Mining the works of Raymond Smullyan

Raymond M. Smullyan is a mathematician and logician (and a concert pianist and magician — a real polymath) who has written several books of puzzles and logic games, generally riffing on simple or classical puzzles and taking them to ever increasing extremes.

For example, readers of this blog are likely familiar with the  scene in Labyrinth where there are two doors, guarded by a two-headed knight, one of whose heads lies and the other tells the truth, and the heroine must ask one question to determine which door to take (one leads to certain death). This is derived from ancient Greek logic problems (“All Cretans are liars…”) and the solution is fairly straightforward.  But Smullyan develops a series of increasingly difficult permutations of this problem (he calls these “Knights and Knaves” puzzles — knights always tell the truth and knaves always lie), with additional layers of complexity. Smullyan’s problems usually involve a set of rules about when people are knights or knaves (it might depend on the day of the week, or other things) and provide a set of statements from which the reader deduces who is a knight, knave, or other (some characters might not always lie). So you might vex your players with problems where the informants are known to be knights or knaves but they don’t know which. Obviously the problem will always have to impose some limits on the number of questions that can be asked — perhaps the “Speak with dead” spell always contacts either a knight or a knave but you don’t know which and you only get one question… Here is a cool Knights & Knaves puzzle generator.

You may also be familiar with the famous story “The lady or the tiger?” by Frank Stockton.  Smullyan has a book (of the same title) which riffs on this sort of puzzle, usually with more than two doors, but with the added feature that the correct door can be induced from the inscriptions on the doors (at least one of which is true). This is related to a similar puzzle somewhere in The Merchant of Venice (a Shakespeare play I never read) where Portia’s suitors need to choose the correct box to win her hand, and each box is inscribed with a statement but only one is true. Smullyan riffs on and complicates this puzzle to create much more challenging versions in his book What is the name of this book? (Yes, that is the title. A little self-referential.)

So, if you’re tired of “Which lever do we pull?” type puzzles, check out the works of Raymond M. Smullyan! Your players will hate you forever.

Published in: on July 8, 2010 at 10:28 am  Comments (3)  
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3 CommentsLeave a comment

  1. Excellent… Just what I need as I begin to stock my megadungeon!

  2. Those logic puzzles always kill me. My solution to the Knight and Knave problem, is kill the guardian, throw the body through the door, open it but don’t go through, throw the body in and wait to see what happens. If nothing happens to the body, you found the right door. If something pounces on the incoming body, then close the door real fast, and locktight it–a T & T spell for holding doors shut. IN fact, I have a number of solutions for the death beyond the door problem–none of which actually involves just stepping through the door assuming we’ll be ok. The great philosopher Yogi Berra is my guide in such situations when he said, “You can see a lot by simply watching.”

    Yes, Smullyan sounds like an excellent resource for dungeon designers. Thanks for the great blog.

    • Thanks, Ken, you are as always too kind.
      Actually, Berra’s famous aphormism “When you come to a fork in the road, take it,” seems more appropos* here.

      *If that is how it’s spelled.**
      **There, I saved myself typing five or six letters by using a pretentious foreign term. Mission accomplished!

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