Added "Gods, Demons, and Mortals"

src/Advanced/Gods, Demons, Mortals/main.typ

@@ -0,0 +1,12 @@
+#import "@local/handout:0.1.0": *
+
+#show: handout.with(
+  title: [Gods, Demons, and Mortals],
+  by: "Mark",
+  subtitle: [Based on Raymond Smullyan's _To Mock a Mockingbird_.],
+)
+
+#include "parts/00 warmup.typ"
+#pagebreak()
+
+#include "parts/01 gods.typ"

src/Advanced/Gods, Demons, Mortals/meta.toml

@@ -0,0 +1,6 @@
+[metadata]
+title = "Gods, Demons, and Mortals"
+
+[publish]
+handout = true
+solutions = true

src/Advanced/Gods, Demons, Mortals/parts/00 warmup.typ

@@ -1,34 +1,36 @@
 #import "@local/handout:0.1.0": *
 
-= Miscellaneous Puzzles
+= Warm-Up
 
 #problem("The Flower Garden")
 In a certain flower garden, each flower was either red, yellow,
 or blue, and all three colors were represented. A statistician
 once visited the garden and made the observation that whatever three flowers you picked, at least one of them was bound
 to be red.
+
+#v(2mm)
+
 A second statistician visited the garden and made
 the observation that whatever three flowers you picked, at
 least one was bound to be yellow.
 
-Two logic students heard about this and got into an argument. The first student said: "It therefore follows that whatever three flowers you pick, at least one is bound to be blue,
+#v(2mm)
+
+Two logic students heard about this and got into an argument. \
+The first student said: "It therefore follows that whatever three flowers you pick, at least one is bound to be blue,
 doesn't it?" The second student said: "Of course not!"
 Which student was right, and why?
 
 #solution[
   The first student was right, and here is why. From the
-  first statistician's report it follows that there cannot be more
+  first statistician's report it follows that there cannot be more than one yellow flower, because if there were two yellows, you could pick two yellows and one blue, thus having a group of three flowers that contained no red. This is contrary to the report that every group of three is bound to contain at least one red flower. Therefore there cannot be more than one yellow flower.
-  than one yellow flower, because if there were two yellows,
+
-  you could pick two yellows and one blue, thus having a group
+  #v(2mm)
-  of three flowers that contained no red. This is contrary to the
+
-  report that every group of three is bound to contain at least
+  Similarly, there cannot be more than one blue flower, because if there were two blues, you could pick two blue flowers and one yellow and again have a group of three that contained no red. And so from the first statistician's report it follows that there is at most one yellow flower and one blue.
-  one red flower. Therefore there cannot be more than one yellow flower.
+
+  #v(2mm)
 
-  Similarly, there cannot be more than one blue
-  flower, because if there were two blues, you could pick two
-  blue flowers and one yellow and again have a group of three
-  that contained no red. And so from the first statistician's report
-  it follows that there is at most one yellow flower and one blue.
   And it follows from the report of the second statistician that
   there is at most one red flower, for if there were two reds,
   you could pick two reds and one blue, thus obtaining a group
@@ -36,8 +38,10 @@ Which student was right, and why?
   second report that there cannot be more than one blue,
   although we have already deduced this from the first report.
 
+  #v(2mm)
+
   The upshot of all this is that there are only three flowers
-  in the entire garden-one red, one yellow, and one blue! And
+  in the entire garden---one red, one yellow, and one blue! And
   so it is of course true that whatever three flowers you pick,
   one of them must be blue.
 ]
@@ -63,6 +67,8 @@ Can you figure out what question I could have in mind?
   no, then you are denying that no is your answer, although no
   was your answer.
 
+  #v(2mm)
+
   It is therefore impossible for you to answer
   the question correctly even though the question does have a
   correct answer: Either you answer no or you don't. If you do,
@@ -94,6 +100,8 @@ have computed the probability that there will be a bomb on
 the plane," he explained, "and although this probability is low,
 it is still too high for my comfort."
 
+#v(2mm)
+
 Two weeks later, the friend
 met the statistician on a plane. "How come you changed your
 theory?" he asked. "Oh, I didn't change my theory; it's just

src/Advanced/Gods, Demons, Mortals/parts/01 gods.typ

@@ -2,54 +2,73 @@
 
 = Gods, Demons, and Mortals
 
-#definition()
+#generic("Setup:")
-Shortly after Inspector Craig returned to London from his
+One night, Inspector Craig had a curious dream.
-strange experience in Subterranea, he had a curious dream.
 He had been browsing that day in a library specializing in rare
 books on mythology, another of his many interests. His head
 was filled with gods and demons, and so his dream was perhaps not so surprising.
+
+#v(2mm)
+
 Time sometimes passes in unusual ways in the course of a
 dream. Craig dreamed that he spent nine days in a region in
-which dwelled gods, demons, and mortals. The gods, of
+which dwelled gods, demons, and mortals.
-course, always told the truth, and the demons always lied. As
+
-to the mortals, half were knights and half were knaves. As
+#v(2mm)
-usual, the knights told the truth and the knaves lied.
+
+The gods, of course, always told the truth, and the demons always lied. As to the mortals, half were knights and half were knaves. As usual, the knights told the truth and the knaves lied.
 
 #problem("The First Day")
 Craig dreamed that on the first day he met a dweller of the
-region who looked as ifhe might be a god, though Craig could
+region who looked as if he might be a god, though Craig could
 not be sure. The dweller evidently guessed Craig's thoughts,
 smiled, and made a statement to reassure him. From this state-
 ment, Craig knew that he was in the presence of a god.
+
+#v(2mm)
+
 Can you supply such a statement?
 
 #solution[
-  One statement that works is: "I am not a knight." If the
+  One statement that works is: "I am not a knight."
-  speaker were a knave or a demon, then it would be true that
+
-  he was not a knight, but knaves and demons don't make true
+  #v(2mm)
-  statements. Therefore the speaker was neither a knavtr nor a
+
+  If the speaker were a knave or a demon, then it would be true that he was not a knight, but knaves and demons don't make true statements.
+
+  #v(2mm)
+
+  Therefore the speaker was neither a knave nor a
   demon, hence he was a knight or a god and his statement was
-  true. Since it was true, then he really is not a knight; hence
+  true.
-  he must be a god.
+
+  #v(2mm)
+
+  Since it was true, then he really is not a knight; hence he must be a god.
 ]
 
+#v(1fr)
+
 
 #problem("The Second Day")
-In this episode of the dream, Craig met a terrifying-looking
+In this episode of the dream, Craig met a terrifying being who had every appearance of being a demon.
-being who had every appearance of being a demon.
+
-"What sort of being are'you?" asked Craig, in some alarm.
+"What sort of being are you?" asked Craig, in some alarm.
-The being answered, and Craig then realized that he was confronting not a demon, but a knave. What could the being have
+
-answered?
+The being answered, and Craig then realized that he was confronting not a demon, but a knave. \
+What could the being have answered?
 
 #solution[
   A statement that works is: "I am a demon." Obviously
   no demon can claim he is a demon, so the speaker is not a
   demon. Therefore his statement was false and since he is not
   a demon, he must be a knave.
-  Incidentally, this and the last puzzle are essentially the same
-  as Problems 4 and 5 of Chapter 1, the puzzles about the prizes.
 ]
 
+#v(1fr)
+#pagebreak()
+
+
 #problem("The Third Day")
 In this episode, Craig met a totally nondescript-looking being
 who from appearances could have been anything at all. The
@@ -61,19 +80,26 @@ Can you supply such a statement?
 #solution[
   This is a bit more tricky: A statement that works is: "I
   am either a god or a knave." That could be said by a god,
-  since a god is either a god or a knave; it could also be falsely
+  since a god is either a god or a knave; it could also be falsely said by a demon.
-  said by a demon. It couldn't be said by a knight, because a
+
-  knight would never lie and claim that he is either a god or a
+  #v(2mm)
-  knave, and it couldn't be said by a knave, because a knave
+
-  would never admit to the true fact that he is either a god or
+  It couldn't be said by a knight, because a knight would never lie and claim that he is either a god or a knave, and it couldn't be said by a knave, because a knave would never admit to the true fact that he is either a god or
-  a knave. And so the speaker must be either a god or a demon,
+  a knave.
+
+  #v(2mm)
+
+  And so the speaker must be either a god or a demon,
   but there is no way to tell which.
 ]
 
+#v(1fr)
+
+
 #problem("The Fourth Day")
 Craig next met a being who made the following two statements:
-1. A god once claimed that I am a demon.
+- A god once claimed that I am a demon.
-2. No knight has ever claimed that I am a knave.
+- No knight has ever claimed that I am a knave.
 What sort of being was he?
 
 
@@ -82,52 +108,74 @@ What sort of being was he?
   it were true, a god would have once claimed that the speaker
   was a demon, which would mean that the speaker really was
   a demon, but no one who tells the truth can be a demon. Since
-  the first statement was false, so was the second statement, since
+  the first statement was false, so was the second statement, since it was made by the same speaker. Therefore a knight did once claim that the speaker was a knave, hence the speaker really
-  it was made by the same speaker. Therefore a knight did once
-  claim that the speaker was a knave, hence the speaker really
   is a knave.
 ]
 
+#v(1fr)
+
+
 #problem("The Fifth Day")
 A being made the following two statements to Craig:
-1. I never claim to be a knave.
+- I never claim to be a knave.
-2. I sometimes claim that I am a demon.
+- I sometimes claim that I am a demon.
 What sort of being are we now dealing with?
 
 #solution[
-  The speaker's second statement was obviously a lie, be-
+  The speaker's second statement was obviously a lie, because no truth-teller would ever say that he sometimes claims
-  cause no truth-teller would ever say that he sometimes claims
+  to be a demon.
-  to be a demon. Therefore the first statement was also a lie,
+
+  #v(2mm)
+
+  Therefore the first statement was also a lie,
   hence the speaker does sometimes claim to be a knave, hence
   he must be a demon.
 ]
 
+#v(1fr)
+#pagebreak()
+
+
 #problem("The Sixth Day")
 In this episode, Craig came across two beings, each of whom
-made a statement. Craig could then infer that at least one of
+made a statement. \
-them must be a god, but he could not tell which one. From
+Craig could then infer that at least one of
-neither statement alone could Craig have deduced this.
+them must be a god, but he could not tell which one. \
+From neither statement alone could Craig have deduced this. \
 What statements could the beings have made?
 
 #solution[
-  Many solutions are possible; here is one. Let us call the
+  Many solutions are possible; here is one.
-  two beings A and B. Now, suppose A and B make the fol-
+
-  lowing two statements:
+  #v(2mm)
-  A: B is a knight.
+
-  B: A is not a knight.
+  Let us call the two beings A and B. \
+  Now, suppose A and B make the following two statements:
+  - A: B is a knight.
+  - B: A is not a knight.
+
   A is either telling the truth or lying.
-  Case 1-A is telling the truth: Then B really is a knight,
+
-  hence his statement is true, hence A is not a knight, therefore
+  #v(2mm)
-  A must be a god, since he is telling the truth.
+
-  Case 2-A is lying: Then B is not a knight, since A says
+  *Case 1: A is telling the truth.* \
-  he is. Also, since A is lying, then A is certainly not a knight,
+  Then B really is a knight,
-  hence B's statement is true. Therefore B is telling the truth,
+  hence his statement is true, hence A is not a knight, therefore A must be a god, since he is telling the truth.
-  but is not a knight, hence B is a god.
+
-  So if Case 1 is true, A is a god; if Case 2 is true, then B is
+  #v(2mm)
-  a god. There is no way to tell whether A is telling the truth
+
-  or lying.
+
+  *Case 2: A is lying.* \
+  Then B is not a knight, since A says he is. Also, since A is lying, then A is certainly not a knight, hence B's statement is true. Therefore B is telling the truth, but is not a knight, hence B is a god.
+
+  #v(2mm)
+
+  So if Case 1 is true, A is a god; if Case 2 is true, then B is a god. \
+  There is no way to tell whether A is telling the truth or lying.
 ]
 
+#v(1fr)
+
 #problem("The Seventh Day")
 On the next day, Craig again met two beings each of whom
 made a statement. Craig could then infer that one of them was
@@ -136,16 +184,19 @@ was which. Again, from neither statement alone could Craig
 have inferred this. Can you supply two such statements?
 
 #solution[
-  gain let us call the two beings A and B. The following
+  Again, let us call the two beings A and B. \
-  statements would work:
+  The following statements would work:
-  A: Both of us are knaves.
+  - A: Both of us are knaves.
-  B: Both of us are demons.
+  - B: Both of us are demons.
   It is obvious that both are lying. Since A is lying, they are
   not both knaves. Since B is lying, they are not both demons.
   Therefore one is a knave and one is a demon, but there is no
   way to tell which one is which.
 ]
 
+#v(1fr)
+
+
 #problem("Introducing Thor")
 On the eighth day, Craig met a being who had every ap-
 pearance of being the god Thor. The being made a statement,
@@ -155,19 +206,32 @@ What statement could Thor have made?
 #solution[
   A statement that works is: "I am either a knave or a demon
   or the god Thor."
+
+  #v(2mm)
+
   If the speaker were either a knave or a demon, then it would
   be true that he is either a knave or a demon or the god Thor.
-  This would mean that a knave or a demon made a true state-
+
-  ment, which is not possible. Therefore the speaker is neither
+  #v(2mm)
-  a knave nor a demon, hence his statement is true. Hence he
+
-  must be the god Thor.
+  This would mean that a knave or a demon made a true statement, which is not possible. Therefore the speaker is neither a knave nor a demon, hence his statement is true.
+
+  #v(2mm)
+
+  Hence he must be the god Thor.
 ]
 
+#v(1fr)
+#pagebreak()
+
 #problem("A Perplexity Resolved")
 Craig and Thor became fast friends. In fact, on the evening of
 the ninth day, Thor gave a magnificent banquet in Craig's
 honor. "I propose a toast to our illustrious guest!" said Thor,
 as he raised his glass of nectar.
+
+#v(2mm)
+
 After a round of cheers, Craig was asked to speak.
 "I am very perplexed!" said Craig as he rose. "I wonder
 if this may not all be a dream!"
@@ -179,6 +243,9 @@ could possibly make. Then this afternoon I met someone else
 who also made a statement which no dweller of this region
 could possibly make. That is why I suspect that I may be
 dreaming. "
+
+#v(2mm)
+
 "Oh!" said Thor. "Be reassured; you are not dreaming.
 The two incidents have a perfectly rational explanation. You
 see, we have had two visitors here from another realm. Both
@@ -187,60 +254,64 @@ although he is not called a knight since he is not from this
 region. The other is Alexander, who sometimes tells the truth
 and sometimes lies. It must have been those two whom you
 met today. What statements did they make?"
+
+#v(2mm)
+
 Craig then told the company what each had said.
-"That explains it perfectly!" said Thor. "Moreover, it fol-
+"That explains it perfectly!" said Thor. "Moreover, it follows from their having said what they did that Cyrus was the
-lows from their having said what they did that Cyrus was the
 one you met in the morning. And interestingly enough, if you
 hadn't met Alexander in the afternoon, you could never have
 known whether the one you met in the morning was Cyrus
 or Alexander."
-Craig thought the matter over and realized that Thor was
+
-right.
+#v(2mm)
-What statements could these two outsiders have made
+
-which fulfill all of the above conditions?
+Craig thought the matter over and realized that Thor was right. \
+What statements could these two outsiders have made which fulfill all of the above conditions?
 
 #solution[
-  Here is one possible solution.
+  Here is one possible solution:
-  MORNING SPEAKER: "I am neither a knight nor a god."
+  - morning speaker: "I am neither a knight nor a god."
-  AFTERNOON SPEAKER: "I am either a knave or a demon."
+  - afternoon speaker: "I am either a knave or a demon."
+
   No inhabitant of the region could make either of those
   statements. No knight or god could claim that he is neither a
   knight nor a god; no knave or demon could make the true
-  statement that he is neither a knight nor a god. As for the
+  statement that he is neither a knight nor a god.
-  second statement, obviously no knight or god would claim to
+
-  be either a knave or a demon and no knave or demon would
+  #v(2mm)
-  admit to being a knave or a demon. Therefore both were out-
+
-  siders; namely, Cyrus and Alexander. The statement of the
+  As for the second statement, obviously no knight or god would claim to be either a knave or a demon and no knave or demon would admit to being a knave or a demon. Therefore both were outsiders; namely, Cyrus and Alexander.
-  morning speaker was true and the statement of the afternoon
+
-  sp,eaker was false. Since Cyrus never makes false statements,
+  #v(2mm)
-  he couldn't have been the afternoon speaker. Thus he was the
+
-  morning speaker.
+
+  The statement of the morning speaker was true and the statement of the afternoon speaker was false. Since Cyrus never makes false statements, he couldn't have been the afternoon speaker. Thus he was the morning speaker.
 ]
 
+#v(1fr)
+#pagebreak()
+
 #problem("A Philosophical Puzzle")
-The next morning when Craig was wide awake and recalling
+The next morning, Craig was wide awake and recalling
-his dream, he wondered whether he had been logically inconsistent in his sleep. "The trouble is this," thought Craig: "In
+his dream. He wondered whether he had been logically inconsistent in his sleep. "The trouble is this," thought Craig: "In my dream I believed that Thor was a god and that gods always tell the truth. Yet Thor told me that I wasn't dreaming. Now how could Thor, who tells the truth, say that I wasn't dreaming when in fact I was? Wasn't this an inconsistency on my part?"
-my dream I believed that Thor was a god and that gods always
+
-tell the truth. Yet Thor told me that I wasn't dreaming. Now
+#v(2mm)
-how could Thor, who tells the truth, say that I wasn't dreaming when in fact I was? Wasn't this an inconsistency on my
+
-part?"
 Would you say that Craig's dream was logically inconsistent?
 
 #solution[
-  As I see it, Craig's dream was not necessarily inconsistent. If
+  As I see it, Craig's dream was not necessarily inconsistent. If Craig had actually believed in the dream that he was dreaming, then the set of his beliefs during his dream would have been inconsistent, since the following propositions are indeed logically contradictory:
-  Craig had actually believed in the dream that he was dreaming,
+  - Thor is a god
-  then the set of his beliefs during his dream would have been
+  - Gods make only true statements
-  inconsistent, since the following propositions are indeed log-
+  - Thor stated that Craig was not dreaming;
-  ically contradictory: (1) Thor is a god; (2) Gods make only
+  - Craig was dreaming.
-  true statements; (3) Thor stated that Craig was not dreaming;
+
-  (4) Craig was dreaming.
+  #v(2mm)
-  The contradiction is obvious. However, there is no evi-
+
-  dence that Craig at any time of his dream believed that he was
+  The contradiction is obvious. However, there is no evidence that Craig at any time of his dream believed that he was dreaming, although at one point he wondered whether he might be dreaming. Craig presumably believed that he was awake, and this belief, though false, was perfectly consistent with the other beliefs of his dream.
-  dreaming, although at one point he wondered whether he
+
-  might be dreaming. Craig presumably believed that he was
+  #v(2mm)
-  awake, and this belief, though false, was perfectly consistent
+
-  with the other beliefs of his dream.
+  Curiously enough, if Craig had formulated the belief that he was dreaming, then this belief, though correct, would have created a logical inconsistency!
-  Curiously enough, if Craig had formulated the belief that
-  he was dreaming, then this belief, though correct, would have
-  created a logical inconsistency!
 ]

src/Advanced/Logic Puzzles/main.typ

@@ -1,17 +0,0 @@
-#import "@local/handout:0.1.0": *
-
-#show: handout.with(
-  title: [Bonus: Logic Puzzles],
-  by: "Mark",
-  subtitle: [Based on Raymond Smullyan's _To Mock a Mockingbird_.],
-)
-
-#set par(first-line-indent: 5mm)
-
-#include "parts/00 one.typ"
-#pagebreak()
-
-#include "parts/01 logician.typ"
-#pagebreak()
-
-#include "parts/02 gods.typ"

src/Advanced/Logic Puzzles/meta.toml

@@ -1,7 +0,0 @@
-[metadata]
-title = "Tropical Polynomials"
-
-
-[publish]
-handout = false
-solutions = true