I am a self-learner who became interested in formal logic after stumbling upon some puzzles, like those by Raymond Smullyan in To Mock a Mockingbird.

I am interested in starting with an intro book like this (though I'm open to more suggestions, just took this from an old thread on reddit) and then learning more about how to solve more complex puzzles.

I have some questions about logic puzzles in general though.

What kind of logic does a problem like this (easy, early problem in To Mock a Mockingbird) use? I solved it by just "thinking", but I don't know how to describe the process for solving it and was wondering if anyone could describe the correct method.

We are given three brothers named John, James, and William. John and James (the two J's) always lie, but William always tells the truth. The three are indistinguishable in appearance. You meet one of the three brothers on the street one day and wish to find out whether he is John (because John owes you money). You are allowed to ask him one question answerable by yes or no, but the question may not contain more than three words! What question would you ask?

And would you be able to learn the technique to solve a more advanced problem like this from a textbook, or are solving these kinds of a problem more of a novelty outside of the realm of formal logic?

The problem can be found here.

So after completing a general introduction to logic, what kind of book should I read to be able to solve puzzles like these in a proper manner and learn the theory behind creating them?

Sorry for all the questions, but I these puzzles are so cool and I'd like to learn more!

  • $\begingroup$ That's 5 words. $\endgroup$ – fleablood Apr 30 '17 at 8:38
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    $\begingroup$ The answer is "Are you James" by the way. John will answer yes. The others will answer no. $\endgroup$ – fleablood Apr 30 '17 at 8:41
  • $\begingroup$ Most text books cover symbollic logic pretty quickly and show you how to solve with truth tables. Forming this puzzles and "tricks" though are usually not considered very relevant. $\endgroup$ – fleablood Apr 30 '17 at 8:43

It is a Knights and Knaves type of logic puzzle "where some characters can only answer questions truthfully, and others only falsely. The name was coined by Raymond Smullyan in his 1978 work What Is the Name of This Book?"

You can use Boolean algebra and logic truth tables to solve most problems like these.

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    $\begingroup$ One of the questions the poster asked is "what kind of book should I read to be able to solve puzzles like these in a proper manner?" The Wikipedia page for Knights and Knaves that I linked to gives ways to answer problems like these. $\endgroup$ – Joel Reyes Noche Apr 30 '17 at 8:42
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    $\begingroup$ Answer to what? The op asked for opinions to links and books. S/he didn't ask for a solution to the puzzle. And if s/he he had we are not obligated to give it if we can give advice on how to solve it on our own. I'm upvoting this answer as the downvote was obnoxious. (Especially as the downvoter's, now deleted answer was so very very bad, I don't think he has any right to complain about anyone else's.) $\endgroup$ – fleablood Apr 30 '17 at 8:46
  • $\begingroup$ @JoelReyesNoche Would you recommend reading a general intro book and then jumping into one that covers boolean algebra and the truth tables? Or are these pretty elementary concepts that would be covered in intro books? I'm wary of just choosing random books based off of internet reviews and would rather have a recommendation and then be able to see what people say about it. I just have no experience in this field and don't want to build a bad foundation because I picked a bad book. What book would you recommend for an intro or one that branches into the two concepts you mentioned? $\endgroup$ – Velok Apr 30 '17 at 19:21
  • $\begingroup$ @fleablood yeah, the puzzle is super easy if you just "think" about it, and I was wondering if there are ways to classify this method of "thinking" within formal logic, and then find some books to learn more about it. Spot on with the point of the question, looking for respected books on logic that can help me solve more complex puzzles. $\endgroup$ – Velok Apr 30 '17 at 19:26
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    $\begingroup$ One way to think about the puzzle and harder ones like it systematically is: We need a question that one truth teller and a lie teller will answer the same and one lie teller will answer differently. So it can't be about an objective truth; it must be a question that pertains to their identities. William and James must answer the same despite different parities so it must be something that pertains (or not) to william but not (or does) to james. william and john, and john and james answer differently so it must pertain to william and john but not james or to james but not william and john. $\endgroup$ – fleablood Apr 30 '17 at 19:42

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