes of people:

  • Knights who always tell the truth,
  • Knaves who always lie, and
  • Jesters who sometimes tell the truth and sometimes lie.

There are 3 inhabitants of Xan, A , B , A, B, and C , C, and only one of them is known to be a Jester.

  • A A says, "I'm not a Knight."
  • B B says, "I'm not a Jester."
  • C C says: "I'm not a Knave."

What kind of person is B ? B?

B is a Knight B is a Knave B is a Jester There is not sufficient information

Guillermo Templado by Guillermo Templado , 46, Spain

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3 solutions

Blan Morrison
Mar 3, 2018

We can work out all of the possibilities for B B

  • Knight: If B B is a knight, then he is not a jester. Therefore, he would be telling the truth. He can be a knight.

  • Knave: If B B is a knave, then he is not a jester. Therefore, he would be telling the truth, which is contradictory. He can not be a knave.

  • Jester: If B B is a jester, then he may or may not be telling the truth. If he is lying, then he could be a jester. He could be a jester.

Since we know only one of these three men is a jester, we have narrowed down our answers to "Knight" or "Insufficient information." We must now see if A A or B B is a jester. We know that A A must be a jester, because he cannot lie as a knight, nor tell the truth as a knave. Since A A is a jester, B B can not. Therefore, the only possibility is that B is a knight \boxed{B~\text{is a knight}} .

3 Helpful 0 Interesting 0 Brilliant 1 Confused
Saya Suka
Jan 20, 2021

A denied being a Knight.
B denied being a Jester.
C denied being a Knave.

Denying to be a Knight can only be logically done ONLY by a Jester (truthfully), because a Knight cannot lie about it while a Knave can't be honestly admitting the truth of it.

Denying to be a Jester can only be logically done by a Jester (deceptively) or a Knight (truthfully), since a Knave truly isn't one; any Jester denial claims by a Knave can only be the unspeakable truth.

Denying to be a Knave can be logically done by anyone including a Jester (truthfully) or a Knight (also truthfully) and even a Knave (deceptively), since a Knave truly is one and it's in his nature to deceive others.

As we're already told that there's only one Jester among them, then he must be Jester A since nobody else other than him can logically deny being a Jester. B must be a Knight because it's impossible for him to be another Jester for A is already it, being the one and only.

In conclusion, we have between the three :
1) a Jester A
2) a Knight B
3) a Knave C or a Knight C

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Emily Peng
Dec 30, 2019
  • A A says "I'm not a Knight." It is impossible for a knight to say "I am not a knight", since they would be lying, and a knave to say "I am not a knight", since they would be telling the truth. Therefore, A is a joker.
  • B B Says that "I'm not a Jester". This is obviously a truth, since it is said that there is only one Jester. So, B B is telling the truth. So, B B is a Knight.
0 Helpful 1 Interesting 0 Brilliant 0 Confused

Also, how do you make a new paragraph without using bullet points?

Emily Peng - 1 year, 5 months ago

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