The Solution To The Hardest Logic Puzzle Ever

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SUMMARY

The discussion centers on the "Hardest Logic Puzzle Ever," specifically addressing the logical reasoning behind the puzzle's solution. Participants critique the use of the term "iff" (if and only if) and question the validity of certain assumptions made in the puzzle, such as the geographical context of Rome. Daniel, a computer science major, proposes an alternative approach using XOR logic instead of XNOR, highlighting the flexibility in interpreting the puzzle's constraints. The conversation emphasizes the need for clarity in logical propositions and the implications of asking multiple questions.

PREREQUISITES
  • Understanding of logical operators, specifically XOR and XNOR.
  • Familiarity with the terminology "iff" in mathematical logic.
  • Basic knowledge of propositional logic and compound propositions.
  • Awareness of the context of the "Hardest Logic Puzzle Ever" and its structure.
NEXT STEPS
  • Research the implications of using XOR in logical puzzles.
  • Study the concept of biconditional statements in propositional logic.
  • Explore the historical context and variations of the "Hardest Logic Puzzle Ever."
  • Examine common logical fallacies and assumptions in puzzle-solving.
USEFUL FOR

Logicians, computer science students, puzzle enthusiasts, and anyone interested in advanced logical reasoning and problem-solving techniques.

gravenewworld
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Seems like no one got it so here it is without further adieu (sp?) http://people.ucsc.edu/~jburke/three_gods.pdf
 
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Ouch,mamma,that was...hm...2 smart for me...:cry:

Daniel.
 
I understand how the puzzle was solved, but I have two problems with it.
1. shouldn't be able to make up words "iff"
2. the second question "...iff Rome is in Italy" isn't logically correct. Can't assume Rome is in Italy
 
?

iff=if and only if is standard vocabulary in math and philosophy
 
new one for me, why not say if and only if
 
because mathematicians are notoriously lazy
 
There's a Rome in NY state as well,if I'm not mistaking...:wink:So Trib's right...

Daniel.
 
I figured out the 3 component puzzles before reading on and got answers using XOR instead. Being a computer science major, I thought of XOR before XNOR (XNOR is iff). It works out the same, just reversed.

Still, Boolos limited himself in his choice of questions; if you ask True or False what Random says next, they can only be silent.
 
Ok, that is one brilliant puzzle.
 
  • #10
so by this iff reasoning we can ask things like:
Are you goign to say yes, the 2nd guy no, and the thrd guy yes to the question "blah blah"

I think that's sort of a copout, like asking multiple questions in one.

The original problem should not limit you to asking "only 3 questions" but getting only 3 responses.
 
  • #11
You still get 3 responses.
 
  • #12
I don't know why he assumes the False god would lie about a biconditional (or, for that matter, any compound proposition) but not about its constituent propositions. In [S <-> P], there are 3 propositions in question: S, P, and [S <-> P]. It makes as much sense, if not more, to assume False would lie about all 3. It doesn't effect his conclusion, but still...
Eh, I was going to maybe write and ask him but I see that's unfortunately not possible. Great puzzle still.
 
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  • #13
Bump. I still keep getting PM's asking for the solution to this problem all the time.
 

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