My friend told me this complex story. Everyone in it is either a knight, knave, or liar (more than one person can have the same status). Knights always tell truths, liars always lie, and knaves always alternate every statement.
Everyone knew the status of everyone else except for my friend (he knew nothing at first). If anyone lied about what someone said, they didn’t lie about who, when, or whether they said it; they only lied about what the person said. The story goes as follows.
Aaron and Bill were talking to me.
Aaron told me what he was.
At this point, I could tell what Aaron was.
Bill told me one thing that he wasn’t.
Aaron told me that Cassie was a knight.
I then could figure out what Cassie was.
Bill told me that Cassie was a knave.
I thought about this for a minute.
I soon found that the previous thing Bill said allowed me to know for sure what the last of the three people were.
What type is everyone? The puzzle is solvable.
For simplicity, I will refer to the "storyteller" as Dan, and use first initials for everyone.
Tristan has basically told us D is not a knight. If D is a liar, there is not enough information to determine everything, so D is a knave.
Here are the statements as given:
1 - Aaron and Bill were talking to me.
2 - Aaron told me what he was.
3 - At this point, I could tell what Aaron was.
4 - Bill told me one thing that he wasn’t.
5 - Aaron told me that Cassie was a knight.
6 - I then could figure out what Cassie was.
7 - Bill told me that Cassie was a knave.
8 - I thought about this for a minute.
9 - I soon found that the previous thing Bill said allowed me to know for sure what the last of the three people were
There are two cases: the odd statements are false and the even true, or the other way around.
Case 1: the odd statements are false. I won't go into details in this case, but basically there isn't enough information to determine either B or C. But there are some interesting points: In (2) A says what he is, and in (3) D does not know what A is. But after A says "something" in (5) D knows what C is. A must have said something about C. One possibility is that in (2) A said "I am a knave". This would mean A is a knave and telling the truth, or A is a liar. In either case A's next statement would be a lie. So in (5) A could have said "C is not a liar" (or knight, or knave), and D would know what C is. But D would still not know A. Depending on what B said in (7), D may or may not know what B is, but (9) definitely tells us that in the end, D couldn't figure out who was who. If D cannot figure it out at the end, then neither can we, so this case IS unsolvable.
Case 2: the even statements are false. This starts out well, because A and B WERE talking to D, so (1) being true works. A says something in (2), and in (3) D knows what A is. Anything a knight can say, a knave can say. Anything a liar can say, a knave can say. But a knave can say "I am a liar" or "I am not a knight", both of which only a knave can say. Since (2) as reported by D is false, A did not say "I am a liar", so in fact A must have said "I am not a knight". Thus A is a knave, and was telling the truth when he said this. In (5) A speaks again (lying this time), so we know C is not a knight.
In (7) B says C is a knave. In (9) we find that D can deduce everything. Somehow, whatever B said in (4) provided D with enough information to deduce everything.
What might B have said? He did not say "I am not a XXX" because we know statement (4) (as reported by D) is false. He may have made a statement that was know by D to be true (or false). In neither case can we determine the veracity if his next statement, so no information is gained by it and D could not solve the problem. B could have said "I am a knight/knave/liar". Had he said "knight" then again we could not tell the truth or falsehood of any of his statements. Had he said "I am a knave" then we know is next statement will be false. This would allow D to determine what C is, but not what B is. But by (9) D can determine who everyone is. If B said "I am a liar" the we know he is a knave, his next statement is true, and all is determined.
So the conversation that ACTUALLY took place was this:
1 - Aaron and Bill were talking to me.
2 - Aaron said "I am not a knight"
3 - At this point, I could tell Aaron was a knave.
4 - Bill said "I am a liar"
5 - Aaron told me that Cassie was a knight.
6 - I then could not figure out what Cassie was.
7 - Bill told me that Cassie was a knave.
8 - I did not think about this for a minute.
9 - I then determined that by (4) B is a knave, and hence by (7) C is a knave.
They are ALL knaves.
Solution
