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.

If the Friend didn't figure out Bill until the end then he was either slow or not a Knight. Since we're told in a hint that he is not slow, the Friend must not be a Knight. Could the autor Not be a Knight? He says it's both possible and impossible. If the author isn't a Knight, I can't make sense of the first couple paragraphs (especially sentences 2 and 3 in first paragraph).

If the Friend is a liar then all of the statements are false and he didn't figure out what the three people were so lets go with the Friend being a Knave.

If the first statement is false then either Aaron or Bill are not talking to the Friend, but statements 2 and 4 would be true in which case they are talking to the Friend. The first statement is true.

Can tell what Aaron is (3 is true) but Aaron didn't say what he was (2 is a lie). If Aaron said what he wasn't (assumption)  and it gave his identity away, then he must have said he wasn't a Knight proving Aaron is a Knave on truth.

From 5 (Friend on truth but Aaron on lie), we know Cassie is not a Knight and (6 is a lie) we can't tell what Cassie is (Knave or Liar). On 4 the Friend is on lie, so Bill told me what he was (assumption). If Bill said liar we would know he is a Knave on Lie. Seems we are told when something is figured out in this problem (assumption) so he didn't say he's a liar. If he said he's a Knave he's either a Knave on truth or a Liar. If he said he's a Knight he could be a Knight, Liar, or Knave on Lie. 8 being a lie doesn't help much, but 7 and 9 are true so must be able to figure out Cassie (and Bill). To figure out Cassie, Bill must have said he's a Knave in 4 so his next statement would be a lie (either a liar or Knave on lie) and Cassie is a Liar.

This doesn't tell us what Bill is (either a Knave or Liar) so the last statement (The puzzle is solvable) is false.

Doesn't mean much due to assumptions (1:People either say who they are or aren't not and not things like A said B said C is a Kinght; 2: We're told when something is figured out) but maybe this will get discussion going again.

 

Posted by Rajal on 2004-08-10 10:58:05