From 50d7c030b9ae97bc16260dfe711a588a437c5b3b Mon Sep 17 00:00:00 2001 From: tomit4 Date: Tue, 12 May 2026 14:32:21 -0700 Subject: [PATCH] :pencil2: Fixed logic --- chapter_1/1_1/additional_exercises.md | 0 chapter_1/1_1/investigate_1_1_1.md | 34 +++++++++++++-------------- 2 files changed, 16 insertions(+), 18 deletions(-) create mode 100644 chapter_1/1_1/additional_exercises.md diff --git a/chapter_1/1_1/additional_exercises.md b/chapter_1/1_1/additional_exercises.md new file mode 100644 index 0000000..e69de29 diff --git a/chapter_1/1_1/investigate_1_1_1.md b/chapter_1/1_1/investigate_1_1_1.md index 6e301fa..36097ee 100644 --- a/chapter_1/1_1/investigate_1_1_1.md +++ b/chapter_1/1_1/investigate_1_1_1.md @@ -11,32 +11,30 @@ Troll 3: Either we are all knaves, or at least one of us is a knight. Which troll is which? +Spend a few minutes thinking about the Investigate problem above. What could you +conclude if you knew Troll 1 really was a knave (i.e., their statement was +false)? Share your initial thoughts on this. + A: Let's think this through step by step by assuming the first Troll is lying. If "If I am a knave, then there are exactly two knights here." = False: -Then: Troll 1 = knave, BUT that doesn't meant that there are exactly two -knights. In other words, the other two could be either knaves or knights. But we -know that this troll is a knave. +So we know he is lying. Although he is indeed a knave, as he claims, we cannot +trust that his presumption, that there are exactly two knights here is true, +because we can assume he is lying from the "Try it" assumption. -Moving on, we have: +Moving on we have Troll 2: -Troll 2: "Troll 1 is lying" +Troll 2: Troll 1 is lying. -If Troll 2 is lying, then Troll 1 is not lying (i.e. a knight), and this -invalidates our previous assumption that Troll 1 is lying, and therefore we -still don't know if the other two trolls are knights. +This troll is a knight, since we know that Troll 1 is a knave -Moving on to troll 3: +Troll 3: Either we are all knaves, or at least one of us is a knight. -Troll 3: "Either we are all knaves, or at least one of us is a knight." - -If we assume troll 3 is also lying, then all three trolls are knaves, and we -have solved their riddle and pass, because he is no knight. - -These are just my initial thoughts on this based off the prompt that we could -start just thinking about this if Troll 1 were lying. - -$$ \therefore $$ +Troll 3 is also a knight, since we know there is one knight here, we know that +all the Trolls are not knaves, and his second presumption, that there is _at +least one_ knight holds true, as now we have 2. Interestingly, if he had said +"exactly one of us is a knight", this problem would become inconsistent and +unsolvable.