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chapter_0/0_1/investigate_0.md

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+1.
+
+Q:
+
+The most popular mathematician in the world is throwing a party for all of his
+friednds. To kick things off, they decide that everyone should shake hands.
+Assuming all 10 people at the party each shake hands with every other person
+(but not themselves, obviously) exactly once, how many handshakes take place?
+
+1A:
+
+If we pair off the people into sets, then we get something like this:
+
+{1, 2}, {1, 3}, {1, 4}, {1, 5}, {1, 6}, {1, 7}, {1, 8}, {1, 9}, {1, 10}
+
+{2, 3}, {2, 4}, {2, 5}, {2, 6}, {2, 7}, {2, 8}, {2, 9}, {2, 10}
+
+{3, 4}, {3, 5}, {3, 6}, {3, 7}, {3, 8}, {3, 9}, {3, 10}
+
+{4, 5}, {4, 6}, {4, 7}, {4, 8}, {4, 9}, {4, 10}
+
+{5, 6}, {5, 7}, {5, 8}, {5, 9}, {5, 10}
+
+{6, 7}, {6, 8}, {6, 9}, {6, 10}
+
+{7, 8}, {7, 9}, {7, 10}
+
+{8, 9}, {8, 10}
+
+{9, 10}
+
+As you can see this just becomes 10+9+8+7+6+5+4+3+2+1=55 handshakes. This likely
+is alluding to basic summation mathematical induction.
+
+2.
+
+Q: At the warm-up event for Oscar's All-Star Hot Dog Eating Contest, Al ate one
+hot dog. Bob then showed him up by eating three hot dogs. Not to be outdone,
+Carl ate five. This continued with each contestant eating two more hot dogs than
+the previous contestant. How many hot dogs did Zeno (the 26th and final
+contestant) eat? How many hot dogs were eaten in total?
+
+A:
+
+This is another summation mathematical induction function, just slightly
+different:
+
+(1) +
+
+(1 + 2) +
+
+(3 + 2) +
+
+(5 + 2) +
+
+(7 + 2) +
+
+(9 + 2) +
+
+(11 + 2) +
+
+(13 + 2) +
+
+(15 + 2) +
+
+(17 + 2) +
+
+(19 + 2) +
+
+(21 + 2) +
+
+(23 + 2) +
+
+(25 + 2) +
+
+(27 + 2) +
+
+(29 + 2) +
+
+(31 + 2) +
+
+(33 + 2) +
+
+(35 + 2) +
+
+(37 + 2) +
+
+(39 + 2) +
+
+(41 + 2) +
+
+(43 + 2) +
+
+(45 + 2) +
+
+(47 + 2) +
+
+(49 + 2) +
+
+(51 + 2) +
+
+(53 + 2) = 55
+
+(1) + (1 + 2) + (3 + 2) + (5 + 2) + (7 + 2) + (9 + 2) + (11 + 2) + (13 + 2) +
+(15 + 2) + (17 + 2) + (19 + 2) + (21 + 2) + (23 + 2) + (25 + 2) + (27 + 2) +
+(29 + 2) + (31 + 2) + (33 + 2) + (35 + 2) + (37 + 2) + (39 + 2) + (41 + 2) +
+(43 + 2) + (45 + 2) + (47 + 2) + (49 + 2) + (51 + 2) + (53 + 2) = 784
+
+55 is how many Zeno ate, and the total hot dogs that were eaten is : 784
+
+3.
+
+Q: After excavating for weeks, you finally arrive at the burial chamber. The
+room is empty except for two large chests. On each is carved a message
+(strangely English):
+
+- Exactly one of these chests contains a treasure, while the other is filled
+  with deadly immortal scorpions.
+
+- For either chest, if the chest's message is true, then the chest contains
+  treasure.
+
+The problem is, you don't know whether the messages are true or false. What do
+you do?
+
+A: Honestly, I'd probably walk away, but since that's likely not the answer,
+we'd likely have to consider that these are relating to a form of truth tables.
+
+The first chest's message claims that one chest contains scorpions, the other
+treasure
+
+So if we say T="contains treasure", and f="contains scorpions", then we can say
+that Chest_1 and Chest_2:
+
+Chest_1 = T Chest_2 = F
+
+The other chest's message claims that if it's own message or the other chest's
+message is true, then the chest contains treasure.
+
+This is a contradiction, because if the second chest's message is true, then
+that chest is the one that contains treasure, and the other chest is the one
+that contains scorpions.
+
+If the second chest's message is false, then the chest doesn't contain treasure,
+but then you don't know if the second chest contains treasure or scorpions,
+because the chest containing treasure is no longer contingent on whether the
+chest's message is true or not.
+
+This is probably best expressed again, in some form, of truth notation.
+
+4.
+
+Q: Back in the days of yore, five small towns decided they wanted to build roads
+directly connecting each pair of towns. While the towns had plenty of money to
+build roads as long and as winding as they wished, it was very important that
+the roads not intersect with each other (as stop signs had not yet been
+invented). Also, tunnels and bridges were not allowed, for moral reasons. It is
+possible for each of these towns to build a road to each of the four other towns
+without creating any intersections?
+
+A: This seems possible, as you could just create two roads from each town to at
+least two other towns (a pair as the question alludes to). But something tells
+me this is a trick question.

chapter_0/0_1/reading_questions.md

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+1. Right now, how would you describe what **discrete** mathematics is about, if
+   you were telling your friends about the class you are in? Write one or two
+   sentences.
+
+Discrete Mathematics is about performing some mathematical logic where the
+inputs and outputs of some function contain only elements that are separate,
+_i.e._ they are discrete. The main problems solved by discrete mathematics deal
+with cominatorics, sequences, symbolic logic, and graph theory, though there are
+others.
+
+2. What questions do you have after reading this section? Write at least one
+   question about the content of this section that you are curious about.
+
+The chest problem interested me as the second chest's message creates a logical
+fallacy, such as "This statement is false." I wonder how this problem would be
+"solved", if it's even possible, with discrete math.