Sudoku Tips and Strategies

Hi! My name is Steve, and I am a Sudoku enthusiast. My wife would likely use a different adjective.

I have studied how to solve a typical 9x9 Sudoku puzzle at some length, and have developed a modest but powerful repertoire of potential tips for human solving of a Sudoku puzzle using logic.

The goal of these pages is not only to provide those tips to others, but also to learn new ways of looking at the puzzles.

Hopefully, these pages will invite a free discussion and exchange of ideas regarding manners and methods to humanly solve sudoku puzzles.

Please check out the conventions that I use to label the puzzle grid, and other aspects of language used - including the rules of Sudoku as I see them. This will aid greatly in uniformity of discussion here.


Some Sudoku Definitions

Candidates
The integers 1 through 9
Cells
Small containers that in a solved Sudoku will contain exactly one candidate each. This is one of the normally unwritten rules
Boxes, Rows, Columns
Large containers of cells.
The rule
In a solved sudoku, each large container will contain exactly one of each candidate.
The additional rule
Each Sudoku puzzle has a unique solution.

If the number of cells in each large container equals the number of potential candidates, (as is the case with typical 9x9 Sudoku), the following statements are equivalent:

  • There must be at least one of each candidate in each large container
  • There can be no more than one of each candidate in each large container
Most techniques employ both of these ideas.


Sudoku Puzzle Coordinates

This is completely arbitrary, but I prefer the algebraic notation like that used with chess. Thus the bottom left corner cell is a1, and the top right corner cell is i9. Unfortunately, there is very little uniformity regarding Sudoku puzzle coordinate choices across the web. One can argue that one is better than the other, but they are all completely arbitrary. Additionally, the boxes are defined by the label of their center cell. Thus, the bottom left corner box is Boxb2, or Bb2.

puzzle grid

I have created lots of posts on different solving techniques. Here are some to get you started:

27
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Steve  From Ohio    Supporting Member
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Welcome to my sudoku blog!
Some of you may already be familiar with my propensity to post a bit too much....
A few things about me:
I live in Cincinnati, Ohio where I operate and own a small masonry construction business. I am blissfully married to perhaps the only woman on earth who could put up with me. We have four children - two almost in high school, one in college(our only girl), and one who works with me.

I have almost nothing in my resume' that would qualify me as an expert in puzzle solving, logic, or anything in that vein - except for some proficiency at things logical during my education, intellectual curiosity, and my aforementioned propensity to post too often about sudoku.

I looked at my first sudoku puzzle almost exactly a year ago - some time in mid December of 2005. Having a somewhat addictive personality, I thought that I would spend some time studying sudoku and then, having learned all the tricks, move on to something else. I am still amazed at how interesting a sudoku puzzle can be.

Since I fancy myself as an independent type of thinker, I did not accept easily the teachings of gb - Bruno Greco - who previously frequented sudoku.com.au tough puzzles with sage solving advice. Eventually, I adopted most of his viewpoints on solving sudoku puzzles. I still think of gb as the teacher, and I the student. gb was a frequent poster at this site from its inception through about February of 2006.

Within this blog I intend to:
Provide tips to solving sudoku puzzles.
Provide the necessary background information for understanding the coded language that has developed here.
Provide background logic to the solving techniques.
Learn new ideas from others.
Use illustrations from actual puzzles on how to solve them, start to finish.

The blog will start with easy tips and techniques, and evolve towards more difficult concepts.
For those of you new or relatively new to Sudoku, I hope to provide a roadmap for gradual attack of these puzzles. For those of you whom are already accomplished solvers looking for more techniques, etc. - be patient, as that path will eventually be trampled upon.
Mary  From Bibra Lake WA
terrific idea-long overdue.Look forward to learning more.
Tricia  From Queensland    Supporting Member
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Thanks to Gath for this site and to you Steve for taking it on. I have read your solutions a few times but at times find them somewhat confusing so I look forward to all being revealed. I struggle to solve the tough on most days if I do manage to solve it most of the comments from regulars are that it was too easy.
Linda  From Ohio
I have been playing with sudoku puzzles for a little while and love them. But have found that the tougher puzzles take me a long time. I can't wait for your tips and advice. When will you begin your blog? I do not know how to access a blog, so if you can include that information, I would be grateful. Thank you for your generosity.
gil  From gippsland
Hullo Steve. A marvellous idea! I've been reading your proofs for a fair while and have learnt quite a bit from them. Altho I've been studying Sudoku techniques on the web, there are still a lot of questions - like how rectangular does an XY wing have to be? (Sometimes mine seem to tend towards the rhomboidal and it is probably more good luck when they work) And can you change the pivot from one corner to another? And what are your reservations about guardians? And my fcs are still very shaky. I'm sure we shall all learn a lot from this. Cheers, Gil
Nurn  From Galway
Hi Steve. I haven't had time to do toughs in quite a few months, but I remember your proofs as being very helpful. I hope I'll get a chance soon to check all this out.
Steve  From Ohio    Supporting Member
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Hi Linda from Ohio!
(A great state, BTW). This is the blog, right here. Additional pages will be added periodically. The blog pages will introduce progressively more complicated tips and techniques - and also some hints on how use that information.
bert  From bwi    Supporting Member
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Thanks, Steve. Buckeyes rule. I look forward to learning much here.
   bluey  From Port Kembla    Supporting Member
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Wow!! This is great!! Oftentimes I thank you Steve, when the 'hints' say it is tooooo tough, and I look down at the comments and find that something-or-the-other forbids a cell being a certain number 'up to 81', and IF I have done the setup correctly, it all comes out right!!! Now perhaps I can learn why!!
tricia  From nemo, tx
hopefully i will learn the language of proofs here. thank you.
Pam  From SW Ontario
Thanks Gath and Steve. I look forward to the help. I have been stuggling with a book of 'extremely tough' puzzles. Some have taken a day to complete.
faith  From Maumee, ohio
Thanks Gath & Steve. This is a great idea - I generally am rather sporadic at getting to the tough puzzles on this site and often don't understand Steve's proofs so I am really looking forward to learnng some new and better technigues for the harder puzzles. Most of the time I am working sudokus in the whole stack of sudoku books that I have. I usually skip the 'easy' puzzles. I often tear them out and share them with friends and aquaintances who have never tried sudoku or couldn't figure out haw to start it - making me sort of a sudoku pusher' - at least its much more healthy than drugs!
I like to work the harder ones and the variety of specialty sudokus - but sometimes get stuck and just have to take a guess.
I'm really looking forward to learning some advanced techniques.
   Debby  From Mi,USA    Supporting Member
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Hello Steve - Thanks for taking the time to do this.

Gath - As always, you are great. Thank you
Jim  From Brandon, Mississippi
Great idea, I'm in! You can count on me to be a regular visitor.
Jill  From Tacoma, WA
Steve and Gath, this is wonderful! All of us regular toughies really appreciate it. And Steve, it was fun to read about what you do when you aren't doing sudoku. It's such an amazing thing to have this international community where we all get to know each other. Thanks again!
Dave  From Minnesota
Thanks Steve for providing another brick in the Sudoko wall! Your proofs have been a tremendous tool in learning the logic behind the solutions.
Maggie May  From Sydney    Supporting Member
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Thanks Steve, I need this help. I am slow and often get blocked on hard. Intuition and revelation are poor substitutes for logic.
ang  From india
have been looking forward to this for a long time!
thanks Steve & Gath
   Canuk Greg  From Ottawa, Canada    Supporting Member
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Hi Steve. I'm a bit of a 'look and try forever' person on the toughs. Have tried to figure out your solutions in the past but got a little lost at times. Thanks for this page. Very helpful!
possum  From new zealand
This promises to be very good - but is the information going to be daily, weekly, random...?
Steve  From Ohio    Supporting Member
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The 'plan', subject to change without notice, is to publish two new blog pages per week.
Steve  From Ohio    Supporting Member
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Hi Gil (from gippsland)!
Eventually, more complex techniques like xy wings will be discussed at some length.
Quite a while back, on the tough puzzles page, I may have railed a bit against the guardian technique. In the face of an idea that is new to me, I am always a skeptic. Perhaps I did protest a bit too much.
My primary complaint with the technique is that:
Given the information required to accomplish the eliminations proposed by the technique, there will always be less complex eliminations possible.
Specifically, as the guardian technique is usually presented, it requires that one find (4) perfect links - perfect meaning exactly one of two endpoints is true - and then one can eliminate anything that would cause a chain of (5) such links.
i.e.: (typical guardian set up)
A == B == C == D == E and
A -- B -- C -- D -- E -- A
forbids E == A.(or forbids anything that would cause {E == A} to be true)
but, we already therefor have:
A == B -- C == D forbids E

For those of you as yet unfamiliar with forbidding chains.....
After this blog explains forbidding chains, this post should cease being inscrutable.
Jimbo  From Melbourne
Great stuff - your explanations are spot on.
Breadman  From England
I like your use of algebraic notation, and use of defined vocab like 'container' and 'candidates'. You and your readers may find the freeware Sudoku generator/solver at http://www.geocities.com/mpp_v1/fun of interest.
pdp189  From New Bombay
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Hi Steye. Your information on the net was extremely useful. I shall be highly obliged if you enlighten me more on BUG from fundamentals. Thanks

pdp189
06/Aug/07 12:31 AM
armando  From portugal
If you want to try out something new in sudoku, try shendoku, using the sudoku rules but playing two people, one against the other, like battleshipps. They have a free version to download at http://www.shendoku.com/sample.pdf . Anything else they are bringing out or they are working on you can find at www.shendoku.com or at they´r blog www.shendoku.blogspot.com . Have fun, I am. I specially like one slogan I heard about Shendoku: SUDOKU is like masturbation (on your own)…. SHENDOKU is like sex (it takes two).
08/Oct/07 8:23 AM
Pat  From USA
Check out Sudoku Learning Center(SudokuLearningCenterdotCom)

It has a great set of online tutorials on the various techniques to solve Sudoku puzzles along with specially designed puzzles to aid in mastering the various techniques.
Regards
Pat
03/Nov/07 10:33 AM
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