The Return of Problem of the Week

The start of the spring semester brings with it a new round of Problem of the Week! This term’s theme is “Knights, Knaves, Normals, Werewolves and Other Fanciful Creatures.” That’s right! A whole term dedicated to the most endearing characters ever to populate fictional islands in logical brainteasers. The problems will get harder as we go along, but I always like to start with a few easy ones. So have a go at it, if you like.

Comments

  1. #1 eric
    January 20, 2014

    Easy peasy (I think)!

    So I don’t ruin it for people doing the problem, my answer is hidden in the Samuel L. Ipsum, below.


    The path of the righteous man is beset on all sides by the iniquities of the selfish and the tyranny of evil men. Blessed is he who, in the name of charity and good will, shepherds the weak through the valley of darkness, for he is truly his brother’s keeper and the finder of lost children. A- kv, B-kn, C-kv. And I will strike down upon thee with great vengeance and furious anger those who would attempt to poison and destroy My brothers. And you will know My name is the Lord when I lay My vengeance upon thee.

    lorem ipsum

  2. #2 Lenoxus
    January 20, 2014

    eric: I like that way of hiding answers!

    Jason wrote:

    A whole semester dedicated to the most endearing characters ever to populate fictional islands in logical brainteasers.

    Aha! You have have thought that overly narrow superlative would have to be true by definition, but what about the islanders who don’t know their eyes are blue?

    If I were asked which was more endearing, I’d call it a toss-up. I love knights-and-knaves puzzles, but the blue-eyes one can get very deep, and is fun to work out the confusions people tend to have. I even wrote a long exploration of some of the common counter-arguments to its solution.

    As for knights and knaves, here’s a puzzle I developed myself, in an effort to get a better sense of the structure of solutions…

    In a group of five people are exactly three knights and two normals. What is the fewest number of questions needed to identify the normals in the group, and what would the questions be?

    For purposes of my puzzle, normals are just like ordinary humans, capable of answering yes or no to any question regardless of truth, falsehood, or logical consistency. They can also choose to be silent, which is something a knight may be forced to do if the question would be paradoxical to answer (Like “Is your answer ‘no’ to this question?”)

  3. #3 Gary Sturgess
    January 21, 2014

    Nice and easy for the starter. Later in the semester, are the fictional creatures similar to those from Raymond Smullyan’s insane vampires and so on?

    As for the solution, I have often thought that the Slayer would be considered a paladin in D&D terms, while Foundation’s author and the great detective are truly both named Jack. (Hopefully that is sufficiently obscure that it doesn’t spoil?)

  4. #4 Verbose Stoic
    January 21, 2014

    I come to the same conclusion as Gary and eric. Yep, it’s an easy one, but a good one to start with if you’re just being introduced to the topic, because it really gets you thinking about what it really means to be a knight or a knave. Once you have that, the answer follows.

  5. #5 Karl Lembke
    Tujunga, CA
    January 21, 2014

    Very easy problem, as long as you assume it’s being narrated by a knight. :-)

  6. #6 Lenoxus
    January 21, 2014

    Karl Lembke: Lol. Technically that’s true of all puzzles (well, except for the “very easy” part), but these ones certainly bring the narrator’s trustworthiness to the forefront of our thoughts…

  7. #7 Jason Rosenhouse
    January 22, 2014

    I remember in one of John Dickson Carr’s locked room mysteries, The Three Coffins, he stipulates right at the start certain characters are telling the absolute truth about what they witnessed. He remarks that to have any kind of proper story at all, someone has to be telling the truth. I think you can treat these puzzles with the same spirit!

    Incidentally, I generally try to keep the problems at a level of difficulty where even students in the lower level classes can participate if they choose to. I don’t want a situation where only the top math majors can reasonably attempt the problems. So, the problems will get more challenging, but especially the first five will be fairly straightforward. (I do ten problems in any one term.)

  8. #8 Charles Sullivan
    January 22, 2014

    Figured it out in my head in about 5 minutes, Could have been faster, but I had to double check and triple check just to make sure I didn’t commit a mistake in reasoning.

  9. #9 Gary Sturgess
    January 23, 2014

    I am very keen to solve all of these, but if I’m understanding correctly these are homework problems for your students. Accordingly, are they any guidelines you’d like us to follow about posting solutions in the comments? Say, no posting solutions until the next problem is up, or something?

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