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?
If we look at the meanings of the three words, there are only six combinations:
Grot, Cloysta, and Blard mean one of the following six items:
- Liar, Knight, Knave
- Liar, Knave, Knight
- Knight, Liar, Knave
- Knight, Knave, Liar
- Knave, Knight, Liar
- Knave, Liar, Knight
Case (1)
Jeswin calls himself a Liar and calls Parker a Knight. Since Jeswin calls himself a liar, he can be neither a liar, nor a knight, therefore he is a Knave, and his first statement is false. Therefore his second statement is true. He calls Parker a Knight, but Parker's first statement calls himself a Knave. Since a knight couldn't do this, case (1) isn't possible.
Case (2)
Jeswin calls himself a Liar and calls Parker a Knave. Since, again, Jeswin calls himself a liar, he can be neither a liar, nor a knight, therefore he is a Knave, and his first statement is false. Therefore his second statement is true. Jeswin called Parker a Knave, and Parker's first statement calls himself a Knight, so Parker is a knight and his first statement is false. Therefore his second statement is true. And he calls Crasbo a Knight. But Crasbo's first statement is that he is a liar, and a knight can't say this, therefore, this case (2) is impossible.
Case (3)
Parker calls himself a Knave, therefore he is either a Liar or a Knave.
Case 3.1: If he is a Knave, then his first statement is true, and his second statement is false, and he calls Crasbo a Knave. Crasbo therefore is a Liar or a Knight.
Case 3.11: If Crasbo is a Knight, then his first statement checks out. And his second statement means that Jeswin is a Liar. If so, the Jeswin's first statement checks out, and his second statement means that Parker is either a Knight or a Knave.
This checks out.
Case 3.12: If Crasbo is a Liar, then his first statement is ok, and his second statement means that Jeswin is a Knight or a Knave, but Jeswin is not a Knight because Jeswin calls Parker a liar which he's not, so Jeswin is a Knave, and his first statement is false. Therefore his second statement must be true, but it isn't. So this is not possible.
Case 3.2: If he is a Liar, then his second statement means that Crasbo is either a Knight or a Liar. Either way his first statement is okay, but...
Case 3.21: If Crasbo is a Knight then (same as 3.11) he calls Jeswin a Liar. If Jeswin is a liar, and he calls Parker a Liar, but this it true! So 3.21 can't be the case.
Case 3.22: If Crasbo is a Liar then Jeswin is either a Knight or a Knave.
Case 3.221: If Jeswin is a Knight, then
this checks out.
Case 3.222: If Jeswin is a Knave, then his first statement is false, and his second statement is true.
This checks out.
Case (4)
Parker calls himself Liar. Therefore he is a Knave, and his first statement is false. Therefore, his second statement is true, and Crasbo is a Liar. Crasbo's first statement is that he is a knight (which is okay), and his second statement is that Jeswin is a Knave which must be false. Therefore Jeswin is either a Knight or a Liar.
Case 4.1: If Jeswin is a Liar, then his first statement that he is a knight is okay... but his second statement would be true (that Parker is a liar), so this can't be the case.
Case 4.2: If Jeswin is a Knight, then his first statement is true, and his second statement is also true.
So 4.2 is consistent.
Case (5)
Parker calls himself a Liar. Therefore he is a Knave, and his first statement is false. Therefore his second statement is true, and Crasbo is a Liar. Crasbo's first statement is ok, and hist second statement means that Jeswin is a Knave or a Liar.
Case 5.1: If Jeswin is a Liar, then his statements check out, and
this is possible.
Case 5.2: If Jeswin is a Knave, then his first statement is true, and his second statement is false.
This is consistent
Case (6)
Jeswin calls himself a Knave. Therefore he is either a Knave or a Liar.
Case 6.1: If Jeswin is a Knave, then his first statement is true, and his second statement is false, and he calls Parker a Liar. This means Parker is either a Knave or a Knight.
Case 6.11: If Parker is a Knave, then his first statement is false, and his second statement is true, so Crasbo is a knight, but Crasbo calls himself a Knave, so this is inconsistent.
Case 6.12: If Parker is a Knight, then his second statement (that Crasbo is a Knight can't be correct, because Crasbo calls himself a Knave). Therefore, this is inconsistent.
Case 6.2: If Jeswin is a Liar, then Parker is either a Knave or a Knight.
Case 6.21: If Parker is a Knave, then his first statement is false, and his second statement is true. Then Crasbo is a Knight, but he can't be (since he calls himself a Knave), so this is inconsistent.
Case 6.22: If Parker is a Knight, then his second statement is true and the same inconsistency as above holds true.
So... from this analysis, to recap, we have the following SIX solutions:
3.11 - Jeswin (Liar), Parker (Knave), Crasbo (Knight)
3.221 - Jeswin (Knight), Parker (Liar), Crasbo (Liar)
3.222 - Jeswin (Knave), Parker (Liar), Crasbo (Liar)
4.2 - Jeswin (Knight), Parker (Knave), Crasbo (Liar)
5.1 - Jeswin (Liar), Parker (Knave), Crasbo (Liar)
5.2 - Jeswin (Knave), Parker (Knave), Crasbo (Liar)
Only in two cases are the three of them all different (which was
not a requirement of the problem)
3.11, 4.2
In 3.xx, GROT=Knight, CLOYSTA=Liar, BLARG=Knave
In 4.xx, GROT=Knight, CLOYSTA=Knave, BLARG=Liar
In 5.xx, GROT=Knave, CLOYSTA=Knight, BLARG=Liar
Edited on October 28, 2003, 7:44 pm
Really Full Solution
