Knights and Knaves

A recent discussion with Nate about his D and D games brought the idea of inserting logic questions into the game as puzzles. That prompted a return to the old Knights and Knaves questions that I used to use in my 7th grade math class when we studies logic. In a far-off land, all the people fell into two categories. Knights always told the truth. Knaves always lied. Your task was to decide which category each person fell into. Here is an example:   

A stranger in their country meets a party of 3 and asks to which race each belongs. The first one mumbles an answer, which the stranger cannot understand. The second says: "He said he was a Knave." The third says to the second: "You're a liar!"
Of what race was the third?    

The key is the second person's comment: no one can ever say, "I'm a knave." If they really are a knave, then they'd be telling the truth, which knaves can't do. If they were a knight, then they'd be lying when they said they were a knave, which knights don't do.  So "I'm a knave" is an impossible statement. When the second person said that person number 1 said that, he must be lying and be a knave. Person 3 therefore was telling the truth and must be a knight.    

These puzzles were popularized by Raymond Smullyan, a logician and professor of philosopher at City College in New York who wrote a book about them entitled, What is the Name of This Book? 

I was especially interested in a series of puzzles patterned after Frank Stockton's short story The Lady Or the Tiger (if you are unfamiliar with it, you can find it here). In lieu of a trial, prisoners are given a choice of opening two doors: one holds a tiger, the other holds a beautiful lady.  In Smullyan's puzzles, you should be able to find the right door if you can reason logically. Each door has a sign. For example the signs could read:  


Door 1:  In this room there is a lady and in the other room there is a tiger.  

Door 2: In one of these rooms there is a lady and in the other room there is a tiger.   

When you ask the king if the signs on the doors are true, he tells you that one is true and one is false.  Which door should you open?        

To find other puzzles like this one (and solutions) you can go here, where there is a complete copy of Smullyan's book The Lady or the Tiger. The website is part of Scribd.com, billed as the world's largest online library. Currently featured on their home page is a copy of the Chicago Streets for Cycling 2020 Plan which makes for very interesting reading and may be a topic for another day.