Talk:Sudoku/Archive 3

Archive 1

Archive 2

Archive 3

Archive 4

Article popularity

Wow, this article is very popular all of a sudden, and I'm glad to have had the opportunity to research why, examining others' edits.

Here's what Nikoli has to say about Sudoku's "British Invasion", cut and pasted verbatim from their Puzzle Japan website. It doesn't seem to fit in the article, but I thought it would be interesting to share nonetheless:

Nikoli Puzzles are now Landing in UK!

The United Kingdom has become obsessed with SUDOKU. Many newspapers and magazines feature this puzzle every day. In trains, offices and kitchens, the British are absorbed in solving SUDOKU. They don't call it "Number Place". They call it SUDOKU. This Japanese word will soon be as familiar as Judo.

They seem tickled pink. They've even recently teamed with Puzzler Media to publish a book of their hand-made puzzles in the UK.

It now seems I was just scratching the surface when I first started adding cultural information to this article. I was really just planning on covering all of Nikoli's popular puzzles and figured it'd be easiest to start with the one whose article was already present; I was wrong, and I'm glad for it. This is fascinating. - ZM

Zotmeister 17:45, 25 Apr 2005 (UTC)

illustrate the 'variants' section

could someone please produce some images to clarify the descriptions like these in the 'variants' section in the article:

Five 9×9 grids which overlap at the corner regions in the shape of a quincunx is known in Japan as Gattai 5 (five merged) Sudoku. In The Times this form of puzzle is known as Samurai Su Doku

because, apparently, wikifying terms like 'quincunx' doesn't provide enough of an explanation... if you follow the link and find out what a quincunx is, you may yet not grasp what a Samurai Su Doku grid looks like. I think more images would make this featured article prettier anyway. --86.54.128.148 11:23, 24 August 2005 (UTC)

I think images for all of the variants would be alarmingly excessive, but maybe one of those "single-digit" inline external links to an example would be acceptable for explanatory purposes, giving you the image you want with a single click. Give me a moment and I'll add one for the gattai go. - ZM

Sudoku Variations

I have found a good article about Sudoku Variations at the website of the Mathematical Association of America. Here you have the link. Since I don't know if it would be accepted at the "External links" section I prefer to leave it here. Maybe someone could use it to improve or complete the "Variations" sections. Regards.

...Wow. This may actually have the curious effect of shrinking the Variations section (which could use some touching up), but with this link being added as a reference! Thanks for this - it's great info. - ZM Zotmeister 19:19, 15 September 2005 (UTC)

...As the author of the page, I would certainly like to see my column referenced on the Wikipedia front page. Note that my column goes into historic detail far beyond what is currently listed within the entry. Several details are wrong or incomplete within the current entry. -- Ed Pegg Jr.

Suggestion: Let's change the samurai sudoku link from Top Notch to Samurai Sudoku. The former site charges £2 to use its samurai solver or see the puzzles in the archive. The latter site gives free access to its solver and puzzles. Plus it gives a prominent link to this Wiki sudoku article (linked to #Variants even!) Kristinw 11:21, 2 February 2006 (UTC)

...As no one disagrees, and the link to the former site is in direct violation of Wikipedia policy (Don't link to sites that require payment to view the relevant content), I'm going ahead and changing the link. Kristinw 04:16, 17 February 2006 (UTC)

Could the person who repeatedly removes the reference to a 100x100 sudoku please explain his/her reasons for doing so? It is really very annoying. Surely this is of some interest if commercial 25x25s are so considered. Michael Metcalf (michaelmetcalf@compuserve.com)

I haven't removed it - it's there right now - but I'll respond anyway since I'm pretty sure I know the answer; I'm inches from nixing it myself. To me, it is painfully obvious that whoever inserted it in the first place has not been watching the history of the article. For starters, you say "person"; I check the history and see multiple people have reverted it. Actually, it was added again after I simply MOVED it, which really shows that someone is not paying attention. Now that is something I find annoying.

I also have to ask: why do you have any right to be annoyed by this? Surely you didn't make this edit yourself, right? Referencing your own work at Wikipedia is often considered a major faux pas.

Ultimately, however, whatever the means of the edit may be, it is its content that would lead to its deletion. I don't mean whether the material is notable or not; in this case, it might be. I mean whether the material is true. The simple fact is that the link provided in the edit to the alleged puzzle just doesn't work. The file isn't there. So not only is the link broken, but so is the only means of verification the edit offered. It would seem that the only other way to verify it is to actually join the Yahoo! group mentioned... which would lead one to wonder if the edit was intended solely to generate sign-ups to the group. We get a LOT of linkspam around here, and we find that VERY annoying.

To sum up, none of us have any proof that this puzzle even exists, much less that it is not self-aggrandizing or advertizing, and therefore should be deleted promptly. Personally, I want to see the puzzle and hear more about its construction, for as far as I know this would be a record (at least if it is proven to be error-free with a unique solution, and preferably hand-constructed), and to that end I've actually left the reference in the article - although I moved it to the notable single-instance puzzles section at the bottom, where it would belong, and I've stuck the word 'reportedly' in there to denote that it as of yet remains unproven. This is NOT a good thing to leave in the article while it's in this state; it needs to be confirmed or deleted promptly. I believe the info may be notable, but it needs verification, and apparently absolutely everything one shouldn't do if he or she wants the edit to stay is being done. The annoyance is all ours. - ZM

Zotmeister 15:56, 21 March 2006 (UTC)

...Thank you for your reply. Please note that in the most recent version of the edit I referenced the work done up to 81x81 in Norway. That is not my own work and seems to deserve as much recognition as the (commercial) efforts of Nikoli. As for the link to the 100x100, this is not broken as you imply, and I had no intention of attracting more users to this (anyway relevant) group. I simply have nowhere else to put it. Maybe you have a kind alternative suggestion. As for its validity, the grid is generated by program, and I would be more that happy to send you a note on the methodology, the puzzle and its solution, and the program itself. And as for 'self-aggrandisement', I'm quite happy to have my name removed from the entry. That's not an ethic I'm used to, but I'm happy to go along with it. I really didn't anticipate a dispute on such a simple matter, and look forward to your reply. Michael Metcalf (michaelmetcalf@compuserve.com).

You make a good point regarding the 81×81 puzzle you provided a link to; that link does in fact work, and there does indeed appear to be a valid puzzle there. This probably should be referenced in the article, at least until a verified larger puzzle comes along. As for your side comment regarding Nikoli, it is true they make these puzzles for a profit, but I argue that their 25×25 puzzles are noteworthy for being a regular feature and for being constructed by hand just like their standard-size puzzles. I know of no other constructors, commercial or otherwise, that can make that claim. (Dell comes close with their 16×16 Challenger puzzles.)

I can assure you that the link to 100x100.xls as provided does not work for me. This is what I see upon clicking:

Document Not Found
The document you requested could not be found.

Regarding putting one's name with their work: the ethical issue is not one of removing traceability. If you did something, your name can and should be associated with it as far as I'm concerned; the issue is that by submitting the link yourself, you're deeming your own material notable and worthy of inclusion in the article, which is a conflict of interest. - ZM

Zotmeister 19:55, 21 March 2006 (UTC)

Inverse automatic construction

If an efficient solver is available, there is a very simple method of automatic construction: randomly add a digit to the grid, and then look for a solution

The inverse process is also possible. Start with a completely solved board, shuffle rows, columns and symbols (respecting the sudoku restrictions, of course), make a random walk through the board, visiting every cell trying to remove its given (if the resulting board can't be solved, this given can't be removed, otherwise, remove it before going to the next cell).

Precooked solved boards can be used. This would save time. I still have to measure it, though.

By the way (here comes my little commercial ;-), I use a GPL sudoku "explainer" engine that I wrote in August:

http://sourceforge.net/projects/sudoku-sensei

This is no Sudoku solver, but "explainer". It can list the logical steps taken. It can generate new Sudokus and rank their difficulty. Not only 9x9 grids: MxN, samurai or any layout you can describe! The core is a C/C++ library. Includes sample programs --Como 18:54, 19 September 2005 (UTC)

Sanity check: encyclopedia vs. textbook

Although I probably just made myself extremely unpopular with at least one individual here, I went ahead and did what should have been done: I took that massive addition to the Scanning section and reverted it away. I'm sure the author had the best of intentions, but I must point out Wikipedia policy: Wikipedia:What Wikipedia is not states that Wikipedia is not an instruction manual.

The Scanning section, as it had been written, details the methods people use to proceed through the puzzle, along with a quick mention of advanced technique. At one point a graphic helping to visualize a particular term was added; I have no problem with that. But the weekend's addition saw that section of the article change from being an encyclopedia to a textbook, giving multiple annotated diagrams of the exact same concepts and, even worse, tasking the reader with further problems.

Those three numbered points provided no new information whatsoever. The first two are straight cross-hatching examples; the third is a contingency example. Sure, the paragraphs try to help the reader to recognize those circumstances, but the generic cases were in the article already; the specific cases mentioned are no different and are not individually of encyclopedic merit. Cross-hatching and contingencies don't need region-rows to be filled in order to work.

Good rule of thumb: if you're asking a question, you're not providing encyclopedic information. Encyclopedia articles provide information, not request it. Incidentally, this wasn't the first time someone wrote a question into the article. (This wasn't the first time it was left to me to repair, either.)

I'm sure there is plenty of demand for a good Sudoku tutorial online with precisely that level of detail for specific examples, but this is not the place for it. We list the primary weapons people use to tackle Sudoku puzzles because we're supposed to report that - it's historical info. The line is drawn between telling how people solve the puzzle and telling people how to solve the puzzle; we do the former to the best of our ability and leave the latter to other resources. I appreciate the willingness of many to add to the article, but it's an encyclopedia article (and a featured one at that), and I intend to keep it that way. - ZM Zotmeister 21:22, 4 October 2005 (UTC)

I understand. It was my first attempt at contributing; I basically thought the same looking at it yesterday and started to take out some of it myself, but you beat me to it. Hansonrstolaf 15:30, 5 October 2005 (UTC)

I reverted a similar block of text. I don't want to step on any novice's toes, I hope everyone stays and contributes more and more, but the quality of some of the large additions are well below what's already in the article, or what's available in the external links. --Interiot 21:51, 4 October 2005 (UTC)

I don't feel strongly either way. It's a gray line as to when too much information becomes unhelpful. I was tending to think that a little more information could be helpful in demonstrating to the reader the potential complexities provided by this puzzle. However, I agree that this isn't the place for a detailed list and explanation of solving strategies. --angusj 23:35, 4 October 2005 (UTC)

I tend to agree with Zotmeister. The coal mining article might mention something about coal and something about a mining pick, but it doesn't say "step 1) to find the best place to mine ... ... step 2) find an able-bodied person to crawl down the hole, step 3) make sure you have a bright light, step 4) start swinging, ...". Same goes for computer programming or ice skating or anything else. People don't expect to become proficient in a task just by reading Wikipedia. --Interiot 00:34, 5 October 2005 (UTC)

The stated goal of Wikipedia is to

...create... the largest encyclopedia in history, in both breadth and depth.

How do we distinguish encyclopedic depth from textbook instruction? As there are already adequate web tutorials on how to solve Sudoku (the contingency link is a good example), I generally agree with limiting HowTo instruction in the main page. Note however that the Official Policy embraces algorthmic discussions, so it would also seem appropriate to have a related page devoted to Sudoku Stategies and Algorithms

Personally, I would like to start a page(s) disucssing the mathematics behind analyzing the properties of Sudoku. The Sudoku.com Maths BB forum is ripe with content for using symetries, deriving the number of grids, bounding min/max number of clues (givens) etc. However, this content is not easily readable or editable in the BB. A Wikipedia page would well serve this purpose (education, reference, readability, editability) The page could be an excellent practical adjunct to other math concepts in Wikipedia.

I would be very interested in this, having just written the Sudoku Assistant this weekend and "discovered" (personally only) that X-Wings, Swordfish, and such are EXTREMELY easy to code for because they are specific examples of a much larger and easily identifyable class of patterns that Angus Johnson refers to on his page.

Do people establishing a Wiki communicate at all by E-mail, or is that declasse? I could imagine a group of likeminded people setting up a nice page (maybe that uses the assistant?) to illustrate the basic strategies with live examples. Hansonrstolaf 15:30, 5 October 2005 (UTC)

I would appreciate comment on using Wikipedia as a mechanism for developing community-based structured knowledge vs. blog and BB message-thread anarchy.

Also, what is the policy on the breakout of in-depth subpages? --LarryLACa 08:32, 5 October 2005 (UTC)

A separate page studying Sudoku solving algorithms more deeply strikes me as an excellent idea. The article covers the general principles, and one of the References links is a wonderful tactical resource (one page of which is linked inline), but given the urges of many people here to expand both "Solution methods" (which really should be fine as is, barring some amazing future advance) and "Computer solutions" (which could actually stand for some carefully-crafted compression), I believe we have enough motivation, interest, and justification to start another article on that specialization. Hey, we don't just have a "mathematics" article, right? We have hundreds on its many elements. Just as the list of newspapers carrying Sudoku was historically significant to track (we were watching a phenomenon in action), so is tracking the many varied means people have developed - and are continuing to develop - in order to solve these puzzles efficiently. But, just like that newspaper list, a separate article is called for. - ZM

Zotmeister 13:29, 5 October 2005 (UTC)

The restriction of information - any sort of information whatsoever should be condemned in this forum. Why not leave the information on there and let the READER DECIDE whether it is relevant or not. I was looking specifically for the sections that you deleted. Information must run free. Secondly, accepting your arguments that the encyclopedia is not an instruction manual, those deleted sections are not a 'how to solve sudoku' manual but they outline algorithms in the solving of complicated mathematical problems. They are no more an instruction manual than the showcasing of a proof to a complicated problem. It is like you eliminating the proof of how and why e=mc^2 based on it being 'instructional in nature' and 'contrary to Wikipedia policy'. Man are you raving mad? Certainly it is not an instruction manual, but a way at looking at a complicated problem. I am against anyone taking out information, especially information that has USE, that is accurate, and that promotes thinking and the enlightenment of the millions who access this site for information. And lastly, in deference to your last argument: there really aren't other tutorial websites out there - most of them are there to make a quick buck. So brothers and sisters, I implore NOT TO DELETE ANYTHING that is of any use from this website.

Diagrams

For what it's worth, I wish you'd consider adding one or two more diagrams. Some people learn better by text, others learn better visually, so it shouldn't be considered a problem if there's overlap between the two. If there's disagreement over what diagrams are good, then maybe some discussion should take place about which are needed, before diagrams are created. --Interiot 02:58, 5 October 2005 (UTC)

I agree. Hansonrstolaf 16:50, 5 October 2005 (UTC)

Strategies and Computer Methods

I edited the strategies and computer section. I hope these will be seen as "friendly ammendments."

1. Marking. Last week, when I first read this Wiki, it was not obvious to me what this "marking" was all about. I've added an image to help other novices catch on more quickly. I'm pretty sure this is the "standard order" of these as alluded to in the text.

1. Strategies. I found the section on elimination only minimally helpful. In particular, I had figured out the {p,q,r} business myself, so that wasn't very helpful (to me). What was missing was the sort of "X-Wing" analysis that is necessary to solve harder puzzles. So I've added a bit there, including two (maybe people can add a few more?) guiding principles of analysis that I have found helpful. I think a SHORT NON-TEXTBOOKY introduction to "X-Wings and Things" would be appropriate here. Just a diagram or two similar to what is at [1] .

1. Computer Solutions. I've been studying this the last couple of days and was extremely pleased to discover how extraordinarily simple it is to code for these contingencies. So the comments in this section that seemed to make judgements or claims regarding how hard and complex it is to program for contingencies just seems out of place now. Adding 20 lines of code gave me every sort of X-Wing/Swordfish, et al. Placing the "human-like" solution strategy up front seems appropriate as a segue into this section, which gets increasingly un-undertandable to the nonmathematician (i.e., me) as it goes along.

So, in short -- hope this is acceptable to the community of contributors here.

Looks alright to me. - ZM

Zotmeister 21:50, 6 October 2005 (UTC)

The Computer Solutions section contains a POV re: what is simpler to code: back-tracking or human logic emulation. The 16:24, 5 October 2005 edit by User:Hansonrstolaf inverted the perspective (was: back-tracking easier, new: emulation easier). I believe this is wrong. I code. I have Java code (snagged from web)for a backtracking solution. It even implements an optimized choice of next digit and is still quite simple code. In general, back-tracking uses the built-in recursion capability of the computer language, which leave very little else to code. Add a few data structures and you're done. Given the small amount of code, these tend to be relatively error free and reasonably robust.

Emulating human logic is much more difficult, requiring hand-crafted data structures and complicated what-if branching. I.e. these tend to be complex.

I would like to see a reversion to the origninal (pre 16:24, 5 October 2005) POV that back-trackig is simpler to code. Let's disuss this first.. --LarryLACa 18:08, 7 October 2005 (UTC)

That's not how I'm reading it at all; as the section is presently written, I'm not seeing any opinion whatsoever on relative coding difficulties. It seems to read that all methods are simple. Whether or not that is a biased POV can perhaps be debated, but I discern no implication of the superiority of one method over another. - ZM

Zotmeister 21:17, 11 October 2005 (UTC)

I thought (I guess that makes it my POV) that a qualification like 'relatively strightforward' was a POV, particularly when compared to just 'straightforward'. Ditto 'fairly simple' vs. 'simple', or 'far from computationally efficient' vs. 'not computationally efficient', or 'method now preferred by many'. Maybe I'm confusing POV with writing style.

Anyway, I've abbreviated the wording (see my 10/14 edits) to eliminate some POV stuff (like: how constraint program solvers work internally or how humans solve problems) and am inclined to leave the article as it stands. Whether it's more computationally efficient to use optimized backtracking or try to work through constraint combinations is a matter of much debate. --LarryLACa 21:28, 14 October 2005 (UTC)

BTW- shouldn't we eliminate the use of 'now' (in the last Dancing Links paragraph), since articles generally don't define when 'now' is --LarryLACa 21:28, 14 October 2005 (UTC)

Difficulty Rating?

The article mentions that there is a standard rating of difficulty to sudoku puzzles. I don't think that there's a universal difficulty rating, that seems to vary quite widely across puzzles.

My question is that since every puzzle should be solvable without any guessing, and only have one unique solution, why should "guessing" and "backtracking" be included in the difficulty if a human will never do something like that?

Users *are* expected to do backtracking in difficult puzzles. Only one "path" of backtracking will validate all the way, others will just end up with impossible boards.

I agree that there aren't set in stone difficulty ratings, but providing examples with some samples for each difficulty certainly helps the end-user and is informative and insightful. Just because there is only one solution doesn't mean that you will have at each point in time a certain digit to be placed in a certain spot. Backtracking and such occures in unique solution puzzles as well, when solved by humans. It's important to specify the difficulty and offer an insight about it, since some users hate backtracing for example and might prefer an easier difficulty.

What sort of analysis does the guessing computer program offer to guarantee that the solution is entirely unique? In my experience with brute-force solvers on said "guessing" puzzles, I frequently come up with multiple solutions. What fun is a puzzle for a human who must depend on chance to reach a valid solution, to find out that it's not the "original" solution?

I can't speak to all programs, but my own program (gnome sudoku -- gnome-sudoku.sourceforge.net) handles this pretty simply. To determine if a puzzle is unique, it simply tries every possible guess. In other words, when generating a puzzle, it checks all possibilities any time it has to "guess" -- if more than one possibility for victory exists, it invalidates the puzzle (or, if it doesn't have more than the maximum number of clues it's set to generate, it simply adds more clues at the branch points to make the puzzle unique. Tom

Even though I don't enjoy guessing puzzles, I suppose I can't argue that the this difficulty rating will assure the person that their time will be spent erasing blocks, or finding alternate solutions. Most publications, however, seem to offer human-solvable puzzles whose solutions are deduced entirely with logic, so perhaps there should be two entries for rating difficulty?

Time to archive "Links for inclusion" and "Subpages Removed"?

The "Links for inclusion" section has become totally unmanageable and all recent links proposed seem to be of very average quality. The obvious links for inclusion have already been added to the main Sudoko article so I'd like to archive this whole section now, but thought it appropriate to solicit opinion before doing so. I also intend to archive the "Subpages Removed". --angusj 23:28, 12 October 2005 (UTC)

I've just realised that "Links for inclusion" is a subsection of "External link explosion (discussion/vote)", so what I'm proposing is the archiving of "External link explosion". --angusj 23:31, 12 October 2005 (UTC)

Actually, this whole Talk page is a mess and I think it could use a re-factor. At the very least, a consolidation of the links being considered/voted on and the discussion around that. Al 12:25, 13 October 2005 (UTC)

Given that the main Sudoku page has only the barest minimum of links to Sudoku sites how about including a good links site under External Links such as http://www.sudokulinks.com/sudoku.html Nxn 07:02, 11 November 2005 (UTC)

Math Comments

I am very disappointed by the quality of the page on Sudoku. Who is in charge of this page? Who wrote the math part? Sudoku is NP-complete! I am dreaming...Sudoku is not NP-Complete. Please check your undergraduate math course. Also, why do you add a link to the programmers'forum? Many readers just want to play sudoku...add some good links to site where you can play sudoku. I had to go to other languages to get what I needed. —Preceding unsigned comment added by 217.136.13.109 (talk • contribs) 07:59, 12 October 2005

You ask who's in charge of the page — well, nobody, and everybody, really. On Wikipedia, anyone is free to edit the page and make improvements and corrections. We've had a lot of trouble with external links in the past, so we've been rather strict in how many "Play Sudoku" websites we've listed (earlier we had 100+ links). We do link to the Open Directory project, which is a better place to have lots and lots of Sudoku links. — Matt Crypto 15:46, 13 October 2005 (UTC)

Thanks for your comment. That's more clear about the external links. I agree with you, a link to the Open Directory is enough. Regarding the math section, I hope that a mathematician will write a correct article.

Did you check out the link next to the NP-complete comment? I haven't yet (link seems to be down at the moment) but presumably that's the source used for the statement. It's certainly quite plausible, though — quasigroup completion is NP-complete. — Matt Crypto 19:54, 13 October 2005 (UTC)

I don't see the problem. The general Sudoku problem of order n is NP-complete. Sudoku constraints (much less restictive than the usual publishers constraints for the simple order 3 Sudoku), are not sufficient to avoid exhaustive search, hence the problem is in NP (Non-deterministic, Polynomial time). Yato and Seta (the referenced article) establish completeness as an application of ASP-completeness (ASP: Another Solution Problem). Additionally, given the Sudoku connection to Latin Squares, which are themselves NP-Complete, I assume NP-completeness can also be derived from Latin Squares directly. (Sudoku=LatinSquare + block constraint). Did I miss something here?--LarryLACa 22:35, 14 October 2005 (UTC)

In simple terms, NP-complete problems are known to be difficult to solve by a computer. No algorithm can reach a solution in a timely period, so we usually use heuristics to get a 'good solution' but we are not sure that the solution is the optimum. If we look at sudoku, it is damn easy to solve a puzzle by an algorithm. You just have to navigate the tree of possibilities and stop a leaf if a constraint is broken. You can find many web that propose a solver based on this algorithm. It takes usually less than a second to find a solution. Also, if Sudoku puzzle is NP-complete, it would mean that the algorithm to solve this problem could solve all other NP-complete problem. It is clear that it is not the case. You cannot for instance solve the 'traveling salesman problem' (which is NP-complete) by navigating the tree of possibilities. I can be wrong but I would like to get the opinion of a mathematician.

Computational complexity is a measure how the difficulty of solving a problem increases as you increase the size of the problem. The fact that 9×9 Sudoku is easily solved doesn't contradict the statement in the article: "the general problem of solving Sudoku puzzles on n² x n² boards of n x n blocks is known to be NP-complete". (You could certainly solve the Traveling Salesman Problem by navigating the tree of possibilities if there were only three cities, say.) The opinion of a mathematician has already been provided in the article because we reference an academic paper. — Matt Crypto 08:09, 15 October 2005 (UTC)

In order to prove that a problem is NP-complete, you must show that every other problem that is NP is polynomial-time reducible to that problem. In essence NP-completeness means that a problem captures the "essence" of what it means to be NP. The other way to prove NP-completeness is to show that another, already proven NP-complete problem is reducible to the problem in question. These are solid theoretical ideas with firm meanings. We must be careful that we use these terms in the right way. Just because a problem "seems hard" or "seems like another hard problem" does not make is NP-complete. Proofs are required.--KrazyMage 14:29, 16 December 2005 (UTC)

FYI: a Mathematics of Sudoku article has been initiated 10/15/05)LarryLACa 20:32, 23 October 2005 (UTC)

69.158.114.165 16:34, 18 January 2006 (UTC)I'm not a mathematician, but I think that before you decided whether a problem is "NP-complete" or "NP-incomplete", you have to define the problem a little more precisely. So I'd like to offer this definition of the problem:

1. There must be only one solution to a Sudoku puzzle. If there is more than one valid solution, it isn't a valid puzzle.

2. "Brute-force" (ie, making guesses and back-tracking if they don't work out) is not allowed. Of course, this would be a trivial problem for any computer of even moderate capacity, given a 9X9 puzzle.

I'm currently working on a solver written in Python, and using only deterministic algorithms, I'm able to solve most of the puzzles on the Daily SuDoku web site (see http://www.dailysudoku.co.uk/), even the "very hard" ones. So without doing any mathematical analysis (I'm not really qualified), my hunch is that any Sudoku puzzle (as defined above) can be solved deterministically in a reasonable period of time. My program usually finishes within a second or two (either successfully or not) on a 2 gHz Intel processor. I'm still working on the program, looking for additional algorithms or techniques to add to it. But as for proving that the problem is NP-complete, I'll leave that up to the mathematicians.

By the way, check out Dr. Dobb's Journal, February 2006, for an article on Sudoku solvers. --david dot kettle at sympatico do ca

David: you hypothesize that deterministic algorithms can solve any puzzle that has been constructed so as not to require backtracking. Isn't that a tautology? Eclecticos 22:38, 12 February 2006 (UTC)

The current article says: "When using marking, a couple of similar [local] rules applied in a specified order can solve any Sudoku puzzle, without performing any kind of backtracking." What is the justification for this statement? It seems to say that there is a polytime algorithm, which (unless P=NP!) clashes with the NP-completeness claimed elsewhere in the article. At least there is a citation for the NP-completeness result. Eclecticos 22:40, 12 February 2006 (UTC)

It's nonsense, for the reason you state. 9x9 Sudoku is solvable in constant time because it's constant size, so with a sufficiently large lookup table you can solve it instantly without backtracking just by looking it up; but because the problem is NP-complete, yes, for general sizes you can't usefully solve it with less work than backtracking unless P=NP. The statement in the article (besides being implausible) is not sourced, ought to be for such a far-reaching and significant statement, and so I'm removing it. 129.97.79.144 17:18, 8 April 2006 (UTC)

I took a look at some of the mathematical article claimed to show NP-completeness. As I read it, it shows NP-completeness of the problem of deciding whether an NxN Sudoku problem has at least one solution, without including the requirement that a problem has a unique solution. There is no guarantee that the Sudoku problem instance generated from a given NP problem instance would have at most one solution, unless the original problem also has that property. The restriction that a problem has a unique solution might make it much simpler to solve. Not that I would bet on it. --Ørjan 23:57, 16 May 2006 (UTC)

Consensus on spelling

I know that some spell it as Sudoku and some as Su doku, which is referenced in the first sentence, but can we decide on one version of the other to use throughout the rest of the text? We currently have it spelled out both ways later in the article. Al 20:29, 13 October 2005 (UTC)

Nevermind. I'll just be bold.

For all intents and purposes, you chose correctly. The company that created the name itself spells it as one six-letter word when written in romaji. - ZM

Zotmeister 18:42, 18 October 2005 (UTC)

Clear sheets for marking up

Just a comment about the section on marking up: What I do when I can't figure out any more numbers by scanning, I lay a sheet of clear paper over the puzzle, trace the outer edges with a marker then write in my guesses. When my guesses lead me to a logical contradiction (e.g., two 4s in the same row) I can just move the clear sheet over and start anew.

I doubt I'm the first to do this, but I don't see anything in the article about it. PrimeFan 17:32, 18 October 2005 (UTC)

Ariadne's thread is Ariadne's thread no matter what material the thread is made of. Tracing paper, bingo chips, computer memory... it's a neat idea, but indeed it's nothing new (the article already covers the concept, although I do intend to overhaul that portion in the near future, including creating an actual "Ariadne's thread" article which is long overdue). - ZM

Zotmeister 18:39, 18 October 2005 (UTC)

Solving Sudoku

Please include more information and pictures to accompany techniques on solving Sudoku. Without pictures, the text described seems obscure. It would be very useful. Thanks!

See previous discussion under Strategies & Methods. Wikipedia is by design not a how-to-cookbook, which is more appropriately addressed by WikiBooks, but there is some latitude in describing algorthyms, and documenting the state of exisiting strategies. Somebody, will eventually create a Sudoku related page with this focus. The article contains links to other sites that do a very good job of explaining how-to. e.g. Keys to Solution. - LarryLACa 22:44, 30 October 2005 (UTC)

Level of Difficulty and Givens

Under the heading "Difficulty Ratings" in the article, it says, "Perhaps surprisingly, the number of givens has little or no bearing on a puzzle's difficulty." If this is true, then why is "Number of filled squares" listed as one of the four major factors influencing difficulty?

I agree. I've now edited that section and removed the "four factors" which I disagreed with anyhow. --angusj 12:24, 31 October 2005 (UTC)

I don't completely disagree, but the number of givens must be a bit of a factor. I mean, in general 40 givens will be a lot easier than 20 givens. 128.231.88.4 You can call me Al 14:27, 4 November 2005 (UTC)

Yes, 40 givens puzzles are easier than 20 givens puzzle if they only require very basic solving strategies. In that case they are only easier because there are fewer steps. However, for puzzles requiring more challenging solving strategies, there's generally a point midway through solving (usually when a little more than half the cells have been completed) where these more complex solving strategies are required. For these puzzles, whether they start with 20 or 30 givens has no bearing on the real challenges that lie ahead. --angusj 22:54, 4 November 2005 (UTC)

Template:Sudoku 9x9 grid available

Sudoku 9x9

5 3   6       9 8	7   1 9 5	6
8     4     7	6   8   3   2	3     1     6
6	4 1 9   8	2 8       5   7 9

I've created a template for displaying Sudoku grids/puzzles Template:Sudoku 9x9 grid. This is an example usage based on the puzzle shown on the Sudoku main page with some arbitrary colors added.

To see the example's parameter list, edit this topic. The diagram can float left or right, cellsize is variable, background colors can be set for the diagram, boxes or individual cells. For usage details see Template_talk:Sudoku 9x9 grid. -- LarryLACa 08:58, 8 November 2005 (UTC)

Template Sudoku 3x9 band available

Case 0 Matching Cells Triplets

1 2 3 4 5 6 7 8 9

7 8 9 1 2 3 4 5 6

4 5 6 7 8 9 1 2 3

I've created a template for displaying a Sudoku band Template:Sudoku 3x9 band. This example shows one of the 2 pure cases for the top band used in enumerating all possible solutions, as explained in Mathematics of Sudoku.

Case 0: No Overlap. The choices for the triplets can be determined by elimination.

r21 can't be r11 or r12 so it must be = r13; r31 must be = r12 etc.

-- LarryLACa 19:11, 18 November 2005 (UTC)

Template Browser Compatability?

I developed the templates under Internet Explorer V6 SP1, but haven't had any feedback yet about how they appear in other browswers. I know older versions of Netscape don't display the major/minor grids at all (Should be thick black/thinner grey respectively). Comments appreciated at User_talk:LarryLACa. -- LarryLACa 19:11, 18 November 2005 (UTC)

Simple Sudoku

I discovered http://www.angusj.com/sudoku/hints.php the other day, which I think is one of the clearest descriptions of "how to solve" Sudoku I've ever seen. Of course it is actually a site that is selling promoting a free Sudoku solving program. So maybe some would not deem the link appropriate for the article. Jooler 07:57, 11 November 2005 (UTC)

Firstly, I'm delighted with your praise of my site. However, considering the angst we've been through over the last few months trying to agree on which sites to link to, I'd rather leave the External Links section just as it is :). --angusj 08:26, 11 November 2005 (UTC)

I disagree. That site, and also the Wikipedia article of today, suggest that it is a good idea to write down all possibilities for a given square. That is a rather wasteful, time-consuming procedure, that I never needed for any newspaper puzzle. (My annotation can be seen from http://www.cwi.nl/~aeb/games/sudoku/solving0.html .)

Pronunciation

There seems some debate, but from my brief google search this link displays the most accurate pronunciation of the alternatives. Is this the general consensus? If so, is anyone able to represent this using the International Phonetic Alphabet? --angusj 04:57, 13 November 2005 (UTC)

I'd forgotten that there's been prior discussion about this ( see http://en.wikipedia.org/wiki/Talk:Sudoku/Archive01#Pronunciation ). --angusj

I looked at the pronunciation reference for the first time in months and find it has been changed to SUE-dough-coo. This is just plain wrong.

* the SUE implies the first syllable is emphasised. Japanese does not have stressed syllables. In the case of sudoku there is a slight lift in pitch on the second syllable;

* the "do" in Japanese is NOT pronounced like "dough". No Japanese syllable is pronounced that way. As I said some months back, it it short like the "do" in "dot".

I'd change it back to something more accurate, but why bother if people can freely replace it with incorrect versions (FWIW, I speak Japanese with what I am told is a good accent.) JimBreen 22:47, 18 December 2005 (UTC)

Are you sure you have your English pronunciations correct? Last time I checked, the 'o' in "dot" is pronounced with an 'a' sound (like the 'a' in 'father'). It's "dote" that's pronounced with an 'o' sound. (Just "do" would be a 'u' sound.)

You are describing the US pronunciation. Outside America the 'o' in "dot" is usually pronounced [ɒ]. — Haeleth Talk 16:30, 21 December 2005 (UTC)

The first syllable is "accented" because it's a double-'u' sound (that is, it's basically two syllables to the Japanese). It would perhaps be better spelled as Suudoku, but good luck trying to get that to catch on now. The English tongue naturally wants to speak accented syllables slower; it's the closest approximation to Japanese speech metering we have that I'm aware of.

What mainly concerns me is the people I've heard saying "sue-DAW-coo" or even "sue-DOCK-ooh". Now that is "just plain wrong" - it's the wrong vowel, and in the latter case the wrong syllabic division. The intent with "SUE-dough-coo" is to provide a quickly-recognizable fascimile built of English words; it is not intended as a substitute for a proper IPA listing as asked for above, which could obviously be definitive. Since you obviously wish to provide a perfect pronunication, might I suggest you construct one with the proper tools?

I say we send an email to Nikoli and have them send back an audio recording of Kaji Maki pronouncing it. It's his word; it's his final call. If we say it's for the Wikipedia - which it would be - then he'd probably do it. Then we can upload the file and give people a link to click on to hear the pronunciation directly from the source. In fact, I think I'll be bold. I'll let you know what I hear back (no pun intended).

Personally, I still think it should be pronounced "NUMB-burr-PLACE". But I digress. - ZM, who has it on good faith that anyone told by a nihonjin they have a good Japanese accent is being lied to (your mileage may vary, of course)

Zotmeister 23:30, 19 December 2005 (UTC)

[indent reset] Okay, I'm quick to admit that I'm FAR from an expert on IPA, but I am well aware of what schwa is and I'm not seeing at all how it enters into the pronunciation of the word "doe" (which is a homonym of "dough" and two letters shorter, I suppose). People are saying "SUE-doe-coo", not "SUE-duh-coo". (I must admit I have heard "suh-DOE-coo", which I maintain is sufficiently incorrect as to warrant correcting those who speak it; at the very least, if the article is going to list it, it should list it last.) I'm not going to edit what is there now until I've researched it further, but I feel something there now is probably misleading at best and I'd like it properly dealt with. (For the record, I did send that email; I haven't heard back yet.) - ZM Zotmeister 16:42, 22 December 2005 (UTC)

In British English, the "long o" sound of "doe" is pronounced as the diphthong [əʊ], whereas in American English, it is pronounced as the diphthong [oʊ]. The difference between [oʊ] and [əʊ] is that in the latter, the first part of the diphthong is unrounded (meaning the lips are not rounded) and fronted (meaning the tongue is further forward than as far back in the mouth as possible). See IPA chart for English. I have added American pronunciations to the ones given (and labeled the existing ones as British). Nohat 01:41, 11 January 2006 (UTC)

Aha! That explains a lot - this article is in British English, and I didn't realize the pronunciation of 'o' was that different "across the pond". Thanks for that. - ZM

Zotmeister 15:52, 11 January 2006 (UTC)

The number or pronunciations has suddenly jumped to 7!! This seems excessive to me. Surely two or three would be more than sufficient (eg one each for Japanese, British English & American English). --angusj 22:21, 7 February 2006 (UTC)

List of Sudoku terms and jargon

I have created List of Sudoku terms and jargon in anticipation o f needing this for work on the Mathematics of Sudoku article.

Is this a useful endeavor? If so, we can ref. it from the Sudoku.

See also Talk:List of Sudoku terms and jargon for my suggestion on how to organize a talk page to provide clarity about consensus.

Link quibbling on the list page will probably be worse than here, since I found it necessary to give a minimal link example for most terms, to document accept usage. -- LarryLACa 04:49, 15 November 2005 (UTC)

Bug LaTeX

X = X disappears in the section Sudoku#Mathematics_of_Sudoku. Don't understand why. It would be nice to correct the interwikis as well (at least french and german have this bug)

Proposed External Link

I propose the following external link:

• SuDoku Java Applet - Create, solve or save your SuDoku game with this java applet. Highly maintained by SourceForge.net. This page is completely advertisement-free and the applet is so comprehensive.

This is an interactive flash Sudoku where you don't even need the keyboard. Every new game is of varying difficulty and number placement. And at any given stage, the user can ask for a hint (which will descrease his score). Also, it's possible to find a blank printable Sudoku. And yes, the site name uses the Sudoku spelling (Soduku) that many of us use.

• OnlineSoduku.com

This daily puzzle maybe of interest to you. Every day the puzzle is updated with varying difficulties.

• Daily Sudoku

YAELP (Yet Another External Link Proposal)

• http://ironsudoku.com
  

One of the few Sudoku sites that lets you mark subscripts. It's also slickly done with AJAX. And there's always a bunch of players on the site chatting in the chat log.

Several sudoku sites are available to play sudoku online. One that has the best game play in my opinion is Count to Nine Sudoku (http://www.counttonine.com), where you can play and print free sudoku puzzle online.

I'd like to propose the following link for the Sudoku page:
http://sudoku.bookthoughts.co.nz
Its a subdomain offering a free service where sudoku fans can sign up to recieve daily sudoku puzzles sent to their inbox. Invers_Cheif

Seeing the note at the bottome of the article I decided to propose this here rather than simply add it. It is an open source Sudoku solver which runs in the user's browser.

• http://sudoku.sourceforge.net/

-=# Amos E Wolfe ^talk #=- 03:30, 20 November 2005 (UTC)

Here's another external link proposal:

• http://www.thetoolboxsite.com/Sudoku.aspx

It's an online Sudoku solver. The unique thing about this site is that it uses 100% deductive reasoning instead of brute-force search, which means it will actually explain to you how it solved the puzzle. There's a 'solve next square' feature that's useful if you just want a single hint; and it can explains how you could have figured out on your own to solve that square. This feature is sufficiently unique and something that Sudoku fans would really appreciate, so I believe there is great value in having that site as an external link here. It also rates difficulty of puzzles, (which it can calculate based off the complexity of deductions), and generates new Sudokus.

I propose the following external link:

• http://www.logicando.net

Here you can play Sudoku online, talk in a forum, participate to challenges, and more. You need to register, but it's worth to, because the game is very well made.

I would like to propose the following external link also:

• http://www.claytopia.net/sudoku.php

This is Chisai Sudoku, a 100% free Sudoku game I wrote for Windows (no ads, adware, spyware, or any junk like that). It can produce over 2 billion gameboards at three different difficulty levels, display visual cross hatching and several other features. I made it free because I like sudoku and I love programming and I like making free software.

207.161.57.208 03:36, 19 January 2006 (UTC) Clayton Rumley

Hello, I found the following ad-free website having a solver and free puzzles. The website is very userfriendly, so it's worth to add it to the link list. http://sudoku.nanosim.net/en John, 21:13 25. January 2006 (CET)

I propose the website *http://www.sudokuearth.com , it's a website where players can generate unlimited sudokus for free, play them online or print it out with the solution key, you also can play at a sudoku challenge every day. the site also includes a sudoku solver.

I'd like to add a link to my online, browser based, Sudoku game, but I noted the external links warning, so here I am :-) The URL is http://www.web4sudoku.com/

i like to add a link to my webpage http://www.zoozle.net/sudoku/ where one can play sudoku online. Am I allowed to add this link to the "External Links" section?

Any additions to "External Links" will need enthusiastic endorsement from the 'regulars' here. So far, in my opinion, none of the proposed links here (including this one) demonstrate 'exceptional' qualities that would warrant inclusion in External Links. --angusj 10:13, 18 March 2006 (UTC)

I found another Sudoku Tournament Based Website and Forum. As a result, I updated the Links Section. The site is http://www.unitedstatessudoku.com/

I found the greatest web site for Sudoku WWW.SodukuPro.com Why Censorship!!!!!!!!!!!!!! this for everyone to add the comments and thier right to have links other links like www.sudoku.com are commercial!!!!!!!!!!!!!!!!!!!!..

I don't think the fact they're commercial is the problem (at least that's what I was told) --KSnortum 03:31, 30 June 2006 (UTC)

I would like to propose my site http://www.sokudo.be/sudoku/ for inclusion in the external links section. It has a Javascript solving assistant that IMHO makes it pretty unique.

I would like to propose my site http://sudokuplayer.net for inclusion. It offers a unique online flash based sudoku game.

I propose the following external link (and apologize for just flat out including it earlier without running it through here first (newbie)):

• Writing Sudoku This would be a replacement reference for the (now defunct) Nikoli "Let's Make Sudoku!" article. Yes, it is my site, but my intentions are good.

MDWthing

Invented by Leonhard Euler?

According to Swiss Radio International, Sudoku was invented 222 years ago by Swiss maths genius, Leonhard Euler. (The Wikipedia entry for Leonhard Euler does not yet mention this alleged fact either).

I've read that before. Every now and then, someone tries to edit our Sudoku article giving Euler credit for inventing the puzzle; it's reverted every time. Euler was indeed a mathematical genius and did, for all intents and purposes, invent the Latin square. Latin squares are a basis for Sudoku puzzles - all Sudoku solutions are Latin squares - but he did not develop the third dimension (regional restriction) that distinguishes a Sudoku puzzle, nor did he present his Latin squares as puzzles. Swiss Radio International is exaggerating, if not worse. Sudoku was invented (though not under that name) by Howard Garns, just as the article presently reads. This is one play at national pride that just isn't true.

It could be worse - Uwe Meffert's Kokonotsu website claims his variant predates the standard by millenia, claiming the creation of the lo shu as the birthdate of his puzzle just because his version happens to require the lo shu be present in the solution. (Even his explanation of his title is incorrect: "kokonotsu" means "nine objects", not simply "nine". Besides, the accent in "kokonotsu" is on the second syllable.) It frightens me how willing some people are to try to twist history itself to their own ends. - ZM

Zotmeister 18:20, 29 November 2005 (UTC)

Given that this misinformation is looking to become widespread, and that people are habitually adding it to Wikipedia, it might be worth considering adding a brief note about this to the article. — Matt Crypto 18:28, 29 November 2005 (UTC)

I was just thinking the same thing. I'll find a place to squeeze it in and a polite way to phrase it. - ZM EDIT: Done.

Zotmeister 18:31, 29 November 2005 (UTC)

Looks good. — Matt Crypto 18:56, 29 November 2005 (UTC)

What Makes Sudoku so Addictive?

This section looks like original research to me. Any cites? You can call me Al 19:12, 19 December 2005 (UTC)

Fair enough, Al. I thought it was just general opinion, but I didn't read up on the rules properly. --IE 09:36, 20 December 2005 (UTC)

-- 21 December 2005 --

I managed to find a verifiable source for some of the points I raised in the section "What Makes Sudoku so Addictive?". Carol Vorderman shares some of the same opinions in her published book "Carol Vorderman's How to Do Sudoku".

More information about the book

More information about Carol Vorderman

I'm not sure if I am allowed to quote sentences from a published book, so I will just reference the page numbers and paragraphs for now:

What Makes Sudoku so Addictive?

Vorderman admits that she's a Sudoku addict - page 4, paragraph 1.

Many people enjoy solving Sudoku puzzles...

Vorderman describes Sudoku as compulsive (page 4, paragraph 2), wonderfully challenging, and utterly absorbing (page 5, paragraph 1). However, this is just one person, so may not count. But she then explains how millions of people are devoted (page 5, paragraph 2)

Simplicity of the playing rules - This makes it easy for beginners to get into. For example, Sudoku doesn't require mental arithmetic, so you don't need to be good at math to be good at Sudoku.

Vorderman says same thing about math requirements in relation to Sudoku skills - page 6, paragraph 2. She also states how easy the game rules are (page 5, paragraph 3).

Quickly build up your skills - By completing a few beginner puzzles, you can quickly build up your Sudoku skills, to solve more complex puzzles later.

Vorderman explains that her book guides and instructs people to help them build up their Sudoku skills, from beginner to master level - page 8, paragraph 3.

Easy to save and continue - You can start a puzzle one day, get halfway through and finish it off on another day. It can be especially satisfying if you were stuck on the puzzle the 1st day, and what seemed like an impossible-to-find number is found surprisingly quickly at second glance.

Haven't got a strong source here, but Vorderman mentions how you can return to a puzzle after a break - page 10, paragraph 1.

Easy to travel with - You can write down a puzzle on a scrap of paper, and you don't really need to carry solutions - you just "know" when a puzzle is complete.

Vorderman says she would often rip out puzzles from newspapers (page 4, paragraph 4). Not quite the same but does verify the portability of the puzzles.

It can be relaxing and help to relieve stress.

No sources here.

--IE 10:21, 21 December 2005 (UTC)

Am I alone in thinking the article doesn't need this section? - ZM

Zotmeister 16:31, 22 December 2005 (UTC)

Possibly. I just get a lot of people asking me what's the big deal about a simple puzzle game. What's so special about it, etc... Perhaps it's not in the right section, and the article length is quite long already, so you can remove it if you want.

--IE 17:14, 22 December 2005 (UTC)

I wouldn't necessarily want to delete it if people would actually be looking for that information, but I figure all the bold text needs to be dealt with. Somehow. Not sure at the moment. - ZM

Zotmeister 17:25, 22 December 2005 (UTC)

I feel that this whole section should be removed. --angusj 23:43, 23 December 2005 (UTC)

Sodoku and Sudoku

On fr:Sodoku and sv:Sodoku, Sudoku is a game and Sodoku (with an « o ») is a disease... Isn't it one problem? --David 21:10, 19 December 2005 (UTC)

Soduku. -- ALoan (Talk) 21:36, 19 December 2005 (UTC)

Category

Surely someone should create Category:Sudoku? violet/riga (t) 12:23, 10 January 2006 (UTC)

Done. violet/riga (t) 21:40, 10 January 2006 (UTC)

Personal communication

Am I the only person here who has been getting private emails about the content of this public article? I am not the only person in charge of this thing. If someone has something to say about the article, post it here to this discussion page - do NOT email it to me directly. I don't care who you think you are or who you think I am: knock it off.

My apologies to all the other sane and courteous editors here; multiple irritants prompted this. - ZM Zotmeister 20:48, 10 January 2006 (UTC)

Solution Methods, Computer Solutions "edit war"

It appears some anonymous user is insistent upon taking our featured article and rendering it sophomoric. The edits made to the Analysis section destroy it, most of the "new" material simply repeating what appears in the sections above it; the Computer Solutions edits now constantly reference times without context, a computer-science taboo. It is also painfully obvious that the editor has no grasp of proper English grammar, British or American. I have attempted to revert this twice, only for the revert to be promptly negated by that same editor. Surely I am not the only one concerned by this. I could agree that those sections can benefit from some tidying, but that's not what is happening here - this is at least a clear lack of wisdom, at worst a hijacking. I'm giving it the third revert, but if it recurs afterwards, Wikipedia policy would frown upon me to right the article again. I may need help here. - ZM

I agree that the Analysis and Computer Solutions sections still need considerable work (which I'm not prepared to do myself just yet at least). However, where there's disagreement over changes, the appropriate way to manage it is to revert the article to the former state (as Zotmeister has done) and open a discussion here soliciting feedback from other interested parties. --angusj 22:04, 11 January 2006 (UTC)

Have you read both texts? Do you have an opinion about the difference? The current text is full of misleading or false or silly statements. Not what one would expect from a featured page. But if you guys insist on having junk in this page, so be it.

(The current text has the false "Mixed integer linear programming is also an efficient method." - but of course it is not efficient at all. Indeed, no linear programming is involved, and this is just a very slow and complicated way of doing a backtrack search.)

I do not understand your statement. Efficiency is quite relative, but efficient MILP solvers solve a Sudoku in about 0.01 sec. There is linear programming involved to find the solution of the continuous relaxation of the problem, which is often quite near the integer solution. Moreover, empirical evidence show that backtracking is almost never needed for solving a Sudoku using a linear solver: the presolve will either find a solution by itself or the solution will be found at the root node of the relaxation (either using cuts or heuristics).

I agree that this is not the most efficient method, and that with most solvers, much more than linear programming is involved. Yet it is still a very simple (about 10 lines in AMPL), reasonnably fast method to solve a Sudoku. -- J-S 12:22, 31 January 2006 (UTC)

(The present article describes an extremely silly way to do backtracking, and reports that it takes 2 seconds, or maybe 1 minute. Correctly written programs are a million times faster than that. I don't know why anybody would want a description of a silly way to do backtracking in this article.)

(The Analysis section is almost unreadable, with strange and incorrect statements like 'Only certain "closed circuit" or "n×n grid" possibilities exist'.)

(What happened to the Uniqueness argument? Killed by the zot.)

The Register wrote about the phenomenon that experts improve articles only to see the improvements reverted within hours. Indeed - now I see for myself - the experience was illuminating.

I suggest reading the Heyawake article history for a proper example of taking an overbloated article and streamlining it nicely. Speaking as the person whose work was largely overwritten in that circumstance, I quickly admit that it was a good thing. Some small copyedits are in order (the word 'orthogonal' is still needed, for example), but for the most part, the article is far more approachable while still providing most of the original information. There is little negative impact to be pointed out there. Wikipedia is not a powertrip. If you want one, you're at the wrong site; if you think I'm on one, you're not paying attention. It's "Zotmeister", by the way, not "the zot".

Regarding the Sudoku article, I do agree to be fair that as it stands, the Analysis section is largely impenetrable. However, your suggested replacement was largely recycled material from the Scanning and Marking Up sections. You imply we did not read what you changed; I imply you did not read what you did not change.

Backtracking algorithms are last resorts - one codes a brute-force search when they don't know what they're doing. I don't see the need to discussion variations of those in this article at all. But regardless of my opinion on that, any discussion of computer algorithm efficiency in terms of real-world times is obviously misleading; one must speak in terms of computer cycles, as not all computers run at the same speed - something I don't need my computer science degree to tell you. I couldn't help but notice how your edit was riddled with real-world times. And you're implying that you're an expert?

As for that "Uniqueness" paragraph, that at least was genuinely new material on your part, but the fact of the matter is that it's too generic for the article. A discussion of the application of metalogic to puzzle-solving doesn't belong here any more than it belongs in all the other specific logic-type puzzle articles. Your following paragraphs serve to again detail something that applies to all logic puzzles and does not belong in the specific Sudoku article. I intend to expand the metalogic stub and create an Ariadne's thread article in the near future, giving these subjects the proper treatment they deserve, and will make sure this article links to those as appropriate; explaining these concepts in all the individual articles they could apply to is not the answer.

For the record, The Register is a great publication. They are very right. You've seen first hand what it's like to revert the work of experts; you can stop it now. I'm tired of speaking with you in this manner; if you could drop your holier-than-thou attitude and instead assume a more rational whatever-is-best-for-the-article mindset, I think you'll find future discussions with me much more fruitful. I also have an issue with those who argue hiding behind anonymity; if you insist to be an expert, might I suggest registering here at Wikipedia and proving it? - ZM

Zotmeister 19:53, 13 January 2006 (UTC)

It's my opinion that both Zotmeister and 209.64.21.132 are getting a little too huffy about this. There seems to have been some agreement that this section needs some revising. 209.64.21.132 was trying to do this. How would you feel, Zotmeister, if you tried to help out as best you could, and then someone said you had 'no grasp of proper English' and called your edit 'sophomoric'? Not too good, I'd bet. However, there seems to be agreement among at least two knowledgable users that 209.64.21.132's edit was unsatisfactory, albeit well-intended. Therefore, my suggestion is this: we look calmly at 209.64.21.132's edit and figure out what is good about (perhaps some of the form, if not the content?) and work from there. And Zotmeister, I'd watch out for your own 'holier-than-thou attitude', even if it may be well-deserved. I think we can all be understanding and mature here, and talk about things politely here before engaging in edit wars (expert edit wars are still edit wars). Hope this is helpful GlamdringCookies 20:30, 13 January 2006 (UTC)

You have the wrong other user: it's 62.163.97.27, not 209.64.21.132 - part of the reason I don't care for anonymous users, but no excuse to not be careful who you attribute quotes to.

Personally, I was merely responding in kind to the way I was addressed. (I find it the only way to get through to some.) You didn't see the original messages that user sent to me (via private email), either. I don't want to have to resort to the sort of language I used, I really don't, but although it looks like this just started, it's really at "at wit's end". As I implied, I have no such pompous attitude, I can assure you - I'm just very good at faking one when I need to.  :) Besides, I didn't even write the parts replaced by 62.163.97.27 - there's nothing of mine at stake here I could consider better. It was that user, not me, who used the term "edit war" (hence the quotation marks, even in the topic header). I was approached from square one as an opponent. I deeply appreciate that I'm not the only one who sees no need for fighting here, but I was attacked, and I intend to defend myself.

For the record, if any of my edits are of poor grammar and/or sophomoric, then by all means call me on it; tact won't help the article any more than complacency will. I assure you I wouldn't be offended at all if I were truly guilty. On the other hand, you would have every right to be offended if I simply tried to continually repost the same info with the same easily-recognizable-and-repairable errors. All I'm asking for is common sense.

Zotmeister 22:21, 13 January 2006 (UTC)

To Zotmeister: Yes, I am convinced you are on a power trip and entirely prepared to damage Wikipedia in the process. You are a liar as well. "I couldn't help but notice how your edit was riddled with real-world times." said about an edit that did not increase the number of timings given, but replaced precisely one misleading time by precisely one more illuminating time. You do not sound like an expert either - at least not one who has experience with generating puzzles. A fast solver is required. And yes, there was still overlap with sections I had not edited yet. But your edit war prevented further work.

To GlamdringCookies: Yes, well said. However, I wonder where you see two people that had a negative opinion about these changes. I see only one, and he is mostly lying, struggling to find reasons why his revert was necessary. There is also Angus who says that if there is disagreement things should be discussed here, without otherwise voicing an opinion, as far as I see. Of course he is right. Or are you the second one with a negative opinion?

62.163.97.27, thank you for agreeing with my attempt at mollification, but you are still out of line. I have no authority to say anything about your edits, but pay attention to the No Personal Attacks rule. For one, it's immature. Two, it's hurtful. Three, it does nothing to advance your perspective. 'You are a liar as well' seems to qualify, as well as several of your other comments. Please check out the No Personal Attacks page, it's very well put-together. And also note that for repeated violations, users have been known to be banned. But I do not wish to appear too antagonistic to you: Wikipedia would surely welcome you with open arms to create an account. It would mollify (good word) Zotmeister on one point, and would enable some of this conversation to move to your own talk page, a much more suitable location for it. Oh yes, and I was indeed wrong about Angus, as you say, he merely commented on disagreement, not the content. I also thought of a possible solution: Why don't we make edits in small increments instead of large ones; I think a lot of people would be happier that way. Just an idea, up to y'all if it works. GlamdringCookies 22:56, 13 January 2006 (UTC) (PS: Zotmeister appears to have started doing just that...)

Yes, GlamdringCookies, you are right in all you say. But I have given up on editing (at least this article in) Wikipedia, it is a waste of time spending thought on an article, and seeing things reverted immediately afterwards. It is true that Zotmeister is doing more edits, but that is just to bring the text in accordance with his latest theory, not an improvement at all. I hope to bring up that point later, must address his lies and incorrect views one by one.

In response to what I was targeted with: it appears that both your version and the original are riddled with real-world times. I wasn't lying, but I was unobservant. I started to clean out such references from the present version, but I obviously didn't get them all. This is now done. As for puzzle construction, I'd like to think I'm fairly competent, but I don't do it for a living. Yet. Incidentally, a fast solver isn't required at all. I'm a very slow solver, in fact.  :) (I, of course, generate puzzles properly - that is to say, by hand.) I have no desire to try to get a computer to make puzzles at all, which is why I hadn't fiddled with that section of the article for some time after I first added it. Actually, I thank you for bringing the timing issues in it to my attention. I won't comment about any potential future edits you may make until they are made, but I expressly disclaim ownership of this "edit war". - ZM

Zotmeister 22:41, 13 January 2006 (UTC)

Good, that was one misleading statement of yours that you withdraw. Here is the next lie: "Backtracking algorithms are last resorts - one codes a brute-force search when they don't know what they're doing. I don't see the need to discussion variations of those in this article at all." - suggesting that I added discussion of variations of backtracking algorithms. On the contrary, I removed discussion of a silly variation, and left only the meaningful one. You reverted, adding the silly variation again.

The quoted statement is not only a lie in what it suggests about my edit, it is also incorrect. As said, for the (computer-)generation of puzzles one needs a fast solver.

1. Please stop the personal attacks - it does nothing to support your case and, by continuing to flout Wikipedia policy, makes me (and I suspect others) less sympathetic to your suggestions. 2. Please use the signature & timestamp feature so we know who's saying what. At the moment I'm confused as to where one person's comments start and one ends. 3. Smaller edits is a good idea since it's then much easier for 'regulars' to review changes. 4. Major changes should be proposed in 'Discussion' first to avoid Revert wars. --angusj 23:49, 13 January 2006 (UTC)

Yes, Angusj, you are right, just like GlamdringCookies. My use of "lie" was prompted by the webpage of Zotmeister that said when I last saw it that he had not lied the past several years. But he makes false statements about my edit.

Considering "my case" - well, I saw that the Solution Methods part of the page was of very, very low quality and decided to improve things a bit. That time was wasted, but I am learning how Wikipedia functions, that is also interesting.

Minimax / hill climbing?

While we're pondering over the vandalism war....

"A highly efficient way of solving such constraint problems is the Minimax Algorithm. This method can be directly applied to solving Sudoku problems, counting all possible solutions for most puzzles rapidly."

(or "Hill climbing" in some versions of the page)

Would somebody care to elaborate on how either method can be applied to Sudoku solving? Besides, the second sentence makes little sense, considering that one of the basic rules of Sudoku composition is that there is only one solution. -- Smjg 10:23, 18 January 2006 (UTC)

The original text, mentioning that Knuth's "Dancing Links" algorithm is very fast, was correct. I see that the CPLEX is gone. Good riddance - except that it is a widespread idea that LP would work, and it is good to mention explicitly that it is no good. Algorithms like Hill Climbing are indeed not useful, and somebody should restore the Dancing Links.

I do not know where you got this idea that (MI)LP cannot work. Not only it works, but it is reasonnably fast (about .01 sec on a standard PC), and if you have access to an MILP solver/modeler, it is probably one of the simplest way to write a Sudoku solver (about 10 lines in AMPL for example). -- J-S 12:02, 31 January 2006 (UTC)

On the other hand, counting solutions, or at least distinguishing the cases of 0, 1, more than 1 solution, for a given partially filled grid, is a useful activity. If one wants to design a puzzle one has to check that the answer is 1. If one wants to remove redundant givens, one has to check that after removing any given the answer is more than 1. Sometimes improper puzzles are set that have several solutions.

Regardless of algorithm effectiveness, simply removing one name from a sentence in the article and replacing it with another is indeed vandalism, especially where the rest of the paragraph is built around it. I will revert this.

The anonymous poster has a good point; although a by-hand composer should know the solutions to es puzzles are unique and a by-hand solver shouldn't need metalogic, a computer solver and/or composer isn't doing its job if it doesn't completely scan the available solution space. That's well worth mentioning. - ZM

Zotmeister 13:51, 18 January 2006 (UTC)

Good, Dancing Links are back. Now Dancing Links is a good way to do backtrack. There is still a discussion about the wrong way to do backtrack. Someone should remove it. Zotmeister, it is a mistake to keep stressing by-hand work when discussing a section headed Computer solutions.

Perhaps you misinterpreted me - I implied that the difference is important to note, something that sets computer solving apart from human solving. - ZM

Zotmeister 17:19, 18 January 2006 (UTC)

www.sudopedia.org

A lot of discussions about the required level of detail in this popular Sudoku topic have been going on, lately.

Another concern of mine is the vast amount of very detailed postings by users on the various Sudoku forums, that are slowly disappearing under a mountain of 'Help me, I'm stuck' topics. This information should be reorganized in a structured environment. For this, I have started the Sudopedia, an information database in MediaWiki dedicated to Sudoku.

The Sudopedia can be found at [2]

It may be a good idea to keep the article here in the Wikipedia a little more encyclopedia-like and put the details in the new Sudopedia.

I am looking for authors who can help me set up the foundation of the Sudopedia. Please sign up and help me out.

Thanks,

Ruud.

2 questions

While programming a sudoku-solver two questions ocurred:

• Has each sudoku only one solution or can there be more than one solution for a sudoku?
• Is a sudoku wich has no solution still a sudoku?

--84.185.162.12 12:32, 1 February 2006 (UTC)

There's a sentence in the article on this; my personal opinion is that it's not a proper puzzle if its number of solutions is not exactly one. I would think, however, that in writing a solving program, one shouldn't assume anything - it should be able to determine all "solutions", if any, a grid has (or at least determine if the number of "solutions" is greater than one), and find out if the puzzle is valid on its own. - ZM

Zotmeister 16:44, 1 February 2006 (UTC)

New terminology & rating system

Hello fellow sudoku addicts. I have just updated my Website to promote my new product Sudoku-Help-Plus. This of course is irrelevant from an encyclopaedic perspective. However I have introduced some new terminology (see SHP Solving Rules) some of which may be of general and/or encyclopaedic interest. I have also introduced what I believe to be a new puzzle variant which I have christened Cluedoku.

But likely to be of most interest is my new system of rating the difficulty of puzzles, the SHD Rating (Sudoku-Help Difficulty Rating). If it was adopted widely it would enable the Sudoku community to campare the relative difficulty of puzzles to each other with a standard and much more meaningful metric, than the somewhat arbitrary generic terms currently in use.

I will leave it to the main contributors to this excellent article to determine if any of the above is worthy of a mention anywhere in the primary article. Sudoku-help-greg 03:28, 2 February 2006 (UTC)

I think I would prefer someone to tell me that my new terminology and rating system is uninformed garbage than to elicit no comment whatsoever. Sudoku-help-greg 01:52, 10 February 2006 (UTC)

OK. For a start I don't see any benefit in introducing new terminology since it only confuses people more than they already are with the existing terms. Also, I think your proposal (like many others here) borders on link-spam (ie just a thinly veiled attempt to generate interest in your site). --angusj 13:17, 10 February 2006 (UTC)

Unless and until your new system is adopted by the Sudoku community at large it can't be included here. Wikipedia is not the place to promote new things. —Wrathchild ^(talk) 13:18, 10 February 2006 (UTC)

Better than no feedback, thanks. That was not the intention at all (Link Spam), but you can think what you like. I will leave this entry here for a couple more days, and if you all think I am offering nothing of merit here (or there is no further commentary), then I will remove the entire entry myself - no problem! But I did think this page was a discussion forum. It is not as if I edited the main page. I have no doubt my n x n Gridlock terminology is much more meaningful and less confusing than the "fishy" names for those techniques. Regards Sudoku-help-greg 04:08, 11 February 2006 (UTC)

OK, I'm happy to accept that your primary intention was to contribute to Sudoku discussion (which is focused at improving the Sudoku article here in Wikipedia). However, when you state in your very first sentence that you're website is to 'promote my new product', hopefully you can understand why I think you're treading a fine line. The problem is that many/most of us who have Sudoku webpages think that our own webpages are special and worthy of attention. Unfortunately, none of us can be objective about our own sites. --angusj 12:43, 11 February 2006 (UTC)

Thanks for that I appreciate you taking me at my word. Note that I said I had "updated it to promote" not that that was the site's whole purpose. FYI - I removed my entry as agreed, but Wrathchild restored it, so I guess it stays. Sudoku-help-greg 23:22, 15 February 2006 (UTC)

The free CBD weekday afternoon (News Ltd) Newspaper, mX, distributed in Sydney and Melbourne with an estimated readership of 288,000 is now publishing my Sudoku puzzles daily (using my new nomenclature and rating system). Does that meet Wrathchild's requirement for "adoption by the Sudoku community at large" and possibly warrant some recognition in the main article, even if only in the "Popularity in the Media" section or not? (Sudoku-help-greg 06:14, 31 May 2006 (UTC))

Two Player Sudoku

I do realize there are perhaps 100's of multi-player Sudoku variations. However, I decided to add yet another to the mix that would offer something other than the standard race type style. It's called Sudoku Sensi and can be played here [3].

The main premise is that you're trying to outscore your opponent. Each player has his own set of colored stones, and a unique color is used to establish the starting puzzle layout, which is based on a 5 star difficulty system.

Points are awarded as you place stones, into the grid. Penalties are given when entries are made and successfully challenged by the opponent. The key strategy is to place the higher valued stones (i.e. 9) first since they're worth their face value in points and then work your way down as the game progresses. Placing the big point stones may not be plausible in the early stages of the game so additional strategy can be used to guarantee a win when playing weaker opponents. As you play you will learn the advantages of bluffing and challenging.

You will need to find another player when playing at this site since there's no computer player at this time. Full rules are available.

I apologize if this comes off as a plug.

I do hope you bring a friend and collectively solve any puzzle as you compete against one another.

Number of solutions

It seems to be that, using the typical rules of sudoku, there can only be so many possible final solutions. If 9 is the number in the uppermost, rightmost square, than there can be only so many filled puzzles with 9 there. Anyone know the grand total of possible grids?

Read the main article under "Mathematics of" for one answer, but to my way of thinking you will find a better answer in an article I stumbled across the other day by an American science writer, Brian Hayes. You'll find it in American Scientist Online. I think it takes better account of the symmetries of the puzzle than other discussions on the subject that I have read. Zotmeister might even want to add a link to it in the main page. Sudoku-help-greg 23:01, 16 February 2006 (UTC)

Urban Myth

So the story about Soduko being an an ancient Japanese game are is just an urban mith! Well I certainly fell for it Springald 19:48, 20 February 2006 (UTC)

Yeah, we've been getting a lot of wishful origins for the puzzle: ancient Chinese, ancient Japanese, not-so-ancient Swiss... Thankfully, we had Will Shortz the enigmatologist on the case.

A big part of the confusion comes from how Sudoku is essentially an extension of the Latin square concept, which in and of itself is related to the magic square. Those mathematical concepts do have their history; our article was edited not long ago to note the Latin square connection in the History section specifically to dispel a very common myth. - ZM

Zotmeister 14:44, 22 February 2006 (UTC)

Springald gets double bonus points for getting all three vowels in "Sudoku" wrong. :P 21:38, 26 June 2006 (UTC)

Excel Templates

I created an excel template on commons.wikimedia.com. I also noticed there is also an excel Sudoku program there too. The program creates puzzles and the solutions. The template can be useful for helping you solve sudoku's. It has border area where you can write in numbers. I'm thinking it should be linked in the see also section. What do you think?

http://commons.wikimedia.org/wiki/Sudoku

The spreadsheets can be improved. I was also thinking of creating spreadsheet template that is more compatible with open office.

Daniel.Cardenas 00:46, 6 March 2006 (UTC)

Hi Daniel. Thanks for eliciting feedback about your excel template. I was the person who removed your link from the main Sudoku article earlier today so perhaps I should explain why I did so. Firstly, I have a significant concern with linking to any files which can contain viruses (even though Wikipedia warns about the dangers of downloading such files). Anyhow, since I have a fairly robust antivirus setup I took the smallish risk and downloaded and opened your file. To be frank, it seemed very primitive - a few bolded borders making an empty grid. There was no documentation, no solving tips and no macros to assist the solver. (Fortunately there were no macros viruses either.) Anyhow, I feel strongly that Wikipedia is not the place for this sort of file (but that's just my opinion). --angusj 02:48, 6 March 2006 (UTC)

Minor issue with the new 'dot' markup image

I'm concerned that the new dot markup image doesn't illustrate the most widely used dot layout - ie 123 across the top, 456 across the middle and 789 across the bottom of a nine dot grid. I would like to see this changed. Do others feel strongly about this too? --angusj 22:30, 9 March 2006 (UTC)

I can agree with changing it. The layout as you describe it matches the layout of a telephone's number pad, and is certain to be the most prevalent schema for marking up, whether with dots or numbers. The other graphic uses this layout - the disparity is an issue. Actually, I'd be all for deleting the image and simply adding a sentence to the caption of the other graphic: "Some mark dots instead of numbers, using their locations within each cell to distinguish them, usually as shown here." - ZM

Zotmeister 17:39, 10 March 2006 (UTC)

I like your suggestion (simply adding an extra sentence to the other graphic).--angusj 21:51, 10 March 2006 (UTC)

I dont agree, I think an image to illustrate the method is needed here. Its was the dot method that got me into Suduko and what may be obvious to you in a short sentence is not so to every reader. It needs to be plainly stated with an image to show how its done. Lumos3 13:10, 13 March 2006 (UTC)

Image hyperlinked to solution

This is the caption to the image at top of article. The image is not linked. I changed the description but someone reverted.. Please fix.. Gregorydavid 09:21, 13 March 2006 (UTC)

Every image displayed in a Wikipedia article is linked to a page that displays the image along with a description of the image. And in this instance, the description contains the solution to the puzzle. So what do you mean that it isn't linked to the solution? -- Smjg 11:52, 13 March 2006 (UTC)

Hi, I am not sure that the link reacts like a normal hyperlink, but thank you for the explanation. I shall go and see.. Regards Gregorydavid 09:41, 1 April 2006 (UTC)

Proposing External Links

Please do not create new sections to propose another "External Link". There is already a section for that above. At least that way they'll all be in one place. Also, please do not propose a site unless you genuinely feel it is truely exceptional. My impression of the current list is that none of them are exceptional.

Also, due to the ongoing abuse of the "External Link" section in the main article I propose that no new external links be considered and we simply have one link to the Sudoku entry in the "Open Directory Project". --angusj 21:42, 19 March 2006 (UTC)

Friends of Sudoku

A Nikoli ( http://www.nikoli.jp ) Puzzle Collection game for GBA featuring all their non-word puzzles, including:

• Divide by Box
• Fillomino
• Hashiwokakero
• Heyawake
• Hitori
• Kakuro
• Masyu
• Number Link
• Nurikabe
• Light Up
• Ripple Effect
• Slither Link
• Sudoku
• Where is Black Cells
• Edel (AKA Picross)
• Javanoid
• All the language independent ones on their Japanese site which strangely haven't been put on the English site.

Inaccurate Removal and Labeling as Link Spam

Hi, Editor Angusj has incorrectly titled my contribution on 22:49, 4 April 2006 as link spam. My contributed link pointed to http://www.chessandpoker.com/sudoku-strategy-guide.html which when visited displays a pertinent Sudoku strategy guide. Referrences of relevency can be noted by searching 'sudoku strategy' or 'sudoku strategy guide' via Google.com or by visiting the page. Editor Angusj may be displaying bias as the site http://angusj.com/sudoku/hints.php is in direct competition for similiar keywords. I request an unbiased pageview from Editor Zotmeister and if applicable revert.Amazing Backslash 23:25, 4 April 2006 (UTC)

Firstly, I'm not an editor any more than anyone else is in Wikipedia. As to why I removed your link - there is an edit comment at the top of the External Links section that you should have seen before you inserted your link. Anyhow it says: "NB: External links are being reviewed on the Discussion page ("Talk:Sudoku") at present. Please join in that discussion before adding new links here, particularly if you are promoting your own site." Consequently, links which have not gained overwhelming approval by regulars (as opposed to a rent-a-crowd which one person tried) will be removed immediately. It's not a question of relevancy. (The External Links section has been abused beyond reason and my preference is to remove it entirely.) Finally, I can't understand why you think I'm trying to protect my own site from competition, it's not even listed in the Wikipedia article. --angusj 10:15, 5 April 2006 (UTC)

Unsure as to why it's "not a question of relevency". No ill-will intended, but does anyone know why there are seperate rules imposed for this page instead of the usual free-editing found throughout Wiki? Links don't have to be included, but should not be labled in public as spam when they clearly are the opposite. I'm interested in seeing relevent links as they are produced (and the spam weeded out), not throwing out all the links for some bad apples. Based on the manager's requirement, here is a proposal: Chessandpoker.com/sudoku-strategy-guide.html.

I for one look forward to quality user contributions for many years to come. Wiki is for everyone, not a personal homepage or forum with individual governing sets of rules.Amazing Backslash 02:19, 8 April 2006 (UTC)

If you'd witnessed the total free-for-all that happened about 6-9 months ago when there was no editing of the external links section, you'd understand the current arrangement that's been agreed upon by consensus here. (Have a look at the archived discussion and you should get some idea of what happened - though I'm not sure if all the proposed links were archived too.) Anyhow, I now consider anyone who chooses to ignore the request at the top of the Links Section (asking contributors to refrain from adding links directly to the main article) as spamming. Incidently, in case you're wondering, I wasn't the person who added that request. If you have a better idea on how to manage the literally hundreds of proposed links and how to fairly arbitrate which few links might be worthy of inclusion in the Links Section, I'm all ears. --angusj 04:41, 8 April 2006 (UTC)

it's originally dervied from Euler

"Will sudoku, whose origins lie in an 18th-century Swiss mathematician's game called “Latin squares”, follow suit? " The Economist. That Swiss Mathematician, namely, is Leonhard Euler! The Japanese stole the idea from Latin squares. Fucking scheming japs. [Uncredited comment by 128.226.160.234 2006-04-22 11:06:47]

While the solution to a Sudoku is a latin square, most latin squares are not valid Sudoku solutions, much less a Sudoku problem. [Specificly most 9x9 latin squares violate the block constraints.] And I'm missing what your comments have to do with the article. Nahaj 01:43, 23 April 2006 (UTC)

Nor is Sudoku a Japanese invention. As the article states, it was created by Howard Garns, a United States citizen. It just so happened that Nikoli and rivals made the puzzle into an art form, and one former Hong Kong judge computerized it and brought it to England, where it ballooned.

Euler certainly can be assumed to have inspirational credit, but not invention credit. Sudoku lends much of its popularity to a variety of sources across the planet; Euler can certainly be counted among them, and perhaps even the ancient Chinese study of magic squares could be considered a seed. Sudoku is an international phenom, and frankly, the constant attempts by some to misattribute the entirety of its history to a single country - whether it's their country or not - sickens me. - ZM

Zotmeister 16:28, 24 April 2006 (UTC)

New York Times

This article was briefly mentioned in the Arts section of the New York Times today, everybody. If you have access to the newspaper, I suggest you go check it out! I wouldn't be surprised if the history of sudoku part of the article was researched here -- the Wikipedia article is just said to have more info. --Fbv65edel ^{(discuss | contribs)} 12:04, 1 May 2006 (UTC)

modified opening paragraph

I made a minor change (adding full and complete name of the US magazine which first published sudoku, and a citing weblink. Lost my nerve and tried to reverse my change but can't see how. Sorry. Tychocat 03:34, 17 May 2006 (UTC)

I did it for you :). --angusj 06:23, 17 May 2006 (UTC)

Symmetry constraint undefined.

I'm trying to figure out what exactly the symmetry constraint is . It's referenced but undefined in many of the articles as far as I can tell. Image would be ideal.Thadk 06:08, 18 May 2006 (UTC)

Cited in June 2006 Scientific American

Scientific American ran an article on Sudoku in their latest release (which had a lot of the same info you can find here in it...) and put this page under the "More to Explore" section at the end of the article. Just a heads up --Tossrock 08:57, 23 May 2006 (UTC)