Talk:Knight's tour

message: "A knight's tour is called a closed tour if the knight ends on a square attacking the square from which it began"
But there are a few references to the trivial case of a closed tour on a 1x1 board. I would say that a knight can not attack any square on a board smaller than 2x3, and therefore can not complete a closed tour.  — Preceding unsigned comment added by 76.251.81.253 (talk) 19:49, 15 October 2011 (UTC)
replies: text: I agree. There can't be an open or closed tour on a 1x1 board, so the sloane number must be changed to T=0 for n= 1. The word tour implies that some movement has been established. 99.135.167.202 (talk) 00:06, 23 September 2013 (UTC)
replies: text:  There is no connection between tour and movement. Tour here simply refers to a Hamiltonian path or cycle on the knight's graph, while for the 1x1 board this graph is a singleton graph which is considered Hamiltonian (i.e. having a Hamiltonian cycle) -- see http://mathworld.wolfram.com/SingletonGraph.html Maxal (talk) 02:46, 23 September 2013 (UTC)
replies: text:  Please don't be so quick to judge my observation. When was the last time anyone ever toured without leaving from the place they started. I'm trying to understand the knight's tour from the most basic and objective viewpoint, and I disagree !!tremendously!! with you for having quoted something from mathworld. They don't review new ideas. I've asked them.99.135.166.191 (talk) 23:26, 8 October 2013 (UTC)

text:  Think of "touring without leaving from the place they start" as an empty tour with no movements. This is similar to how sets may have no elements etc. Maxal (talk) 01:16, 9 October 2013 (UTC)
replies: text:  I agree with Maxal.  Similarly, what is the sum of zero numbers? 0.  What is the product of zero numbers? 1.  Bubba73 You talkin' to me? 02:30, 9 October 2013 (UTC)
thread_title: Trivial 1x1 closed tour?

message: Will someone please cite Across the Board properly in the bibliography and point the Schwenk's theorem section to the same reference? I am too inexperienced/lazy-to-find-out-how to do so. Leon math (talk) 22:15, 8 December 2008 (UTC)
replies: text: OK, I did it, assuming that the theorem is in Watkins.  (I don't have the book.)  Bubba73 (talk), 23:13, 8 December 2008 (UTC)
replies: text:  Thanks, it is. Leon math (talk) 00:44, 9 December 2008 (UTC)
thread_title: ''Across the Board'' Citation

message: I read this page and have no idea what "Directed" and "Undirected" mean. They are used but not defined.  Could someone please add a definition?  —Preceding unsigned comment added by Spril4 (talk • contribs) 04:18, 14 February 2008 (UTC)
replies: text: Added links from "directed" and "undirected" to Glossary_of_graph_theory#Direction. Alexdow (talk) 20:11, 24 March 2009 (UTC)
thread_title: Define Directed?

message: For the paragraph regarding Hamiltonian paths, can someone correct the Conrad link?  I'm not sure of what it refers to.  --Ricky81682 09:04, Nov 27, 2004 (UTC)
:Done, we don't have an article about that particular mathematician. Btyner 22:36, 28 May 2006 (UTC)
thread_title: Conrad

message: Edit: I overlooked the word "closed" knight's tour. Tobias Pfanner 13:07, 17 December 2006 (UTC)
replies: text: I suppose it does need to be made clearer that Schwenk's Theorem only holds for closed knight's tours. Does anyone agree?Leon math 20:56, 18 December 2006 (UTC)
thread_title:  Schwenk's Theorem 

message: The article astutely observes, in the last section, that "Simply proving the above three conditions does not prove the theorem, it is still required to prove that all rectangular boards that do not fall in one of the above three categories have knight's tours." But, uh, where's the proof? Solemnavalanche 15:52, 11 January 2007 (UTC)
replies: text: Not every page with a theorem has the complete proof of it, as this would often make it ridiculously long and rather formidable. Perhaps someone with access to Schwenk's proof can judge whether it is appropriate for Wikipedia. Leon math 22:50, 11 January 2007 (UTC)
replies: text:  giving half the proof leaves the reader (like me) eager to read the other half, so at least give a link (external) with the rest of the proof or a reference where the proof can be found  —Preceding unsigned comment added by 62.1.238.203 (talk) 02:05, 27 April 2008 (UTC)
thread_title:  Proof 

message: All right, no one's said anything, I'm making the merge with Warnsdorff's algorithm now. Leon math (talk) 00:30, 28 January 2009 (UTC)
thread_title:  Merge 

message: Who wrote the sample code to solve the knight's tour?  I don't think Wikipedia is a good place to publish beginner's code, and the sample is pretty bad. 165.189.101.177 (talk) 21:09, 4 June 2009 (UTC)
replies: text: If it was written by an editor it shouldn't be in the article because of wp:rs.  Code should be from a published reliable source and cited. Bubba73 (talk), 21:56, 4 June 2009 (UTC)

text: May I suggest this online sample? Okkay (talk) 03:25, 16 September 2012 (UTC)
thread_title:  Poor code examples 

message: It's said here there isn't any tour if shorter side is 4, so what with 4x4 square?  —Preceding unsigned comment added by 79.191.120.75 (talk) 15:57, 9 May 2011 (UTC)
thread_title: 4x4

message: The partial proof of the Schwenk algorithm seems out of place to me - lots of detail in the middle of a survey article. What do others think?  — Preceding unsigned comment added by 2.24.222.110 (talk) 19:06, 7 May 2012 (UTC)
thread_title: Schwenk algorithm?

message: It seems to me that the tour given by "The Turk" is not closed. The square f3 is not reachable from h7 by a knight's move. I am removing the "closed" comment. Kingsindian (talk) 20:49, 9 December 2012 (UTC)
replies: text: It looks like it starts and ends on d4, which is closed.  Bubba73 You talkin' to me? 21:48, 9 December 2012 (UTC)
replies: text:  Sorry for the delay. It does start and end on d4, but one move is illegal (from f3 to h7) Kingsindian (talk) 16:56, 21 December 2012 (UTC)

text: No, the diagram is OK.  It goes from f3 to g5 and then to h7, which is in a straight line, so there is no corner in there.  The diagrammed tour can't start on f3 and end on h7, otherwise it would never go to g5.  It gets g5 between f3 and h7. Bubba73 You talkin' to me? 17:34, 21 December 2012 (UTC)
replies: text:  Ah you're correct. Kingsindian (talk) 17:56, 21 December 2012 (UTC)
replies: text:  It would help if the diagram had a dot on g5.  Bubba73 You talkin' to me? 18:02, 21 December 2012 (UTC)
thread_title: Turk's tour is closed?

message: Is it possible that after N*(N-3) moves that either no ties can be broken, or that an alternate tour cannot be chosen when applying Warnsdorff's rule (succesively) to a board of NxN size where N is odd? 99.135.166.138 (talk) 02:52, 12 October 2013 (UTC)
thread_title:  no knight's tour for NxN size boards, N is odd 

message: The poem in the History section is fascinating. What does it translate to in English? --Rosekelleher (talk) 12:40, 22 November 2014 (UTC)
thread_title:  Sanskrit poem 

message: Should backtracking be mentioned? It's not the best solution, but it's not rock bottom, and it comes up in class assignments (or did). "Brute force search should not be confused with backtracking, where large sets of solutions can be discarded without being explicitly enumerated" --Rosekelleher (talk) 13:46, 22 November 2014 (UTC)
thread_title:  Backtracking 

message: I've asked for a citation for the claim that a brute force approach is impractical except for the smallest boards, as this claim is unsourced, and seems very dubious based on my own experience. 
In the late 1980s or early 1990s, just for fun (and/or because I had been told that Erwin Schroedinger had found a solution manually within about an hour during World War II), I tried writing a brute force knight's tour algorithm for a standard 8 x 8 board starting on one of the 4 middle squares and ending on one of the remaining 3 middle squares (I can't remember whether it was one of the 2 neighboring squares or the diagonal one). I was using Nixdorf Business Basic on a Nixdorf mini-computer (probably an 8870, but possibly a Quattro). It was taking ages but from its behavior on screen it was clearly wasting lots of time searching areas of the board from which it had already cut off its only exit. I worked out how to fix this (which took perhaps 15 to 30 minutes - and obviously I can no longer remember the precise details of the fix a quarter of a century later - but it is probably not be too difficult to code 'Is there still an exit from this area of the board?' with at least moderate efficiency). It then started churning out new knight's tours at a rate that I think was slightly faster than one a minute. Unfortunately I then deleted the program as it was proving too much of a distraction from work. (Anybody who wants to try that out for him/herself is welcome to do so).
Clearly none of this can go into the article as that would violate WP:OR. But it does strongly suggest that the current unsourced text is unverified, highly questionable, and seemingly needs a citation from a Reliable Source and/or a modification/rewording. Tlhslobus (talk) 07:59, 11 February 2015 (UTC)
thread_title:  Citation needed for allegedly impractical brute force approach 

message: The article is generally pretty vague and incomplete and should be expanded with more information. To the "external pages" section I added a complete (probably the most complete) study on the knight's tour, so it can be taken into consideration to expand the article. Other links and books may be suggested if I'm permitted to do so. Luisa Valencia (talk) 18:56, 8 October 2016 (UTC)
thread_title: Expanding the article

message: There are some new contributions having to do with games involving knights. These do not seem relevant to the knight's tour problem, so I plan to delete them on my next editing pass. Open to discussion here.  
Deleted as irrelevant.
— Preceding unsigned comment added by 91.110.143.77 (talk) 19:25, 2 August 2020 (UTC)
replies: text:  Restoring sections for now until we can discuss whether the variations are truly irrelevant; they appear to be based on the Knight's tour and I'm not sure where else these sections could fit on WP.  Are they truly irrelevant? Myoglobin (talk) 16:36, 10 August 2020 (UTC)
replies: text:  These sections on games have nothing to do with the knight's tour, which is not a game but a problem or puzzle. They are about games that involve knights and other chess pieces and so belong in Chess variant. Deleting. 95.149.237.145 (talk) 12:43, 1 November 2020 (UTC)
thread_title:  Knight's games 

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thread_title:  A Commons file used on this page or its Wikidata item has been nominated for deletion