You are on an island and you meet three people, Jeswin, Parker and Crasbo. You know that they are either liars, knights or knaves (someone who alternates between truth and lie). They have a strange religion - for one half of the year they talk in English and for the other half they talk Gambalidarian (their language). Naturally, you arrive during the latter part of the year. You know that if you ask them what they are, they either say 'Blarg', 'Grot' or 'Cloysta', but you don't know which means what out of liar knight and knave. You also know that 'Jappa' means 'is a' and 'Bokka' means 'I am a'. They give the following statements:

Jeswin : Bokka Grot. Parker Jappa Cloysta.

Parker : Bokka Blarg. Crasbo Jappa Blarg.

Crasbo : Bokka Grot. Jeswin Jappa Cloysta.

What does Blarg, Grot and Cloysta mean in English, and what are each of the people?

Starting with a more meaningful rewrite:<o:p></o:p>

 

Jeswin : I am a Grot. Parker Is a Cloysta.<o:p></o:p>

Parker : I am a Blarg. Crasbo Is a Blarg.<o:p></o:p>

Crasbo : I am a Grot. Jeswin Is a Cloysta.<o:p></o:p>

What does Blarg, Knight and Cloysta mean in English, and what are each of the people?<o:p></o:p>

<o:p> </o:p>

<o:p> </o:p>

(1) If Grot means Liar...

Jeswin and Crasbo are Knaves (Neither Knights nor Liars can claim to be Liars).  Their opening statements are the lies so their second statements would both be true: Parker is a Cloysta and Jeswin is a Cloysta. Hence, Cloysta means Knave, so Parker is also a Knave, making his first statement (that he is a Blarg) a lie. So his second statement should be true, but it contradicts what we already know i.e. that Crasbo is a Knave/Cloysta. So Grot does not mean Liar.

<o:p> </o:p>

(2) If Grot means Knave...

Jeswin and Crasbo are either Liars or Knaves who have told the truth in their first statements. Either way their second statements must each be lies.

So Neither Parker nor Jeswin can be Cloystas.

<o:p> </o:p>

(2a) If we take Blarg to mean Knight and Cloysta to mean Liar...

Jeswin and Crasbo have both lied but aren't Liars, so they are both Grots/Knaves.

Parker claims Crasbo is a Blarg/Knight, which he cannot be, as he claims to be a Grot/Knave. So Parker's second statement is false, which makes his first statement (that he is a Blarg/Knight) also false. So Parker is a Cloysta/Liar. But this means that Jeswin's second statement is true, and a knave cannot tell two true statements or his first statement about being a knave becomes untrue. So if Grot means Knave, then Blarg can't mean Knight (and Cloysta can't mean Liar).

<o:p> </o:p>

So...

(2b) If we take Blarg to mean Liar and Cloysta to mean Knight...

Then Parker is a Grot/Knave (because he claims to be a liar) making his second statement true i.e. Crasbo is a Blarg/Liar.

Jeswin's first statement could be truth or a lie (either would work), giving us the uncertain:

<o:p> </o:p>

Jeswin - Grot/Knave OR Blarg/Liar

Parker - Grot/Knave

Crasbo - Blarg/Liar

<o:p> </o:p>

So Grot could mean Knave with two working solutions.

<o:p> </o:p>

(3) If Grot means Knight...

(3a) ... and Cloysta means Knave (Blarg means Liar)...

Jeswin's second statement is true (in claiming that he is a Blarg/Liar, Parker proves himself a Cloysta/Knave). But Jeswin's first statement could be true (making him a Grot/Knight) or a lie (making him a Cloysta/Knave).

Parker's second statement must be true, so Crasbo is a Blarg/Liar.

That means that Jeswin is NOT a Cloysta, and is therefore a Grot/Knight.

This gives us the configuration:

<o:p> </o:p>

Jeswin - Grot/Knight

Parker - Cloysta/Knave

Crasbo - Blarg/Liar

<o:p> </o:p>

... But...

(3b) if Cloysta means Liar (Blarg means Knave)

Then Parker is a Liar or a Knave who started with the truth. Either way, his second statement is a lie. Crasbo is NOT a Blarg/Knave.

That means Crasbo is a Grot/Knight or a Cloysta/Liar.

<o:p> </o:p>

(3bi) If Crasbo's a Grot/Knight, then Jeswin is a Cloysta/Liar and Parker is NOT a Cloysta/Liar, so Parker is a Blarg/Knave. Configuration:

<o:p> </o:p>

Jeswin - Cloysta/Liar

Parker - Blarg/Knave

Crasbo - Grot/Knight

<o:p> </o:p>

(3bii) If Crasbo's a Cloysta/Liar, then Jeswin is NOT a Cloysta/Liar, making him a Knight or a Knave who lied in his first statement. Either way his second statement is true i.e. Parker is a Cloysta/Liar.

Uncertain configuration:

<o:p> </o:p>

Jeswin - Grot/Knight OR Blarg/Knave

Parker - Cloysta/Liar

Crasbo - Cloysta/Liar

 

<o:p> </o:p>

Thus we have all the permutations:

<o:p> </o:p>

Jeswin - Grot/Knave OR Blarg/Liar

Parker - Grot/Knave

Crasbo - Blarg/Liar

<o:p> </o:p>

Jeswin - Grot/Knight

Parker - Cloysta/Knave

Crasbo - Blarg/Liar

<o:p> </o:p>

Jeswin - Cloysta/Liar

Parker - Blarg/Knave

 Crasbo - Grot/Knight

<o:p> </o:p>

Jeswin - Grot/Knight OR Blarg/Knave

Parker - Cloysta/Liar

Crasbo - Cloysta/Liar

<o:p> </o:p>

Disappointingly, not ONE of these types or translations is common to all permutations, meaning we can prove ABSOLUTELY nothing... NONE of their types can be discerned. Very poor.

Posted by scott on 2013-04-17 17:01:57