I met two natives on an island - Benny and Lenny. They are either a knight, a liar or a knave. Knights always tell the truth, liars always lie and knaves alternate between truth and lie. They tell me this:

Benny : We are both of the same type.
Lenny : I am a knave.
Benny : Lenny is a liar.

A knight then tells me what Lenny is. From this I was able to work out what they were.

What are Benny and Lenny?

Benny - Knave; Lenny - Liar

The first thing I notice is that Lenny can't be a knight, since he calls himself a knave. Also, Benny can't be a knight, because then he would be claiming that both men are liars.

Since Lenny made only one statement, we can't tell if he is a liar or knave from that alone; he could easily be either. So, we have to look at Benny's statements.

If Benny is a liar, his first statement must be false, so Lenny is not of the same type, and Lenny is a knave.
Benny's second statement would also be false, leading us to the same conclusion (he's a knave). So, one possibility is that Benny is a liar, and Lenny is a knave (whose statement is true).

If Benny is a knave, and his first statement is true, then Lenny must be of the same type and is also a liar. Then, Benny's second statement is false, and Lenny is not a knave, which again agrees with itself. So another possibility is that Benny is a knave (whose first statement is true and second statement is false) and Lenny is also a knave (whose only statement is true).

Lastly, Benny could be a knave who is lying at first and then telling the truth. If that is the case, then his first statement implies that Lenny cannot also be a knave; he must be a liar. Similarly, Benny's second statement (which must be true) agrees that Lenny is a liar. If Lenny is a liar, of course, his only statement is indeed false. So, a third possibility is that Benny is a knave (whose first statement is false and second statement is true) and Lenny is a liar.

In sum, there are three possibilities from the statements alone:
Benny - Liar; Lenny - Knave
Benny - Knave; Lenny - Knave
Benny - Knave; Lenny - Liar

If then, a knight reveals Lenny's type, and it is possible to work out what both are, Lenny must be a Liar (if he were a knave, there are still two possibilities) and Benny is a Knave. Incidentally, Benny's first statement is false and his second is true.

Posted by DJ on 2003-08-16 20:06:19