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## #1 2023-06-28 08:53:36

mathassistant
Novice
Registered: 2023-06-27
Posts: 2

### Are there even puzzles related to The Hardest Logic Puzzle ever?

Greetings! I’m an assistant of a mathematical scientific researcher, and my research programme evolves around finding and developing all the (possible) solutions regarding all unsolved mathematical, logic, exact, and IQ puzzles ever created. If you search on the internet for: “The hardest unsolved logic math/iq puzzle/problem ever possible”. You would find the well-known "The Hardest Logic Puzzle Ever" (https://en.wikipedia.org/wiki/The_Hardest_Logic_Puzzle_Ever). I would like to gather some of your thoughts around this puzzle.

Quote:
This puzzle involves three gods, A, B, and C, who are named True, False, and Random. True always speaks truly, False always speaks falsely, and Random's responses are completely random. The goal is to determine the identities of A, B, and C by asking three yes-no questions, with each question directed at only one god. The gods respond in their own language, where the words for yes and no are da and ja, in some order, and we do not know which word corresponds to which answer.
End quote.

The proposed solution on Wikipedia assumes that one of the gods must answer a factual question truthfully, leading to the conclusion that "ja" corresponds to "yes" and "da" corresponds to "no." However, this assumption is not valid within the constraints of the puzzle, as Random's responses are completely random, and there is no guarantee that a factual question will elicit a truthful response.

Furthermore, the solution on Wikipedia violates the rule that each question must be directed at only one God. In the proposed solution, the same god is asked the third question, which is not in accordance with the puzzle's requirements.

Considering the difficulty of this puzzle, I have a few questions for you:

Given that “puzzle” is a puzzle related to:
-    Math
-    Logic
-    Insight
-    Strategic
-    Tactic
-    Intelligence
-    Exact

1.    Is it ever possible that a harder, unsolved puzzle compared to "The Hardest Logic Puzzle Ever" exists? If so, what makes it more challenging?
2.    Is there a definitive solution to "The Hardest Logic Puzzle Ever"? Are there any alternative valid solutions? Because based on all our research, the “solutions” available are all the same type (which are all false because of violations of the rules or assumptions).
3.    If there is a solution, can a valid truth table be constructed to represent the possible answers of the gods and their identities?

I would greatly appreciate your insights and any additional information you can provide regarding the puzzle. Your contributions will aid our ongoing research into unsolved mathematical, logical, and IQ puzzles.”

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## #2 2023-06-29 01:08:08

Bob
Registered: 2010-06-20
Posts: 9,719

### Re: Are there even puzzles related to The Hardest Logic Puzzle ever?

Like Deep Thought in The Hitchhikers Guide To The Galaxy, I have to say this may take some time.

Thought process exgaged; don't hold your breath though.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

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## #3 2023-06-29 21:09:03

Bob
Registered: 2010-06-20
Posts: 9,719

### Re: Are there even puzzles related to The Hardest Logic Puzzle ever?

hi mathassistant

1.    Is it ever possible that a harder, unsolved puzzle compared to "The Hardest Logic Puzzle Ever" exists? If so, what makes it more challenging?

Hardest is subjective.  Someone might say "It was easy for me to solve this."

'Very complicated' might be a better way to describe the puzzle.  So how about having four 'gods', one a truth sayer, one a false sayer, one a random, and one of which we don't know its nature.

2.    Is there a definitive solution to "The Hardest Logic Puzzle Ever"? Are there any alternative valid solutions? Because based on all our research, the “solutions” available are all the same type (which are all false because of violations of the rules or assumptions).

You say "In the proposed solution, the same god is asked the third question" but Boolos has made this clarification: "a single god may be asked more than one question ...." so I don't think the proposed solution does violate the rules.

3.    If there is a solution, can a valid truth table be constructed to represent the possible answers of the gods and their identities? Yes. Because that's what truth tables do.

The four colour problem and Fermat's last theorem (until Wiles) were considered hard because no one could either come up with an answer nor prove them false.  The claim that it's the hardest is not valid since it is not possible to state with certainty that a harder puzzle doesn't exist.

I'll continue to ponder this puzzle. Just going through the truth tables will take quite a while.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

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## #4 2023-07-09 10:14:46

mathassistant
Novice
Registered: 2023-06-27
Posts: 2

### Re: Are there even puzzles related to The Hardest Logic Puzzle ever?

Hi Bob, thank you contributions made in response to my question about the Three Gods Puzzle. However, after some consideration, I feel compelled to point out some inaccuracies in the post.

The Wikipedia page indeed did not state anything about repeating questions. If I impose a restriction on the puzzle, such as one question per God, it would make the puzzle even harder. How would you go about solving that?

Also, I personally think asking a god the same question twice is not a good strategy, because if you turn out to be asking random twice, one is done for.