Brain Puzzle Results

THE RESULTS ARE IN!

By popular vote, the answer to the riddle is:

Amanda = Knight

Boris = Can't be determined.

As it turns out, the readers of this e-blog are very astute and clever and the voters got it RIGHT!  The correct solution to the riddle is that Amanda is a Knight and Boris could be either a Knight or a Knave.  There are some very good explanations in the comments section of the original post.  John's is the easiest to understand, Wor's is the one most likely to be understood by a computer, and Phillip's has the best links.

Here is the basic reasoning behind the answers to this brain puzzle.  Let's consider the four possible outcomes:

1. Amanda = Knight; Boris = Knight
2. Amanda = Knight; Boris = Knave
3. Amanda = Knave; Boris = Knight
4. Amanda = Knave; Boris = Knave

I think we can agree that there is no other possible outcome.  Amanda must be either a knight or a knave and Boris must be either a knight or a knave.  Now, let's see in which of these possible outcomes Boris' statement, "Amanda would say that I am a Knight" is true.

1. If Amanda = Knight and Boris = Knight, then the statement is true.  Why?  Because in this case, Boris actually is a knight.  Amanda, being a knight herself, would say that Boris is a Knight.  And Boris, a knight, is telling the truth when he says, "Amanda would say that I am a Knight."  Conclusion: YES!
2. If Amanda = Knight and Boris = Knave, then the statement is still true.  Why?  Because in this case Boris is a knave, so Amanda, a knight who always tells the truth, would not say "Boris is a Knight".  But Boris, a lying knave, would not report truthfully about this.  He would lie and say "Amanda would say that I am a Knight."  So, even though Boris' statement is false, it is still consistent with Boris' being a knave.  Conclusion: YES!
3. If Amanda = Knave and Boris = Knight, then Amanda would not say "Boris is a knight".  He is a knight, but as a knave, Amanda would not say so.  This would make Boris' statment, "Amanda would say that I am a knight" false, which is not consistent with Boris being a knight.  Conclusion: NO!
4. If Amanda = Knave and Boris = Knave, then Amanda would lie about Boris and say that he is a knight.  Boris, however, being a knave, would then lie about Amanda's lie, and so he would not say "Amanda would say that I am a knight."  Conclusion: NO!

Summary:  In the first two possible outcomes, Boris' statement, "Amanda would say that I am a Knight" is consistent with the premises.  In the second two, it is not.  In both of the consistent outcomes (the first two) Amanda is a Knight.  We can therefore conclude that Amanda must be a knight.  Boris, on the other hand, may be either a knight or a knave because there is a consistent outcome in which he is a knight and a consistent answer in which he is a knave.