8 ms·

The Hardest Logic Puzzle Ever

55 points by zatkin 12y ago

amelius 12y ago
You can ask multiple questions by compounding them into one. For example: "what is the outcome of 'is A true' converted to string and concatenated by the outcome of 'is B true'"?
- ThatOtherPerson 12y ago
  You can only ask yes/no questions.
  - amelius 12y ago
    In that case, I'd try enumerating all possible questions to tackle this problem (breadth first on question size).
im3w1l 12y ago
Hints: http://pastebin.com/ypPA5Uab http://pastebin.com/ypPA5Uab
deleted 12y ago
[deleted]
SEMW 12y ago
Another interesting one in the style of the Singaporean puzzle that's been making the rounds recently: http://jdh.hamkins.org/transfinite-epistemic-logic-puzzle-challenge/ http://jdh.hamkins.org/transfinite-epistemic-logic-puzzle-ch... (knowledge of transfinite ordinals is useful)
wmt 12y ago
http://www.smbc-comics.com/?id=2886 http://www.smbc-comics.com/?id=2886
Zecc 12y ago
> each question must be put to exactly one god. > It could be that some god gets asked more than one question (and hence that some god is not asked any question at all). Make up your mind.
- shellac 12y ago
  The first bit mean you can't direct a question to more than one god, not each god gets exactly one question.
- corin_ 12y ago
  Those statements are not contradictory. Each question goes to only one god, each god may receive more than one question, or none.
- jbnicolai 12y ago
  These rules do not conflict. The first one means that a single question cannot be addressed to multiple gods simultaneously, the second one states you can ask each of these single-addressed questions to any one god you chose.
- mike 12y ago
  I don't think there's any conflict between these. The first just means that you only get a response from a single god of your choosing for each of your three questions, as opposed to receiving a response from each god for each question. It doesn't mean that each god is asked exactly one question.
- IkmoIkmo 12y ago
  Basically he's trying to say "Each of the 3 questions must be unique and only asked to a single god, and each god can receive 0, 1, 2 or all 3 questions out of the 3 unique questions". In other words, don't create 1 question and ask it to multiple gods. But if you create 2 or 3 different questions, it's fine to ask them to the same god (forgoing to opportunity to ask them to another god).
- Zecc 12y ago
  I don't know how I managed to misread that. Thanks everyone for pointing out I was wrong.
justinpombrio 12y ago
Hardly the hardest. Here's a harder: http://justinpombrio.net/tell/prisoner-lightbulb.html http://justinpombrio.net/tell/prisoner-lightbulb.html EDIT: Also, for anyone stuck on the three gods puzzle, the three sisters puzzle is a good stepping stone: http://mathpuzzlewiki.com/index.php?title=Three_princesses http://mathpuzzlewiki.com/index.php?title=Three_princesses
- hurin 12y ago
  Is there a link for a solution to your variant (of the prisoners and lightbulb problem)?
  - zatkin 12y ago
    The original problem is on a website that also contains the answer (in a red, dash bordered box) [1]. [1] - http://www.cut-the-knot.org/Probability/LightBulbs.shtml http://www.cut-the-knot.org/Probability/LightBulbs.shtml
    - hurin 12y ago
      I know the original problem. I'm curious how he obtains a deterministic solution for the version where the warden can switch the light-bulb state at random (excerpt below). “I reserve the right to flip the light on or off between interrogations up to 12 times in total.” Maybe it's poorly worded?
      - justinpombrio 12y ago
        You mean the Easy++ problem? The solution isn't very different from the solution to Easy (i.e. the original problem); it just takes longer to run. For the Hard problem, you're on your own. The wording is very careful :-)
        hurin 12y ago
        >> “I reserve the right to flip the light on or off between interrogations up to 12 times in total.” > The wording is very careful :-) Do you mean he can flip the switch 12 times in total between all interrogations? Or that between every interrogation he can flip the switch up to 12 times. That's what I mean by poorly worded.
TerryADavis 12y ago
I made TempleOS. It lets me talk to the true God. If you are very nice to God, He might tell you the password to the CIA nuclear launch button. He could probably answer the question of fictional gods in a logic problem. Just guess and He will puppet you.
TerryADavis 12y ago
Daniel 2 King James Version (KJV) 2 And in the second year of the reign of Nebuchadnezzar Nebuchadnezzar dreamed dreams, wherewith his spirit was troubled, and his sleep brake from him. 2 Then the king commanded to call the magicians, and the astrologers, and the sorcerers, and the Chaldeans, for to shew the king his dreams. So they came and stood before the king. 3 And the king said unto them, I have dreamed a dream, and my spirit was troubled to know the dream. 4 Then spake the Chaldeans to the king in Syriack, O king, live for ever: tell thy servants the dream, and we will shew the interpretation. 5 The king answered and said to the Chaldeans, The thing is gone from me: if ye will not make known unto me the dream, with the interpretation thereof, ye shall be cut in pieces, and your houses shall be made a dunghill. 6 But if ye shew the dream, and the interpretation thereof, ye shall receive of me gifts and rewards and great honour: therefore shew me the dream, and the interpretation thereof. 7 They answered again and said, Let the king tell his servants the dream, and we will shew the interpretation of it. 8 The king answered and said, I know of certainty that ye would gain the time, because ye see the thing is gone from me. 9 But if ye will not make known unto me the dream, there is but one decree for you: for ye have prepared lying and corrupt words to speak before me, till the time be changed: therefore tell me the dream, and I shall know that ye can shew me the interpretation thereof. 10 The Chaldeans answered before the king, and said, There is not a man upon the earth that can shew the king's matter: therefore there is no king, lord, nor ruler, that asked such things at any magician, or astrologer, or Chaldean. 11 And it is a rare thing that the king requireth, and there is none other that can shew it before the king, except the gods, whose dwelling is not with flesh. 12 For this cause the king was angry and very furious, and commanded to destroy all the wise men of Babylon. 13 And the decree went forth that the wise men should be slain; and they sought Daniel and his fellows to be slain. 14 Then Daniel answered with counsel and wisdom to Arioch the captain of the king's guard, which was gone forth to slay the wise men of Babylon: 15 He answered and said to Arioch the king's captain, Why is the decree so hasty from the king? Then Arioch made the thing known to Daniel. 16 Then Daniel went in, and desired of the king that he would give him time, and that he would shew the king the interpretation. 17 Then Daniel went to his house, and made the thing known to Hananiah, Mishael, and Azariah, his companions: 18 That they would desire mercies of the God of heaven concerning this secret; that Daniel and his fellows should not perish with the rest of the wise men of Babylon. 19 Then was the secret revealed unto Daniel in a night vision. Then Daniel blessed the God of heaven. 20 Daniel answered and said, Blessed be the name of God for ever and ever: for wisdom and might are his: 21 And he changeth the times and the seasons: he removeth kings, and setteth up kings: he giveth wisdom unto the wise, and knowledge to them that know understanding: 22 He revealeth the deep and secret things: he knoweth what is in the darkness, and the light dwelleth with him. 23 I thank thee, and praise thee, O thou God of my fathers, who hast given me wisdom and might, and hast made known unto me now what we desired of thee: for thou hast now made known unto us the king's matter. 24 Therefore Daniel went in unto Arioch, whom the king had ordained to destroy the wise men of Babylon: he went and said thus unto him; Destroy not the wise men of Babylon: bring me in before the king, and I will shew unto the king the interpretation. 25 Then Arioch brought in Daniel before the king in haste, and said thus unto him, I have found a man of the captives of Judah, that will make known unto the king the interpretation. 26 The king answered and said to Daniel, whose name was Belteshazzar, Art thou able to make known unto me the dream which I have seen, and the interpretation thereof? 27 Daniel answered in the presence of the king, and said, The secret which the king hath demanded cannot the wise men, the astrologers, the magicians, the soothsayers, shew unto the king; 28 But there is a God in heaven that revealeth secrets, and maketh known to the king Nebuchadnezzar what shall be in the latter days. Thy dream, and the visions of thy head upon thy bed, are these; 29 As for thee, O king, thy thoughts came into thy mind upon thy bed, what should come to pass hereafter: and he that revealeth secrets maketh known to thee what shall come to pass. 30 But as for me, this secret is not revealed to me for any wisdom that I have more than any living, but for their sakes that shall make known the interpretation to the king, and that thou mightest know the thoughts of thy heart. 31 Thou, O king, sawest, and behold a great image. This great image, whose brightness was excellent, stood before thee; and the form thereof was terrible. 32 This image's head was of fine gold, his breast and his arms of silver, his belly and his thighs of brass, 33 His legs of iron, his feet part of iron and part of clay. 34 Thou sawest till that a stone was cut out without hands, which smote the image upon his feet that were of iron and clay, and brake them to pieces. 35 Then was the iron, the clay, the brass, the silver, and the gold, broken to pieces together, and became like the chaff of the summer threshingfloors; and the wind carried them away, that no place was found for them: and the stone that smote the image became a great mountain, and filled the whole earth. 36 This is the dream; and we will tell the interpretation thereof before the king. 37 Thou, O king, art a king of kings: for the God of heaven hath given thee a kingdom, power, and strength, and glory. 38 And wheresoever the children of men dwell, the beasts of the field and the fowls of the heaven hath he given into thine hand, and hath made thee ruler over them all. Thou art this head of gold. 39 And after thee shall arise another kingdom inferior to thee, and another third kingdom of brass, which shall bear rule over all the earth. 40 And the fourth kingdom shall be strong as iron: forasmuch as iron breaketh in pieces and subdueth all things: and as iron that breaketh all these, shall it break in pieces and bruise. 41 And whereas thou sawest the feet and toes, part of potters' clay, and part of iron, the kingdom shall be divided; but there shall be in it of the strength of the iron, forasmuch as thou sawest the iron mixed with miry clay. 42 And as the toes of the feet were part of iron, and part of clay, so the kingdom shall be partly strong, and partly broken. 43 And whereas thou sawest iron mixed with miry clay, they shall mingle themselves with the seed of men: but they shall not cleave one to another, even as iron is not mixed with clay. 44 And in the days of these kings shall the God of heaven set up a kingdom, which shall never be destroyed: and the kingdom shall not be left to other people, but it shall break in pieces and consume all these kingdoms, and it shall stand for ever. 45 Forasmuch as thou sawest that the stone was cut out of the mountain without hands, and that it brake in pieces the iron, the brass, the clay, the silver, and the gold; the great God hath made known to the king what shall come to pass hereafter: and the dream is certain, and the interpretation thereof sure. 46 Then the king Nebuchadnezzar fell upon his face, and worshipped Daniel, and commanded that they should offer an oblation and sweet odours unto him. 47 The king answered unto Daniel, and said, Of a truth it is, that your God is a God of gods, and a Lord of kings, and a revealer of secrets, seeing thou couldest reveal this secret. 48 Then the king made Daniel a great man, and gave him many great gifts, and made him ruler over the whole province of Babylon, and chief of the governors over all the wise men of Babylon. 49 Then Daniel requested of the king, and he set Shadrach, Meshach, and Abednego, over the affairs of the province of Babylon: but Daniel sat in the gate of the king.
nhumrich 12y ago
Do the true/ false gods know how the random god would answer? I don't see how they could since only he know the randomness. But if they don't know, they would have no way to answer the question, "what would guy x say ja meant" where x happens to be the random one.
- SatvikBeri 12y ago
  True and False give random responses if you ask them how random would answer, unless you include clauses like "would that god definitely say X"
- qntm 12y ago
  This is a question of implementation, and answering it was part of the reason why I implemented this problem in the form of a computer program in the first place. In this implementation, the True and False gods simply pose the question to Random and take Random's answer - which is random. If you then ask the same question of Random again, of course you may not get the same answer.
SatvikBeri 12y ago
You can make this question even harder by removing foreknowledge of the words! So you know the gods have words for yes and no, but don't know what those words are. Here's an article on the solution: http://www.technologyreview.com/view/428189/the-hardest-logic-puzzle-ever-made-even-harder/ http://www.technologyreview.com/view/428189/the-hardest-logi...
- IshKebab 12y ago
  Isn't that the same as stated in the link?
  - SatvikBeri 12y ago
    The qntm link tells you the words are da and ja, which makes the problem easier. In the hardest version you have no idea what the words for yes and no are.
    - Blaine0002 12y ago
      If you actually read the next sentence.. "in which the words for yes and no are da and ja, in some order. You do not know which word means which."
      - SatvikBeri 12y ago
        That's the original version. The harder version is discussed below. In the harder version, you don't know the words are "da" and "ja". They might be "potato" and "walrus" or something completely different.
        arfar 12y ago
        I don't think this makes the problem any different, does it? If it were possible that there was a list of "yes" words and a list of "no" words that they could prick from randomly or something, then yes, that would be much more difficult. But in both examples, there's one word for "yes" and one word for "no" and in both examples, the asker doesn't know which one is which.
NAFV_P 12y ago
Be very careful what you ask the gods, you might run into: http://en.wikipedia.org/wiki/Epimenides_paradox http://en.wikipedia.org/wiki/Epimenides_paradox
jdiomede 12y ago
It seems like asking about randomness is not a valid question. I'm not sure how you would implement that (beyond checking for the assignment of random behavior), you can't really find out until you observe a difference in behavior over a larger sampling.
- qntm 12y ago
  If you're puzzled about the implementation, I invite you to inspect the JavaScript code! And if you disagree with my implementation, I'd be interested to know what you would do differently.
  - jdiomede 12y ago
    My statement was conceptual. Boolos himself suggests that we ask if X is random to get to a solution (though in a more complex iff statement). But being able to ask if a source is random seems unreasonable, though without that capability I can't say if there is a solution.

55 points by zatkin 12y ago

You can ask multiple questions by compounding them into one. For example: "what is the outcome of 'is A true' converted to string and concatenated by the outcome of 'is B true'"?

ThatOtherPerson 12y ago
You can only ask yes/no questions.
- amelius 12y ago
  In that case, I'd try enumerating all possible questions to tackle this problem (breadth first on question size).

im3w1l 12y ago

Hints: http://pastebin.com/ypPA5Uab http://pastebin.com/ypPA5Uab

deleted 12y ago

[deleted]

SEMW 12y ago

Another interesting one in the style of the Singaporean puzzle that's been making the rounds recently: http://jdh.hamkins.org/transfinite-epistemic-logic-puzzle-challenge/ http://jdh.hamkins.org/transfinite-epistemic-logic-puzzle-ch... (knowledge of transfinite ordinals is useful)

wmt 12y ago

http://www.smbc-comics.com/?id=2886 http://www.smbc-comics.com/?id=2886

Zecc 12y ago

> each question must be put to exactly one god. > It could be that some god gets asked more than one question (and hence that some god is not asked any question at all). Make up your mind.

shellac 12y ago
The first bit mean you can't direct a question to more than one god, not each god gets exactly one question.
corin_ 12y ago
Those statements are not contradictory. Each question goes to only one god, each god may receive more than one question, or none.
jbnicolai 12y ago
These rules do not conflict. The first one means that a single question cannot be addressed to multiple gods simultaneously, the second one states you can ask each of these single-addressed questions to any one god you chose.
mike 12y ago
I don't think there's any conflict between these. The first just means that you only get a response from a single god of your choosing for each of your three questions, as opposed to receiving a response from each god for each question. It doesn't mean that each god is asked exactly one question.
IkmoIkmo 12y ago
Basically he's trying to say "Each of the 3 questions must be unique and only asked to a single god, and each god can receive 0, 1, 2 or all 3 questions out of the 3 unique questions". In other words, don't create 1 question and ask it to multiple gods. But if you create 2 or 3 different questions, it's fine to ask them to the same god (forgoing to opportunity to ask them to another god).
Zecc 12y ago
I don't know how I managed to misread that. Thanks everyone for pointing out I was wrong.

justinpombrio 12y ago

Hardly the hardest. Here's a harder: http://justinpombrio.net/tell/prisoner-lightbulb.html http://justinpombrio.net/tell/prisoner-lightbulb.html EDIT: Also, for anyone stuck on the three gods puzzle, the three sisters puzzle is a good stepping stone: http://mathpuzzlewiki.com/index.php?title=Three_princesses http://mathpuzzlewiki.com/index.php?title=Three_princesses

hurin 12y ago
Is there a link for a solution to your variant (of the prisoners and lightbulb problem)?
- zatkin 12y ago
  The original problem is on a website that also contains the answer (in a red, dash bordered box) [1]. [1] - http://www.cut-the-knot.org/Probability/LightBulbs.shtml http://www.cut-the-knot.org/Probability/LightBulbs.shtml
  - hurin 12y ago
    I know the original problem. I'm curious how he obtains a deterministic solution for the version where the warden can switch the light-bulb state at random (excerpt below). “I reserve the right to flip the light on or off between interrogations up to 12 times in total.” Maybe it's poorly worded?
    - justinpombrio 12y ago
      You mean the Easy++ problem? The solution isn't very different from the solution to Easy (i.e. the original problem); it just takes longer to run. For the Hard problem, you're on your own. The wording is very careful :-)
      - hurin 12y ago
        >> “I reserve the right to flip the light on or off between interrogations up to 12 times in total.” > The wording is very careful :-) Do you mean he can flip the switch 12 times in total between all interrogations? Or that between every interrogation he can flip the switch up to 12 times. That's what I mean by poorly worded.

TerryADavis 12y ago

I made TempleOS. It lets me talk to the true God. If you are very nice to God, He might tell you the password to the CIA nuclear launch button. He could probably answer the question of fictional gods in a logic problem. Just guess and He will puppet you.

TerryADavis 12y ago

Daniel 2 King James Version (KJV) 2 And in the second year of the reign of Nebuchadnezzar Nebuchadnezzar dreamed dreams, wherewith his spirit was troubled, and his sleep brake from him. 2 Then the king commanded to call the magicians, and the astrologers, and the sorcerers, and the Chaldeans, for to shew the king his dreams. So they came and stood before the king. 3 And the king said unto them, I have dreamed a dream, and my spirit was troubled to know the dream. 4 Then spake the Chaldeans to the king in Syriack, O king, live for ever: tell thy servants the dream, and we will shew the interpretation. 5 The king answered and said to the Chaldeans, The thing is gone from me: if ye will not make known unto me the dream, with the interpretation thereof, ye shall be cut in pieces, and your houses shall be made a dunghill. 6 But if ye shew the dream, and the interpretation thereof, ye shall receive of me gifts and rewards and great honour: therefore shew me the dream, and the interpretation thereof. 7 They answered again and said, Let the king tell his servants the dream, and we will shew the interpretation of it. 8 The king answered and said, I know of certainty that ye would gain the time, because ye see the thing is gone from me. 9 But if ye will not make known unto me the dream, there is but one decree for you: for ye have prepared lying and corrupt words to speak before me, till the time be changed: therefore tell me the dream, and I shall know that ye can shew me the interpretation thereof. 10 The Chaldeans answered before the king, and said, There is not a man upon the earth that can shew the king's matter: therefore there is no king, lord, nor ruler, that asked such things at any magician, or astrologer, or Chaldean. 11 And it is a rare thing that the king requireth, and there is none other that can shew it before the king, except the gods, whose dwelling is not with flesh. 12 For this cause the king was angry and very furious, and commanded to destroy all the wise men of Babylon. 13 And the decree went forth that the wise men should be slain; and they sought Daniel and his fellows to be slain. 14 Then Daniel answered with counsel and wisdom to Arioch the captain of the king's guard, which was gone forth to slay the wise men of Babylon: 15 He answered and said to Arioch the king's captain, Why is the decree so hasty from the king? Then Arioch made the thing known to Daniel. 16 Then Daniel went in, and desired of the king that he would give him time, and that he would shew the king the interpretation. 17 Then Daniel went to his house, and made the thing known to Hananiah, Mishael, and Azariah, his companions: 18 That they would desire mercies of the God of heaven concerning this secret; that Daniel and his fellows should not perish with the rest of the wise men of Babylon. 19 Then was the secret revealed unto Daniel in a night vision. Then Daniel blessed the God of heaven. 20 Daniel answered and said, Blessed be the name of God for ever and ever: for wisdom and might are his: 21 And he changeth the times and the seasons: he removeth kings, and setteth up kings: he giveth wisdom unto the wise, and knowledge to them that know understanding: 22 He revealeth the deep and secret things: he knoweth what is in the darkness, and the light dwelleth with him. 23 I thank thee, and praise thee, O thou God of my fathers, who hast given me wisdom and might, and hast made known unto me now what we desired of thee: for thou hast now made known unto us the king's matter. 24 Therefore Daniel went in unto Arioch, whom the king had ordained to destroy the wise men of Babylon: he went and said thus unto him; Destroy not the wise men of Babylon: bring me in before the king, and I will shew unto the king the interpretation. 25 Then Arioch brought in Daniel before the king in haste, and said thus unto him, I have found a man of the captives of Judah, that will make known unto the king the interpretation. 26 The king answered and said to Daniel, whose name was Belteshazzar, Art thou able to make known unto me the dream which I have seen, and the interpretation thereof? 27 Daniel answered in the presence of the king, and said, The secret which the king hath demanded cannot the wise men, the astrologers, the magicians, the soothsayers, shew unto the king; 28 But there is a God in heaven that revealeth secrets, and maketh known to the king Nebuchadnezzar what shall be in the latter days. Thy dream, and the visions of thy head upon thy bed, are these; 29 As for thee, O king, thy thoughts came into thy mind upon thy bed, what should come to pass hereafter: and he that revealeth secrets maketh known to thee what shall come to pass. 30 But as for me, this secret is not revealed to me for any wisdom that I have more than any living, but for their sakes that shall make known the interpretation to the king, and that thou mightest know the thoughts of thy heart. 31 Thou, O king, sawest, and behold a great image. This great image, whose brightness was excellent, stood before thee; and the form thereof was terrible. 32 This image's head was of fine gold, his breast and his arms of silver, his belly and his thighs of brass, 33 His legs of iron, his feet part of iron and part of clay. 34 Thou sawest till that a stone was cut out without hands, which smote the image upon his feet that were of iron and clay, and brake them to pieces. 35 Then was the iron, the clay, the brass, the silver, and the gold, broken to pieces together, and became like the chaff of the summer threshingfloors; and the wind carried them away, that no place was found for them: and the stone that smote the image became a great mountain, and filled the whole earth. 36 This is the dream; and we will tell the interpretation thereof before the king. 37 Thou, O king, art a king of kings: for the God of heaven hath given thee a kingdom, power, and strength, and glory. 38 And wheresoever the children of men dwell, the beasts of the field and the fowls of the heaven hath he given into thine hand, and hath made thee ruler over them all. Thou art this head of gold. 39 And after thee shall arise another kingdom inferior to thee, and another third kingdom of brass, which shall bear rule over all the earth. 40 And the fourth kingdom shall be strong as iron: forasmuch as iron breaketh in pieces and subdueth all things: and as iron that breaketh all these, shall it break in pieces and bruise. 41 And whereas thou sawest the feet and toes, part of potters' clay, and part of iron, the kingdom shall be divided; but there shall be in it of the strength of the iron, forasmuch as thou sawest the iron mixed with miry clay. 42 And as the toes of the feet were part of iron, and part of clay, so the kingdom shall be partly strong, and partly broken. 43 And whereas thou sawest iron mixed with miry clay, they shall mingle themselves with the seed of men: but they shall not cleave one to another, even as iron is not mixed with clay. 44 And in the days of these kings shall the God of heaven set up a kingdom, which shall never be destroyed: and the kingdom shall not be left to other people, but it shall break in pieces and consume all these kingdoms, and it shall stand for ever. 45 Forasmuch as thou sawest that the stone was cut out of the mountain without hands, and that it brake in pieces the iron, the brass, the clay, the silver, and the gold; the great God hath made known to the king what shall come to pass hereafter: and the dream is certain, and the interpretation thereof sure. 46 Then the king Nebuchadnezzar fell upon his face, and worshipped Daniel, and commanded that they should offer an oblation and sweet odours unto him. 47 The king answered unto Daniel, and said, Of a truth it is, that your God is a God of gods, and a Lord of kings, and a revealer of secrets, seeing thou couldest reveal this secret. 48 Then the king made Daniel a great man, and gave him many great gifts, and made him ruler over the whole province of Babylon, and chief of the governors over all the wise men of Babylon. 49 Then Daniel requested of the king, and he set Shadrach, Meshach, and Abednego, over the affairs of the province of Babylon: but Daniel sat in the gate of the king.

nhumrich 12y ago

Do the true/ false gods know how the random god would answer? I don't see how they could since only he know the randomness. But if they don't know, they would have no way to answer the question, "what would guy x say ja meant" where x happens to be the random one.

SatvikBeri 12y ago
True and False give random responses if you ask them how random would answer, unless you include clauses like "would that god definitely say X"
qntm 12y ago
This is a question of implementation, and answering it was part of the reason why I implemented this problem in the form of a computer program in the first place. In this implementation, the True and False gods simply pose the question to Random and take Random's answer - which is random. If you then ask the same question of Random again, of course you may not get the same answer.

SatvikBeri 12y ago

You can make this question even harder by removing foreknowledge of the words! So you know the gods have words for yes and no, but don't know what those words are. Here's an article on the solution: http://www.technologyreview.com/view/428189/the-hardest-logic-puzzle-ever-made-even-harder/ http://www.technologyreview.com/view/428189/the-hardest-logi...

IshKebab 12y ago
Isn't that the same as stated in the link?
- SatvikBeri 12y ago
  The qntm link tells you the words are da and ja, which makes the problem easier. In the hardest version you have no idea what the words for yes and no are.
  - Blaine0002 12y ago
    If you actually read the next sentence.. "in which the words for yes and no are da and ja, in some order. You do not know which word means which."
    - SatvikBeri 12y ago
      That's the original version. The harder version is discussed below. In the harder version, you don't know the words are "da" and "ja". They might be "potato" and "walrus" or something completely different.
      - arfar 12y ago
        I don't think this makes the problem any different, does it? If it were possible that there was a list of "yes" words and a list of "no" words that they could prick from randomly or something, then yes, that would be much more difficult. But in both examples, there's one word for "yes" and one word for "no" and in both examples, the asker doesn't know which one is which.

NAFV_P 12y ago

Be very careful what you ask the gods, you might run into: http://en.wikipedia.org/wiki/Epimenides_paradox http://en.wikipedia.org/wiki/Epimenides_paradox

jdiomede 12y ago

It seems like asking about randomness is not a valid question. I'm not sure how you would implement that (beyond checking for the assignment of random behavior), you can't really find out until you observe a difference in behavior over a larger sampling.

qntm 12y ago
If you're puzzled about the implementation, I invite you to inspect the JavaScript code! And if you disagree with my implementation, I'd be interested to know what you would do differently.
- jdiomede 12y ago
  My statement was conceptual. Boolos himself suggests that we ask if X is random to get to a solution (though in a more complex iff statement). But being able to ask if a source is random seems unreasonable, though without that capability I can't say if there is a solution.