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Kawoomba comments on Public Service Announcement Collection - Less Wrong Discussion

37 Post author: Eliezer_Yudkowsky 27 June 2013 05:20PM

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Comment author: Kawoomba 27 June 2013 06:33:44PM 8 points [-]

Three gods puzzle (aka "The Hardest Logic Puzzle Ever", I didn't make that name up!) for reference. Try to solve the puzzle first, I've appended the text. The referenced link contains the solution.

Three gods A, B, and C are called, in no particular order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer all questions in their own language, in which the words for yes and no are da and ja, in some order. You do not know which word means which.

Clarifications:

  • It could be that some god gets asked more than one question (and hence that some god is not asked any question at all).

  • What the second question is, and to which god it is put, may depend on the answer to the first question. (And of course similarly for the third question.)

  • Whether Random speaks truly or not should be thought of as depending on the flip of a coin hidden in his brain: if the coin comes down heads, he speaks truly; if tails, falsely.

Comment author: John_Maxwell_IV 30 June 2013 06:12:15PM *  0 points [-]

Here's my solution. Not 100% sure it works.

Nyy dhrfgvbaf ner nfxrq gb nal tbq.
Dhrfgvba 1: Vs vafgrnq bs guvf dhrfgvba, V nfxrq lbh jurgure Gehr'f nafjre gb gur dhrfgvba bs jurgure qn zrnag gehr jbhyq or gur fnzr nf Gehr'f nafjre gb gur dhrfgvba bs jurgure Gehr fng gb gur yrsg bs Snyfr, jbhyq lbhe nafjre or lbhe ynathntr'f rdhvinyrag bs gehr?
Nafjre vagrecergngvba: Vs gur nafjre vf qn, Gehr fvgf gb gur yrsg bs Snyfr. Vs gur nafjre vf an, Snyfr fvgf gb gur yrsg bs Gehr.
Dhrfgvba 2: Vs vafgrnq bs guvf dhrfgvba, V nfxrq lbh jurgure Gehr'f nafjre gb gur dhrfgvba bs jurgure qn zrnag gehr jbhyq or gur fnzr nf Gehr'f nafjre gb gur dhrfgvba bs jurgure Enaqbz fng orgjrra Gehr naq Snyfr, jbhyq lbhe nafjre or lbhe ynathntr'f rdhvinyrag bs gehr?
Nafjre vagrecergngvba: Vs gur nafjre vf qn, Enaqbz fvgf orgjrra Gehr naq Snyfr naq lbh'er qbar.
Dhrfgvba 3: Vs vafgrnq bs guvf dhrfgvba, V nfxrq lbh jurgure Gehr'f nafjre gb gur dhrfgvba bs jurgure qn zrnag gehr jbhyq or gur fnzr nf Gehr'f nafjre gb gur dhrfgvba bs jurgure Enaqbz fng ba gur sne yrsg, jbhyq lbhe nafjre or lbhe ynathntr'f rdhvinyrag bs gehr?
Nafjre vagrecergngvba: Vs gur nafjre vf qn, Enaqbz fvgf gb gur yrsg bs Gehr naq Snyfr; bgurejvfr ur fvgf gb gurve evtug.

rot13

Comment author: [deleted] 28 June 2013 12:19:40PM 0 points [-]

The first time I read that I thought “what difference there is between speaking truly in a language where da means yes and ja means no, and speaking falsely in a language where ja means yes and da means no?” and assumed that the solution was that there's no solution. (I was wrong.)

Comment author: sixes_and_sevens 27 June 2013 09:48:52PM 0 points [-]

This looks superficially similar to the Three Princesses.

Comment author: Kawoomba 27 June 2013 09:54:22PM *  1 point [-]

Differences: The Three Princess riddle only allows for one binary question, however, the princess (same setup of of True, False, Random) answer in plain English. You win if you (edit:) choose a princess who is not random. 1, 2, 3.

Comment author: Benja 28 June 2013 07:11:15PM 0 points [-]

Actually, you win if you are able to choose a princess other than Random -- you do not need to know which of the two remaining ones is Random. Otherwise, this would clearly be impossible since the answer provides only one bit and there are three possibilities. (And that's not even considering that under sensible interpretations of the rules, you don't get any information if you happen to ask Random -- i.e., you're not allowed to ask e.g., "Is it true that (you are False) OR (you are Random and you've decided to answer truthfully this time)", which, if allowed, would be answered in the affirmative iff the one you asked is Random.)

Comment author: ciphergoth 27 June 2013 09:19:00PM 0 points [-]

They all speak the same language?

Comment author: Kawoomba 27 June 2013 09:28:06PM 0 points [-]

Yes.

Comment author: Jack 27 June 2013 08:43:05PM *  0 points [-]

Does each god know which god is which? And can I ask the same question twice to the same god?

Comment author: Kawoomba 27 June 2013 08:46:51PM 0 points [-]

Yes, True and False have to be omniscient to be able to answer consistently correctly or incorrectly, for any arbitrary binary question. There's a version of the answer which (spoiler) relies on asking unanswerable questions, which only Random would answer. There's also solution that doesn't rely on such gimmicks, however.

Comment author: CoffeeStain 27 June 2013 10:41:42PM 1 point [-]

Do True and False know what answer Random would give, or are they required to say "I don't know?"

Comment author: Adele_L 27 June 2013 11:37:54PM 1 point [-]

I interpreted it to mean that the question must be answerable with yes or no.

Comment author: CoffeeStain 28 June 2013 09:46:14PM 0 points [-]

There are questions for which you don't know the answerability, so either the rules must be that questions asked are provably answerable, or else you are allowed to glean information from whether the god answers it or not.

Assuming that True and False do not know the future results of questions to Random, an example is a question to A (True) of "Would B say 1 + 1 = 2?" If B is False, it is answerable (with a 'no'). If B is Random, it is unanswerable.

Comment author: Adele_L 28 June 2013 10:20:53PM 0 points [-]

Provably answerable from your own knowledge.

Comment author: Epiphany 28 June 2013 02:23:48AM 0 points [-]

There's nothing in your wording that suggests random is not able to refuse an unanswerable question as one of it's potential random responses.

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