Xan #3

Logic Level 3

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 . It is known that one and only one of the three people is a Knave. A A says: "I'm a Jester." B B says: " A A is telling the truth." And C C says: "I'm not a Jester."

What kind of person is B B ?

B B is a knave B B is a Knight This is an impossible scenario. B B is a Jester There is no sufficient information.

Guillermo Templado by Guillermo Templado , 46, Spain

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2 solutions

Andrew Knighton
Oct 10, 2018

At first, it doesn't appear as if there is enough information, but there is. A cannot be a knight because knights must tell the truth and he said he was a jester, so if he were a knight he would be lying, and knights always tell the truth. B cannot be a knight, because we already know that A was lying, so C is the knight. If A was a jester, then he would be telling the truth, so B would also be telling the truth. However, if A was a jester, B would have to be a knave. Because in that scenario B would be telling the truth, and B would be a knave, A can't be a jester. A has to be a knave,so B is a jester, and C is a knight.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Why must C be a knight?

Saya Suka - 4 months ago
Saya Suka
Jan 20, 2021

A claimed to be a Jester.
B supported A's claim.
C denied being a Jester.

Claiming to be a Jester can only be logically done by a Jester or a Knave. Denying to be a Jester can only be logically done by a Jester or a Knight. Supporting a true claim by Jester A can only be logically done by either a Knight or another Jester, while supporting a false claim by Knave A can only be logically done by either a Jester or another Knave, but we're already told that there's only one Knave among them. Since we know that C cannot be one, so it must be the case involving a false claim with the existence of at least one Knave being necessary, because a true claim can never be done nor supported by any Knaves. In conclusion, we have between the three :
1) a Knave A
2) a Jester B
3) a Jester C or a Knight C

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Basically, C can't be a knave as that statement would be a truth to one knave C, so the sole knave must either be A or B. The statements by A & B are not contradictory, so both A AND B must be lying, one by nature and the other by association (with one of them a knave and a lie can only get along with another lie). A & B can only be either knaves or Jesters (Knights can't lie), but we're told that there's only one knave, so their partner must be a Jester. A lying Jester cannot admit to be one, so it must be Jester B supporting a knave A's false claim.

Saya Suka - 1 month, 2 weeks ago

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