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?

First, let me start with a disclaimer. Even though I tried to write it all out clearly and redundantly for myself, I got confused at times, so I am admitting up front that I could have goofed up =)

Well, I went through all 6 possible combinations of what Grot, Cloysta and Blarg could mean.

I was able to completely eliminate three of those combinations because they lead to contradictions no matter what the people were. Those combinations that I eliminated are [Grot, Cloysta, Blarg] = [Liar, Knight, Knave], [Liar, Knave, Knight], and [Knave, Liar, Knight]. I'd explain how I eliminated those, but that would take too long.

With the other 3 possible combinations of Grot, Cloysta and Blarg, I got 6 possible situations! If we are allowed to assume that there is exactly one knave, one knight, and one liar in this group, then I can eliminate 4 of those situations. But this still leaves me with two possible solutions:

Grot - Knight
Cloysta - Liar
Blarg - Knave
Jeswin - Liar
Parker - Knave
Crasbo - Knight

or

Grot - Knight
Cloysta - Knave
Blarg - Liar
Jeswin - Knight
Parker - Knave
Crasbo - Liar

I was hoping that out of all the possible solutions, there would only be one where all of the people were different types, but unless I goofed it looks like there are two solutions. The wording of the problem makes it sound like we should see only one situation is possible. Frustration!

Posted by nikki on 2003-10-28 18:23:08