most recent 30 from http://mathoverflow.net 2013-05-24T10:49:49Z http://mathoverflow.net/feeds/question/13972 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/13972/shortest-key-for-the-monte-carlo-lock-of-smullyan domotorp 2010-02-03T13:57:14Z 2010-02-05T11:58:32Z

<p>This question is about a puzzle from the book of <a href="http://www.scribd.com/doc/20905008/Raymond-Smullyan-Lady-or-the-Tiger-and-Other-Logic-Puzzles-Including-a-Mathematical-Novel-That-Features-Godels-Great-Discovery-9780812921175-46403-cop" rel="nofollow">Raymond Smullyan: The Lady or the Tiger?</a></p> <p>The description of the puzzle starts in Chapter 8, p. 103 which I do not repeat here as the whole book is accessible at the above link for those who do not know it. Smullyan provides a key of length 10 on p. 163, however, this is not the shortest, I know a key of length 8. Is this the shortest?</p>

http://mathoverflow.net/questions/13972/shortest-key-for-the-monte-carlo-lock-of-smullyan/14127#14127 Thorny 2010-02-04T09:43:35Z 2010-02-05T11:58:32Z

<p>Edited in recognition of closed-mindedness.</p> <p><s>My brute force search shows no keys shorter than 10. Here are the only keys of length 10 and 11 respectively:</p> <p>RVLVQRVLVQ VRLVQVRLVQ</p> <p>VLRVQVLRVQQ VLVRQVLVRQQ</p> <p>Curiously, there are no keys of length 12. </s></p> <p>The only word of length 7 that does not crash under iteration is RRQRRQQ, and it evolves unboundedly. There are 74 words of length 8 that grow to over 30 letters, I think none of them cycles, and there are two eventually cycling words, one you gave and the other its pair RQVRLVQQ. The first time an odd period greater than 1 appears is at length 12, these are the originating words (all end up with period 3):</p> <p>RQQVLLRLVQQQ</p> <p>RLQVLLRLVQQQ</p> <p>RQLVLLLRVQQQ</p> <p>RQVLLLVLRQQQ</p> <p>RQLVLLLVRQQQ</p> <p>RQLVLLLRVLQQ</p> <p>RQVLLLVLRLQQ</p> <p>RQLVLLLVRLQQ</p> <p>RQLLVLLRLVQQ</p> <p>RQVLLLVQQRQQ</p> <p>RQVLLLVLQRQQ</p> <p>RQLVLLLVQRQQ</p>