Knights, Knaves, Jokers II

Ellis, Farin and Gobi all claim that the next person is a joker.

(Without loss of generality) let 's say that Elis is the joker . Now, trivially Gobi is correct and hence, he must be a knight because there is exactly one joker. This means that Farin is a Knave , since we have established that Gobi is a knight (and hence not a joker).

It is not necessary that Eli is the joker, however, regardless of whoever the joker is, we could repeat the above argument and show that there is exactly one knight. This nice property is because of the fact:

$\text{ Elis } \xrightarrow{\text{claims joker}} \text{ Farins } \xrightarrow{\text{claims joker}} \text{ Gobs } \xrightarrow{\text{claims joker}} \text{ Elis }$

They all claim differently that a different person is joker, and all of them have claims against them about being a joker. Per the instructions, only one of them is a joker. Therefore, only one of them is right (the Knight)

A claims B is a joker, B claims C is a joker, and C claims a is a joker.

Suppose A is the real joker, so B and C aren't jokers. Hence, if B said that C is a joker he's lying, so he's a knave. And when C said that A is a joker that's the truth, so he's the knight.

This pattern repeats even if you suppose B is the joker (C is the knave, and A is the joker) and if you suppose C is the joker (A is the knave, and B is the knight)

And so, you'll always get the number of 1 joker, 1 knave, and 1 knight.

Since only one is joker, the person who 'introduced' this joker cannot be another joker, so he must be a knight. And since there can be only one truth out of the three statements (only one joker), there is only one knight out of them.

Let Ellis be a joker then the other two are either knight or knave. Since Gobi says that Ellis is a joker then he is a knight. One knight is all we know.

Suppose Ellis is a jocker and in first case he tells the truth so by his statement farin is a jocker but in given question only one person is knight so the farin is wrong and in the last statement which was told by gobi that ellis is a jocker so only one and only person who is a knight I think you got it.

If there's a joker,then there must be a knight. If there're two knights,then it's disobeying the facts. So X the number of knights/ 0<X<=1 /