Hardest Logic Puzzle

I have come across “the hardest logic puzzle” and been fascinated with it and its variants. It stems from the classic Knights and Knaves puzzle:

There are two boxes to choose from, one of which you must open. One contains a treasure, and one contains a bomb which will lead to certain death. There are two people who both know the contents of the box, a Knight (who always tells the truth) and a Knave (who always lies). You do not know which is which. You can only ask one person one question, and must determine which box to open based on his answer.

The classic solution, is to point to the other guy and ask the question “would he say this box contains the treasure?” and open the other box if he says “yes”.

Using an embedded question, you can get a consistent and meaningful answer.

Let’s try a difficult version of the hardest logic puzzle.

There are three gods (A, B, C). One will always speak the truth (T), one will always lie (L), and one is completely random (R). Completely random does not mean that sometimes he answers truthfully and sometimes lies; it means the answer itself is random. They all understand English, however each god must reply in his own language, either “ja” or “da”, which means “yes” and “no”, in no particular order. The three gods each speak a different language, and unfortunately “ja” or “da” could mean “yes” or “no” differently in each language.

You may ask three yes/no questions to accurately determine the identities of each god. Each question must be placed to one god only at a time, and the same god may be asked multiple questions, consecutively or not, meaning that some god may not be asked any question at all. You may not ask questions that potentially cannot be answered (e.g., Truth would not be able to answer “would you say ‘ja’ if it means ‘no’ in your language?”)

The way the unanswerable question was phrased gives a hint to how the puzzle can be solved. For this very elegant solution, go to Wikipedia.

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