Advanced methods and approaches for solving Sudoku puzzles


Postby Guest » Wed May 11, 2005 8:14 pm


today was the first time i've tried a su doku. i noted the puzzle when The Times began running it a few weeks back, and then i found that a colleague was really into it. but it wasn't enough to provoke me into giving it a go. however, the catalyst was yesterdays Newsnight report into the phenomenon. hence today i finally succumbed to my curiosity, with a gentle start (Puzzle 9 on this site). took me about half an hour i think, as one who knows no techniques, and didn't fill in the grid with possibilities, but worked out using elimination in my head.

the reason i ventured into the so doku universe is probably my longstanding fascination with informal logic. i love that the philosophy behind this puzzle be logic.

for the past, well, over an hour, i have been devouring the posts on this forum, and would like to extend my gratitude to pappocom (Wayne), and the rest of you, but especially to IJ, whose posts i have found tremendously interesting, well-written and helpful. that spirit of sincerity and altruism is maybe one reason why i'm less nervous about posting than i otherwise might have been.

the reason i decided to post was to ask a few things. and lest anyone direct me to older threads, i have not been lazy, rather, i have done searches on the key words, but still remain unsure, hence the following:

1. having read all the threads on x-wings, i still cannot comprehend this concept as a technique. admittedly, i'm not the brightest, but having read and reread the explanations, i think my struggle lies with the way the diagramatic representations of the explanations are offered on screen, as well as the referents. i cannot visualise the x-wing, nor see how it, as a technique, aids the solution. without imposing unduly upon any of you - and certainly with no offence to your attempts to explain it so far - but is there anywhere which explains this technique in a clearer diagrammatic manner, similar to the onscreen layout method used How to Solve section, which i found very easy to follow? whereby the x-wing is actually shown on the screen, rather than just referred to using co-ordinates? and with a breakdown to the level of a Dummies Guide, for this dolt?

2. how are su dokus created? randomly, using a program, or with much forethought, using human intellect? is there some process which we could be privy too (again, apologies if that is a laughable question, i don't know if su doku is primarily a commercial venture)

3. forgive me, i am not familiar with su doku's history, so what are it's origins? how was the idea behind it first borne?

4. what are the factors that determine an easy su doku as opposed to a fiendish one? just less numbers on the grid to begin with, or the way they are arranged too? i assume the latter plays a role, but to this neophyte i struggle to explain to myself how? that is, what the relationship is between ease/difficulty and the layout of a puzzle?

4. within the 3x3 standard format, what is the finitude of eventual possibilities of the puzzle? like, how many of them can be created before they are all exhausted? (i realise there may be an obvious and easy answer to calculate this, but again, i'm not that bright, and would prefer to ask and appear dumb, than not ask and continue to wonder.

5. having read the extremely intriguing few threads on logic versus trial-&-error, would it be fair to say that the difference between the two is that with the latter one starts from an unfounded and arbitrary postulate, for which there is no preponderating evidence/justification? whereas with a logical attempt to proceed one begins with a valid reason for taking the first step. by way of example:

a. trial and error: "how about if i put a 5 here and see what the implications are"? (having not considered beforehand the context nor circumstance behind placing the 5 there on the grid.) such that you might as well have not even looked at the gird, and with your eyes closed, merely have pointed to a cell and used that as your startpoint (assuming it wasn't already occupied)

b. logic: "okay, so i see that in this first box of 3x3 there is a 2, and in the last box of 3x3 on this same row there is also a 2, so i can use that as a basis for assisting in figuring out where the 2 in the middle box of 3x3 might go"

whilst i can see how trial-&-error could be a valid starting point, i don't think it necessary, and definitely reckon there is more satisfaction from beginning with a justified first step. though i also accept i don't yet have enough experience of su doku to know whether there aren't ever points in the solving process where trial-&-error may be necessary (e.g. i have only done one so far, ever, so have no way of gauging what makes one harder than another, or indeed any experiential notion of what such hardship feels like!). nonetheless, i still harbour a doubt about the need for employing trial-&-error as a tool, as it would erode the edifice of the puzzle being one which can be entirely reasoned, logically, using elimination, or other non-random and arbitrary techniques, from start to completion.

to anyone kind enough to offer some answers/insights, please know that i'm not mathematical by nature, and i find it hard to comprehend abstract formal logical explanations (e.g. boolean formats).

i appreciate i've asked a lot, and recognise that may result in disinclination to answer, so i'd like to express my thanks in advance.

a Wayfarer

Postby lunababy_moonchild » Wed May 11, 2005 9:27 pm

Hello and welcome.

1 I'll leave x-wings to an expert.

2 Depends on the individual puzzle. Pappocom's are generated by computer, the Independent's are generated by computer, can't speak to anybody else's but there is a magazine that is out every two months available through WH Smiths which contains puzzles they say are hand-crafted.

3. Again, depends on the source of your information. Internet search engines generally come up with information which confilicts very nicely. In general the information I've seen in publications is that it's Japanese in origin.

4 Wayne answered that here : Sudoku Players Forum Index -> The Times -> Ratings

5 Yes! Far as I know.

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Postby simes » Thu May 12, 2005 6:08 am

This is my stab at explaining XWings...


Although reading it again, I guess there's room for expansion.
Last edited by simes on Sun Dec 11, 2011 10:06 am, edited 1 time in total.
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Postby jafosei » Sun May 15, 2005 5:50 am

Can't answer most of your questions, but here's what I found on the web.

2. how are su dokus created? randomly, using a program, or with much forethought, using human intellect?

Both ways.

The Let's Make Sudoku website has an explanation of how to do it by hand. Sounds challenging to me.

And of course, this site sells a program that makes them, which is pretty cool.

3. forgive me, i am not familiar with su doku's history, so what are it's origins? how was the idea behind it first borne?

Wikipedia credits Dell magazines as publishing the first ones, under the name Number Place, after which it was popularized in Japan by puzzle maker Nikoli (who also came up with the name Su Doku). This seems to be verified by Nikoli's page on Sudoku. I haven't seen anything that explains Number Place's history before being picked up by Nikoli, though. From what I've read, the Dell versions were pretty easy.
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Postby RaleyD » Sun May 15, 2005 1:32 pm

jafosei wrote:From what I've read, the Dell versions were pretty easy.

I don't know what the original Dell Number Place problems looked like, but based on the descriptions, the current ones are just the same as the originals. The ones in their most recent magazines contains over 30 clues and are asymmetrical. They are also much too easy.

I think it's quite fortuante that almost everyone else seems to be following the Nikoli rules, rather than the Dell rules.

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Postby RFB » Sun May 15, 2005 4:28 pm

Apparently Sudoku puzzles are derived from the Latin Squares introduced by
mathematician Leonhard Euler in 1783.

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Postby lunababy_moonchild » Sun May 15, 2005 4:40 pm

There's a nice article on the subject here : http://news.independent.co.uk/europe/story.jsp?story=638223

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Postby Roger Scriven » Mon May 16, 2005 4:42 pm

Su Doku
column 3 column 8
Row 1 * *

Row 7 * *

In row 1 and 7 the * marks the only possible position for say 8. You have to imagine that there are numbers
all over the grid from your efforts up to this time. What x wings says is that we do not know which * is the 8 but one in each row must be. So that between the * in the two columns you cannot have an 8. ie Row 2 column 3 cannot be 8, and Row 2 column 8 cannot be an 8. And so on for all the rows 2 to 6.
The * must be the only two choices for 8 in that row for x wings to apply.

It also works across the page as well as up and down
Roger Scriven
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Postby Roger Scriven » Mon May 16, 2005 4:45 pm

sorry my digram did not come out right I will give it another try. There is a good explanation in one of the posts I will find the ref for you:(
Roger Scriven
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Postby Roger Scriven » Mon May 16, 2005 4:50 pm

Tha ref is "the times" and "x-wings" The explanation includes diagrams that are mor successful than mine
Roger Scriven
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Postby Guest » Mon May 16, 2005 7:56 pm

your description of X-wings makes sense to me, thankyou very much.
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Postby Roger Scriven » Tue May 17, 2005 5:20 pm

I should have added that the rule that there can be no 8's in row 1-6 columns 3 and 8 also applies to rows 8 and 9.:)
Roger Scriven
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