The Hardest Logic Puzzle Ever

Hardly the hardest. Here&#x27;s a harder:<p><a href="http:&#x2F;&#x2F;justinpombrio.net&#x2F;tell&#x2F;prisoner-lightbulb.html" rel="nofollow">http:&#x2F;&#x2F;justinpombrio.net&#x2F;tell&#x2F;prisoner-lightbulb.html</a><p>EDIT: Also, for anyone stuck on the three gods puzzle, the three sisters puzzle is a good stepping stone:<p><a href="http:&#x2F;&#x2F;mathpuzzlewiki.com&#x2F;index.php?title=Three_princesses" rel="nofollow">http:&#x2F;&#x2F;mathpuzzlewiki.com&#x2F;index.php?title=Three_princesses</a>

<a href="http:&#x2F;&#x2F;www.smbc-comics.com&#x2F;?id=2886" rel="nofollow">http:&#x2F;&#x2F;www.smbc-comics.com&#x2F;?id=2886</a>

Another interesting one in the style of the Singaporean puzzle that&#x27;s been making the rounds recently: <a href="http:&#x2F;&#x2F;jdh.hamkins.org&#x2F;transfinite-epistemic-logic-puzzle-challenge&#x2F;" rel="nofollow">http:&#x2F;&#x2F;jdh.hamkins.org&#x2F;transfinite-epistemic-logic-puzzle-ch...</a> (knowledge of transfinite ordinals is useful)

Hints: <a href="http:&#x2F;&#x2F;pastebin.com&#x2F;ypPA5Uab" rel="nofollow">http:&#x2F;&#x2F;pastebin.com&#x2F;ypPA5Uab</a>

Do the true&#x2F; false gods know how the random god would answer? I don&#x27;t see how they could since only he know the randomness. But if they don&#x27;t know, they would have no way to answer the question, &quot;what would guy x say ja meant&quot; where x happens to be the random one.

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&#x27;t know what those words are. Here&#x27;s an article on the solution: <a href="http:&#x2F;&#x2F;www.technologyreview.com&#x2F;view&#x2F;428189&#x2F;the-hardest-logic-puzzle-ever-made-even-harder&#x2F;" rel="nofollow">http:&#x2F;&#x2F;www.technologyreview.com&#x2F;view&#x2F;428189&#x2F;the-hardest-logi...</a>

It seems like asking about randomness is not a valid question. I&#x27;m not sure how you would implement that (beyond checking for the assignment of random behavior), you can&#x27;t really find out until you observe a difference in behavior over a larger sampling.

Be very careful what you ask the gods, you might run into:<p><a href="http:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Epimenides_paradox" rel="nofollow">http:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Epimenides_paradox</a>

You can ask multiple questions by compounding them into one. For example: &quot;what is the outcome of &#x27;is A true&#x27; converted to string and concatenated by the outcome of &#x27;is B true&#x27;&quot;?

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