# The 3 Gods riddle

I'm not entirely sure which boards would be the correct one for this, however as this board does answer logical question I posted here.

https://en.wikipedia.org/wiki/The_Hardest_Logic_Puzzle_Ever

In the three Gods riddle one tells a lie one tells the truth and the final god gives a random answer we will call the 3 Gods {A,B,C} where it is not known which is the lies, tells the truth or gives a random answer. The gods understands English but only replies in their own language yes and no {da,ja} of which you do not know which is which. You have to determine which of the gods {A,B,C} is the liar,true,random god with only three questions.

The first question from the solution is

If I asked you 'Are you Random?' in your current mental state, would you say ja?

however is this really one question as there are two questions evaluated

$$(are\ you\ Random?) \iff "ja"$$

This is just another way of asking:

1: are you random?
2: was the answer to the first question ja?


can this really be considered as one question if you have a composition/combination of two questions?

• Puzzling.SE would seem more appropriate for this question. In fact, this riddle itself (with different characters) is discussed here, which may-or-may-not address your concerns. – Blue Sep 20 '18 at 9:22

## 1 Answer

This is just one question. It has a yes-no answer. If you were to ask it to either Truth or Liar, they would give you a unique, perfectly well-defined answer: Truth would imagine himself saying no to "Are you random", which would be either "ja" or "da", and then answer you accordingly.

There is a slightly confusing issue that arises when you imagine asking the question to Random, since the concept of "what would you say" doesn't have a well-defined meaning with Random. Random might say several things. One way of getting out of this is to decide that Random should perform a random simulation (flip a coin in their head to decide how they "would" answer "Are you random") and then answer your question (randomly, again) based on that. But really, all self-reflective questions get you into tricky territory in this puzzle, it's not hard to come up with questions where it's much harder to decide on a ruling for what should happen and if the question is allowed. A simple example is asking "Would you answer 'yes' to this question?". Should that be allowed? I'm genuinely not sure, but I'm sure someone has written about this somewhere.

You're not really asking "two questions in one", since you don't get to find out the answer to the first question. You're not getting two questions worth of information out of your one question, so there's no paradox. Similarly, I could ask "Is it true that both snow is black and the sky is pink?" and in some sense I'm asking two questions, but if I get back the answer "no", I can't figure out which of the two statements I asked about is false.

• If the sky was blue and you asked the liar 'is the sky blue or red'? what would the liar say yes or no (true or false)? – Android_Dev Sep 20 '18 at 9:59
• @Android_Dev "Is the sky blue or red?" is definitely not allowed, because it's not a yes or no question. You can only ask yes/no questions. – Jack M Sep 20 '18 at 10:25
• @Jack_M, technically it is a yes/no question, and the answer is yes. – dEmigOd Sep 20 '18 at 11:10
• @dEmigOd Oh, it depends on what OP meant. The question "Is it the case that the sky is either blue or red?" is yes/no. But the question "Which color is the sky, blue or red?" is not. – Jack M Sep 20 '18 at 11:18
• @JackM I think "Is it the case that the sky is either blue or red?" would be correct way to word this question, but the fact that you could not figure out which is which can not exclude it from being a question especially if it is labelled as one in the wiki (I referenced) and any site that gives the solution to this riddle (or similar copies of it). – Android_Dev Sep 20 '18 at 12:38