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yjneb, Oct 18, 2009, 3:46 PM
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I like this way of phrasing the first question (addressed to A) better:
"Of the three statements 'I am True', 'B is Random', and 'Ja means yes', is it the case that an odd number of them are true?"
Obviously, this tells us nothing if A is Random. However, the goal here is to identify any non-Random god, to whom we will ask the second question. So if A is Random, it is safe to ask the second question of either B or C.
Now assume A is either True or False. You can trace through the logic to see that if we get the answer "Ja", then B is Random, while if we get "Da", then B is not Random.
So now we've identified a non-Random god: either B, if A said "Da", or C if A answered "Ja". The next question is addressed to that god, and is exactly the same as the first, except we ask whether or not A is Random instead of B. Now we've identified Random in two questions. The third question can be something like "It is the case that the statements 'You are True' and 'There are three gods sitting here' are either both true or both false?" This will identify whether the god to whom it is addressed is True or False, and we're done.
This seems like a much more complicated variant on one where there are only two gods (True and False), they answer in English, and you have one question to determine, for example, which of the two paths leading away from them leads to certain death. The correct question is "Is it the case that the statements 'You are True' and 'The left path is safe' are either both true or both false?"
"Of the three statements 'I am True', 'B is Random', and 'Ja means yes', is it the case that an odd number of them are true?"
Obviously, this tells us nothing if A is Random. However, the goal here is to identify any non-Random god, to whom we will ask the second question. So if A is Random, it is safe to ask the second question of either B or C.
Now assume A is either True or False. You can trace through the logic to see that if we get the answer "Ja", then B is Random, while if we get "Da", then B is not Random.
So now we've identified a non-Random god: either B, if A said "Da", or C if A answered "Ja". The next question is addressed to that god, and is exactly the same as the first, except we ask whether or not A is Random instead of B. Now we've identified Random in two questions. The third question can be something like "It is the case that the statements 'You are True' and 'There are three gods sitting here' are either both true or both false?" This will identify whether the god to whom it is addressed is True or False, and we're done.
This seems like a much more complicated variant on one where there are only two gods (True and False), they answer in English, and you have one question to determine, for example, which of the two paths leading away from them leads to certain death. The correct question is "Is it the case that the statements 'You are True' and 'The left path is safe' are either both true or both false?"
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Yeah, I've always heard the original one as there are two brothers who guard the fork in the road, one who always tells the truth, the other who always lies, and one nice way of wording a question would be "Would your brother tell me that the left path is safe?"
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I think that the third person in this puzzle makes this puzzle much harder than the one linked to in the post
.

by
Xantos C. Guin, Oct 21, 2009, 12:04 AM
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