[bonanova]

I just met Jane. In many ways she's special, and we've become great friends.

She tells it like it is, good and bad, without ever being critical.

That's a gift I've come to cherish.

She's also a crackerjack logician. So when I won a pair of tickets to the Annual

Knights and Knaves Masked Ball at the Cosmopolitan Club, Jane was my date.

I explained to her as we arrived that everyone inside was either a Knight [who

would always tell the truth] or a Knave [who would always lie] and warned her

that the conversations we'd hear might sound a bit bizarre as a result.

We weren't disappointed. We introduced ourselves to a trio of club members,

Dale, Gene and Lisa, who were conversing.

Conversation 1.

Lisa: I just figured it out: Gene is a Knave.

Gene: Really? Well here's another scoop: You [Lisa] are the same as Dale.

[both Knights or both Knaves.]

Jane whispered, I'm not sure about the other two, but I know what Dale is.

I smiled at my date's logical prowess and asked if she'd like some Chardonnay.

She nodded. When moments later I returned with our drinks, Jane had a puzzle

for me. While you were gone, she said, there were two more conversations, and

I wrote them down. We can look at them later, tho; for now let's just dance and

enjoy the music.

It wasn't until Jane and I were relaxing at her place with a nightcap that she

handed me her notes. Here, she said, see what you can do with these. Since

we already knew a few things about our new friends, I removed all names and

just used letters. She smiled as I read what she'd written.

Conversation 2:

A: B is a Knight.

B: A is not a Knight.

Conversation 3: [Not necessarily the same A and B as above.]

A: B is a Knight.

B: A is a Knave.

It took me a moment, but I was finally able to reply. In each conversation, I said,

I can identify one of the names. In one conversation, it's clear the named person

was speaking with a Knave. In the other conversation, I'm really not sure.

That's the best I can do. Jane smiled and said, You are, quite simply, amazing!

What happened later that evening is material for a different forum.

Can you determine what Jane concluded in Conversation 1?

Can you reproduce my conclusions for 2 and 3?

Good luck!

[Guest]

Jane figured out that Dale is a knave. This is because: if Lisa is a Knight, then Gene lies, and Dale is not the same as Lisa, hence Knave. If Lisa is a Knave, then Gene tells the truth, an Dale is the same as Lisa, hence Knave.

Neither conversation is possible amongst people that are only Knaves or Knights. Hence, a third type of person is involved, and this must be Jane. This is the name that you’re sure of in both conversations. In conversation 3, whether Jane is A or B, the other person is lying, as Jane is neither a knave nor a knight, and hence she is speaking to a knave. However, in conversation 2, it is not clear, as Jane could be person A, and person B would be a Knight, or Jane could be person B, and Person A would be a Knave.