Finding (possible) solutions 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
- Strategy
- 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.”

 

Please forgive me. I am a philosopher not a mathematician. We are well known for "cheating" puzzles without ever actually breaking the rules that are given. It is in this light that I offer a solution to this puzzle. First I will restate the rules to show that I understand them.

1. Only one question may be asked of each God, of which there are three.
2. The God's answer in yes, or no format, of which I do not understand.
3. I am to find the identities of the three Gods.
4. Truth, False, Random: the three Gods given.

My assumption is that you will not accept my "cheat". In light of this, and in the interest of keeping this post short. I will not provide a full table of solutions for all the given combinations. Ergo...the order in which they are approached, the order in which each question is asked, and the combinations of "da" as yes, or no, and "ja" as yes, or no. If you choose to at least "let the cheat play". Then I will happily provide a full table for all the possible solutions. Additionally if you do not accept my "cheat", it is incumbent upon you to change the rules. At which time I will "re-tackle" this puzzle.

*presumptions*
1. Truth, and False =/= Random, and Order (the concepts, not the God's).
2. The Random God always tells the truth, it is just that his verbal answers are random. Therefore they are sometimes lies.
3. Nothing in the rules state that I cannot make a request of the God's, at the same time that I ask my questions.

My three questions are as follows, and will always be in the same order.
1. If my question "Is the sky blue", is true. Blink once
2. If my question "Is the sky blue", is true. Blink once
3. If my question "Are you the Random God" is true. Blink once. If it is false blink twice.

*Of course now you can see the nature of my "cheat".

The single table given will be set as follows...

Da = yes : Ja = No
Truth God is first, False God is second, Random God is third. In the order of my approach of them.

Truth replies = Da: blinks once
False replies = Ja: blinks once (as he also lies in his blinks)
Random replies = Da: blinks once : or : Ja: blinks twice. (as only his verbal replies are random, and as he tells the truth with his blinks)

If then I know the sky is blue, and if then the last statement given by (Random) is a "Da", and is a truthful statement. Then I know that the last God is Random, and that Da = yes. Therefore the first God is Truth, the Second God is False.

If then the last statement given by (Random) is "Ja", and is also a false statement. Then I know that the truth of the last question is actually "Da". Therefore I know that the last God is Random, and "Da" = yes. Then I know the first God is Truth, and the second God is False.

*In any given combination, the moment I speak to Random, is the moment the puzzle begins to be solved.

Even a "you can't do that". As well as a shared laugh would be appreciated.

Thank You.