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"The Hardest Logic Puzzle Ever", how hard is it exactly?

G'day! 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.
Reply 1
Have you tried consulting The Harvard Review of Philosophy?
You should get all of your answers within the book, as this is where the puzzle originated.
Also, the proposed solution on Wikipedia should be valid, since it was presented by the creator of the puzzle, George Boolos.

In response to this:
"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."

It is valid that each question is directed at only one God. This doesn't mean that all three Gods must answer one question each, but instead only one can give a response. For example, you could ask A all three questions (although this would most likely be impractical) and this would follow the guidelines of the puzzle.
Just hook them up to a polygraph machine. You'll soon find out.
(edited 9 months ago)
Original post by EN62938
Have you tried consulting The Harvard Review of Philosophy?
You should get all of your answers within the book, as this is where the puzzle originated.
Also, the proposed solution on Wikipedia should be valid, since it was presented by the creator of the puzzle, George Boolos.

In response to this:
"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."

It is valid that each question is directed at only one God. This doesn't mean that all three Gods must answer one question each, but instead only one can give a response. For example, you could ask A all three questions (although this would most likely be impractical) and this would follow the guidelines of the puzzle.

Hello there!

First off, thank you for your contribution made in response to my question about the Three Gods Puzzle. However, after careful consideration, I feel compelled to point out some inaccuracies in the information posted as responses.

Firstly, even if we were to define “da” as yes and “na” as no, they become redundant due to the possibility of questioning Random at any stage of the process. Consequently, relying solely on such terms proves ineffective.

Secondly, there was a proposal for a second question that assumes prior knowledge of the gods' identities. However, given the presence of the enigmatic Random among the gods, we cannot definitively establish who possesses the attribute of truth-telling. In the scenario where the second god turns out to be Random, their response cannot assist us in determining the identities of the gods. Hence, the suggested second question becomes inconclusive.

Furthermore, if I impose a restriction on the puzzle which was indeed misinterpreted such as one question per God, it would make the puzzle even harder. How would you go about solving that?

I look forward to your thoughts, thanks in advance.
Reply 4
Original post by scienciamathica
Hello there!

First off, thank you for your contribution made in response to my question about the Three Gods Puzzle. However, after careful consideration, I feel compelled to point out some inaccuracies in the information posted as responses.

Firstly, even if we were to define “da” as yes and “na” as no, they become redundant due to the possibility of questioning Random at any stage of the process. Consequently, relying solely on such terms proves ineffective.

Secondly, there was a proposal for a second question that assumes prior knowledge of the gods' identities. However, given the presence of the enigmatic Random among the gods, we cannot definitively establish who possesses the attribute of truth-telling. In the scenario where the second god turns out to be Random, their response cannot assist us in determining the identities of the gods. Hence, the suggested second question becomes inconclusive.

Furthermore, if I impose a restriction on the puzzle which was indeed misinterpreted such as one question per God, it would make the puzzle even harder. How would you go about solving that?

I look forward to your thoughts, thanks in advance.


Id be more willing to put a bit of thought into this if you didnt post identical responses to the other threads youve created on other forums
https://www.mersenneforum.org/showthread.php?t=28733&page=2
You dont seem to be reading the replies.
(edited 9 months ago)

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