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 Knowing the Natives (Posted on 2003-08-16)
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?

 See The Solution Submitted by Lewis Rating: 3.8000 (5 votes)

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 Puzzle Solution | Comment 13 of 14 |

At the outset, Lenny cannot be a knight since no knight will falsely proclaim himself as a knave.

Assume that Benny is a knight. If so, then in terms of his first statement it follows that Lenny is a knight. This is a contradction.

So, neither Benny, nor Lenny can be a knight. Now, if both Benny and Lenny are liars, then Benny's truthfully spoken 2nd statement is a contradction.

Thus, the valid choices are:

Benny      liar        knave      knave
Lenny     knave       liar         knave

Now, if the visitor was told that Lenny is a knave, it would be impossible for him to resolve Benny's type, since in terms of the above table, Benny can either be a liar or a knave. On the other hand, knowing that Lenny is liar will immediately enable the visitor to establish that Benny is a knave.

Consequently, the visitor was told that Lenny is a liar and he deduced that Benny is a knave.

Edited on July 5, 2008, 1:02 pm
 Posted by K Sengupta on 2008-05-14 16:03:00

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