The Logic of AICs in Sudoku / Tutorial #4

Alternate Inference Chain Basics in Sudoku. Also known as AICs. The foundation of all Sudoku Chains and Loops. AICs lead to a verity or a contradiction, which allow you to either eliminate Candidates or Solve Cells.

[@thedoron2]

Hello, I have seen your comment (do not know if it is still actual) about thinking of closing the channel because of lake of followers. Please let me tell you what my teacher (pediatric Ohpthalmology surgery, tough and often frustrating) told me when I had the same thoughts-"you can not beat excellence"! Trust me, after being frustrated by experts level seduko pazzels, and looking at many KZbin series, I found one of your advanced lessons (while googling for "xy chains"),and after two minutes realized that finally I have found a true teacher, and went to tutorial one, opened a copybook, and started learning a clear logic approach for seduko solving. I can't wait each day for the "evening treat" of the next lesson. While on the way, I am already solving expert level with relative ease, and it getting better and better. There is no way that this channel will not become the one that every seduko enthusiast will regard as a must. Just give it time, it is so much better than anything else on the web Doron Neumann

[@thedoron2]

I will ofcourse do my best to spred the word....

[@SudokuSwami]

Hello Doron. Thank you for your comments and support. What you may not realize, is that no matter how good my Tutorials may be, very few Sudoku enthusiasts are interested to solve the puzzles the way I teach, who also have the time and dedication necessary to study and learn all the principles and techniques. You are apparently a serious student. But people like you are few and far between. At best, there is only a very small market for what I am doing. This is the sad reality.

[@thedoron2]

Maybe so, (I do not have the data to contradict), but I know from experience, that things that are spread by " mouth to ear", (much like doctors reputation) have this dynamics of starting very slowly, for relatively long time, and only after reaching a "critical mass" it suddenly goes BOOM. As you say in your videos: bear with us, it will come The two guys whom I have introduced to your work today, did find the first video good enough for subscribing. (two out of two, in a highly selected subjects, not much of a study...)

[@maryberry6947]

Wow...all I can say is THANK YOU! For a few years I’ve been dabbling around with sudoku but then I hit tougher games where more advanced techniques are required. I read and read all the different explanations and they just haven’t sunk in and stop playing. Finally I have found your great series where it makes sense to me. Great videos and I so thank you!

[@SudokuSwami]

Cool. Glad to hear it. Welcome aboard! :-))

[@FlamingHot1]

I've watched this video about 4 times and I'm finally starting to understand! Thank you so much for all the effort and patience you have put into your sudoku course!

[@Michimax1000]

This is like a good TV series. I love your videos - very helpful!

[@ximchix]

Wow, my mind is blown! This is internet gold! Thank you a lot for this course! I have started with a handful of your lessons and after trying several other sources (written and in video format) yours is by far the best. What I really value and respect is that you take the time to go in all the details, repeat the information and give a lot of examples. I choose to watch a lot of it sped up but I am very glad to be able to slow it down when it gets complicated. Speaking for myself, very often when I learn abstract concepts in e.g. mathematics it is not that I am unable to understand the steps but that my mind always finds very specific details which I do not grasp, stopping me from gaining a deeper understanding. So I appreciate that you are trying to encompass all the little ways one might misunderstand a concept. This is something most are not willing to do as it requires on the one hand a lot more work and on the other hand the ability to empathise with 'absolute beginners', imaging what it would be like to not understand any of it. Going quick is always an option, but going slower is not, most of the time. [On a side note, as the attention span shortens for many of us I can imagine that a lot of people are not willing/able to dedicate a few more minutes to find the value in videos like yours, even though many of the videos today try to convey so much information in such a brief time that it becomes absurd. But I think your course would also be a good fit to be linked on sites like Udemy.] Anyways, I'm looking forward to going through every video and practising the techniques and concepts. Cheers, again!!

[@SudokuSwami]

Thanks for this thoughtful comment. Good luck.

[@sl1ckspurs]

Absolute legend. Thank you very much for the fantastic videos! They really are helpful and you do a great job in explaining complex details in an easy to understand manner. Keep up the good work sir.

[@gerryandlizkeogh1817]

Hi Sudoku Swami, thank you so much for this lesson, I didn't really understand it the first time I saw it and moved on a little, but now I have just come back to it by way of revision and realised what powerful stuff it is! I am in the early phase of learning and have been greatly encouraged, so again THANK YOU!

[@SudokuSwami]

Great. Thanks for your kind comment, and I'm glad to hear you are making progress. Just take it one step at a time, and it will all become clear. Good luck! :-))

[@Hz-kw3iy]

I just want to thank you for creating this series. This is a gem!

[@danielmardim5866]

Your tutorials are what can take anyone a quantic jump towards expertise in sudoku

[@jrbr549]

It used to annoy me how much detail you went into. Now I’m finally grateful. Thank you, Swami!

[@pavlosfragkiadoulakis]

This is the most scientific way to present sudoku techniques. As a scientist, I really admire your videos and the way you precisely present your material using pure mathematical logic.

[@SudokuSwami]

Thanks for this very kind comment. You are correct that I try to explain all the Sudoku Solving Techniques in a scientific way. Good luck!

[@rsay19465]

I have been looking for a website with clear instructions and examples of how to solve Sudoku puzzles in a logical way. After trying many other websites I randomly found yours, and your tutorials are by far the best! Please keep up the great work!

[@SudokuSwami]

Thanks for the nice compliment. It is greatly appreciated. I hope you will Subscribe and help spread the word! :-)) Good luck!

[@danielhaacke8641]

thank you so much for this! I have been struggling to understand alternating inference chains from online sources that use text and pictures, and your descriptions are clear and concise and have finally helped me to grasp AIC.

[@SudokuSwami]

Glad to hear it. Welcome aboard. Good luck! :-))

[@ThatGuy-dj3qr]

Tons of info. THANKS! I appreciate the time you took to produce these videos.

[@SudokuSwami]

Glad to hear it. Cheers!

[@MeenaJuneja]

Nice tricks..but yet not gone into my head...!! Will have to repeat watching..!! 👍😇😎

[@gregmiller1644]

Hello Mr. Swami, I just want to thank you for posting this, the best, Sudoku tutorial on the web. I've watched or read, all or part, of many different Sudoku tutorials and have found yours to be the only one that really explains the foundational logic of this complex puzzle. Other tutorials provide a long list of rules or techniques to memorize, but yours is helping me understand the logic and reasoning behind those techniques. I'm certain that once I finish this tutorial I'll be able to apply the reasoning you've taught me to solve puzzles without having to follow a check list of all the various techniques. I'm really looking forward to watching the rest of this tutorial. Again, thank you! BTW: You're a great teacher. Have you ever considered making a tutorial on how to make lots of money without having to work? : ) I'll be the first in line to watch.

[@SudokuSwami]

Hello Greg, thank you so much for this wonderful Comment. I really appreciate it, and it is very rewarding to hear that you are benefiting from my Tutorials. That's what it's all about for me. :-)) When you find a Video that will teach us how to make lots of money without having to work, please let me know, because I would like to watch it with you! Ha ha. Good luck, amigo.

[@karabishopart4153]

Watched this twice and I think I’ve finally got it! Phew thanks for great teaching, I’m going to watch the adjunct teaching now to make sure it’s embedded.

[@sophiasiebert3451]

The best and most educational video on sudoku

[@SudokuSwami]

Thank you so much for this wonderful comment and compliment....! :-))

[@doralrobichaud8838]

Thanks for the great tutorial. It is the best explanation I have seen on chains. I have been solving sudoku puzzles for a while now and it had lost it's appeal because it seemed I needed to guess to solve the expert levels. Now that I am starting to learn chains, I am once more interested in playing. At @20:15, instead of going to R8C3, you can also find an AIC type I by going to R7C7 (candidate 1), R8C7 (candidate 9) and R8C1 (candidate 9) to rule out the 3 in R8C8. Doral

[@SudokuSwami]

Hello, Doral. Thank you for your interest in my Tutorials and for your very kind comment. Please understand that when I give the various demonstrations in these Videos (of my Complete Course), they are simply isolated examples of a particular point I am trying to make. There are ALWAYS lots of other things going on, at the same time. But my intention with each example, is not to SOLVE the puzzle, but only to help you understand the particular concept I am focusing on. In my Random Tips Series, and in my Pencil & Paper Method, we sometimes solve Puzzles from start to finish. But that is not the case here. Good luck! :-))

[@chrismuir8954]

I am glad I found your videos. Your explanations are clear and have really helped.

[@kerrybrown1192]

You're correct : A pen and paper for notes for this tutorial was very handy ! Thanks.

[@SelfishGodLike]

Really thorough video on this rather abstract concept. I saw another video on the AIC logic and the linking bit got me confused with the so called 'surrogate' link and this presentation cleared up the confusion. Pretty hard to spot these relations though - it probably takes quite some experience to spot some of these patterns I reckon.

[@cometier]

Thanks for creating this series. You're an excellent teacher, and I finally feel I am able to progress from the basic techniques. I found the style of lecture to be very useful, especially enjoyed the definitions and examples. very easy to understand the topic. Would you be open to including a list of definitions or terms on your website for quick review? Be Well.

[@SudokuSwami]

Thank you for your comment. There are many places on the Internet where you can find a glossary of Sudoku terms. I am in the process of upgrading and re-building my website. I will consider your request. Good luck. :-))

[@jman12849]

thank you for the videos. i've been struggling to understand these advanced solving methods purely via text.

[@SudokuSwami]

For Beautiful Custom T-Shirts & Coffee Mugs featuring the Swami Logo, and also for Selected Classical Piano Pieces played by me, now available via Digital Download, please visit the Sudoku Swami Gift Shop! sudoku-swami.shopify.com

[@SudokuSwami]

Be sure to visit sudokuswami.com for an Outline of the Entire Course, and news about upcoming Videos!

[@dinhnguyen-sc2mt]

Hello swami! Today I met 1AIC in a sudoku puzzle. In the middle of the puzzle, when everything are deadlocked, it unlocks an important knot. I feel it is really strong. thank you very much!

[@SudokuSwami]

That's great news! Glad to hear it.

[@bachourmerced2590]

Thanks for your teaching videos are great. I didn’t found (ALS )videos! I found one on KZbin but I like your approach of teaching. I’m wondering if you have videos about it to let us know the link. Thank you

[@duaneraeburn8037]

Hi ya swami. I was with you for awhile but got confused and went off in another direction. Then I saw you series on doing paper and pencil solving. I almost exclusively use your 1-9 break in method now. then I stared following your Buddy Harold Nolte, who cannot recommend you highly enough. So then I decided to go back in your series where I stated to get confused which was lesson 3 on strong and weak links. Lo and behold what do I find an xy wing disguised as an AIC. So I am starting over and rewatching this material.

[@Hz-kw3iy]

It feels like this is a sudoku masterclass

[@duaneraeburn8037]

hi ya swami. This is going to take some time to figure out. fortunetly? there are no shortage of sudoku puzzles to practice on. 1400 subscribers and 7900 views doesn't seem all that bad to me. Anyway I am going to keep hanging in there because this is good information. I see this chain technique on cracking the cryptic all the time so I know it works just have to learn how to apply it my self. Thanks again and keep up the good work.

[@meo1960]

Man, who would have thought that such a fun/simple game could be so complicated?

[@SudokuSwami]

Ha ha. Yes, there's a lot to it. It's the difference between being an amateur and an expert. The choice is yours! :-))

[@SudokuSwami]

If you enjoyed this Video, please don't forget to click the SUBSCRIBE button, and the Thumbs Up Icon. It will really help me out. Thank you!

[@macfid]

Thanks for this.

[@noteven5ft2]

THANK YOU SUDOKU SWAMI

[@nammudenaadu9559]

I find it difficult to grasp from 21 minutes onwards in that while 3 is true you adopt same column principle to eliminate endpoint 3.While when start 3 is false, then chain principle is adopted to eliminate end 3 ,Ie in the second case start 4 is not eliminated using one digit in a cell.Am trying to grasp it ! WELL DONE MASTER

[@remyrat8961]

I was thinking about lesson # 4 for a while. And I discovered something important. It's called an alternating chain because it actually alternates between true and false and not between stong and weak links. It's just safer to switch between weak links and strong links to avoid making mistakes. The fact that you can use both strong and weak links in this method increases your chances of coming to a conclusion. What importand is, is that you can only use a weak link in the chain if the link starts with the assumption that the start of the link is true. Therefore it is safer to switch between weak and strong. And to make it easier, you call a strong link a surrogate weak link. Becouse a strong link acts the same as a weak link if you assume that the start of that link is true.

[@SudokuSwami]

Some Chains can begin with a Weak Link. But an AIC Type I or Type II MUST ALWAYS begin and end with a Strong Link. And yes, the assumed values alternate True and False, but the term "Alternating," actually refers to the Links.

[@remyrat8961]

Ah, ok. Is will throw my reasoning from last post overboard. I will strictly adhere to the rules for AICs type I and II. it gives me great satisfaction that I at least understand the rules. I will take small steps at the the time.

[@birgithoffmann-rothe1255]

Finally got into it after watching twice. But how can I remember all the links without the possibility of colouring them blue and yellow?

[@SudokuSwami]

If you are doing the puzzles by hand, you could use colored pencils, or you could use little triangles and circles.

[@Womenmatter2009]

I guess I need to watch it again.

[@blahdiblah2169]

If I understood correctly, then the AIC must start with a strong link and end with a strong link, other than that you are flexible to jump across digits as long as you abide by the rules. You can dance over any digits. I've been playing sudoku for years and didn't know this. This is excellent information. But now I'm wondering how you would spot them. I guess from practice you start knowing what to look for.

[@SudokuSwami]

In an open-ended AIC (i.e., not a Loop), yes, it must begin and end with a Strong Link, and the Inferences must alternate, Strong-Weak-Strong-Weak, etc. I am not sure what you mean by "dance."

[@blahdiblah2169]

@@SudokuSwami Hi Swami, by dance I mean you have flexibility on changing the number of the candidate. So you can go from a 3 to a 1 to a 4 etc, all the way through the open-ended AIC (as long as you're within the aforementioned rules you layed out). So I hope I understood that correctly. I am now on tutorial 4, and I realised I will pitstop here and let this new info really sink in. I'll watch and rewatch and rewatch so that it hits home. Thanks again for the great content and for answering our questions.

[@SudokuSwami]

You can only connect same-digit Candidates between Cells, and you can only connect different-digit Candidates within Cells. For instance, you CANNOT connect a 3 in one Cell to a 4 in another Cell, with a single Link, regardless of whether you are trying to make a Strong or a Weak Link.

[@blahdiblah2169]

@@SudokuSwami Nice, so I understood correctly then. I'll wait till I get further in, because I know you're going to cover practical applications later.

[@remyrat8961]

This is really interesting stuff! I can't believe that I can see what happens in a puzzle by taking a certain position. There must be millions of possibilities, and yet I can see clear connections. If I assume that A is wrong, then I know that D is true. And by assuming that D is false, it gives me the result that A must be true. And I'm sure this is the case because I'm using a method that I understand and proven to be true. When I started your video it was a bit confusing indeed. Stil I could understand it. I was chewing it well before swallowing it. But when you said that both A and D could be true, all my sircuits were suddenly overloaded. It felt like you dropped a bomb. One would assume that A and D act as a conventional strong link, but apparently that is not the case. I had to pauze the video and I tried to scroll back in my memory. Then all the pieces came together again. I get it now! I don’t have to see the overall picture of the complete puzzle, that’s too much for a human brain. With this method, I don't have to figure out whether or not A and D can both be true. What I do know, is that they can’t be both be wrong. What's important is that I'm sure the candidate that can see both A and D must be wrong. And I now understand why that is. This is so much fun, it’s mindblowing knowledge! Thanks!!

[@SudokuSwami]

Yes. It is possible for both endpoints to be True. All you know for sure, is that if either one is False, the other must be True. This insures that at least ONE of them MUST be True, which allows for Candidate eliminations. As you correctly noted, the two endpoints CANNOT both be False.

[@AtlanticZealot]

This is great stuff. Chain logic has always been a weak point of mine in these puzzles.

[@rbloomcfp]

Thank you for the fantastic videos. Do you suggest using paper and pencil when using chains and links etc.? Because most Sudoku apps - there is no way to mark links and chains and a long one would be hard to track.....

[@SudokuSwami]

This is a good question.....and a hard one to answer. On one hand, yes it is easier to draw links by hand, but this also requires you to fill in ALL possible Candidates by hand, which is a tedious, messy and unpleasant task. Whereas on computer Apps, the Candidates are automatically filled in for you (very convenient!), but there is no App available at this time (of which I am aware) that offers the ability to draw Links! I made my first 10 or 15 Videos without the ability to draw Links, and then I finally found software that I can overlay on the Grid, and now I can draw arrows and circles, etc., on the screen. But it is still a bit inconvenient, and the additional software is not free. So, somebody could probably make a lot of money by creating an App that offers automated and complete Candidate Lists...AND...the ability to draw arrows, etc. So, I really don't have an answer to your question, except to do it the best way you can. Good luck. :-))

[@uftdsouzaj]

Awesome videos. Thanks for making these! Can the end points also end in the same block for type 2?

[@SudokuSwami]

Yes, in the same Block. But not in the same CELL, if that's what you mean (?). In an AIC Type II, the endpoints must be different digits, that lie in two cells that can SEE each other. This means the two Cells must be in the same House, i.e., Row, Column, or Block. If the endpoints were both in the same Cell, you would have a Continuous Loop, which we will cover later on in the Course. Thanks for your interest. Good luck.

[@Woofus1]

Am confused at 21:54. If the 3 is false (row 7, col 8), the 4 (row 8, col 8) must be true (which forces the 3 also in row 8, col 8 to be false), which leaves you with no 3 in col 8 at all. What did I miss here?

[@SudokuSwami]

What you are missing is this. The statement, "If the 3 is False, then the 4 is True," is a supposition. As it turns out, the 3 is NOT False. It is True. But if it WAS False, then the 4 in R8C8 would be True, because the chain tells us so.. The idea behind this, is that because of the logical inferences, regardless of whether that 3 is True or False, the 4 in R8C8 would be True, either way. So we can be sure that the 4 in R8C8 is True, which then leads to the 3 in R7C8 also being True.

[@SudokuSwami]

The key word is "IF." :-))

[@SudokuSwami]

Another aspect of this, is that your observation that if the 3 in R7C8 was False, then there would be no 3 in Column 8, is correct. And because this is an impossibility, then that tells you your premise (If the 3 is False) is incorrect. If all cases lead to the same conclusion, then the conclusion must be correct. And if your supposition leads to a contradiction or an impossibility, then your PREMISE must be INCORRECT. I hope this makes sense.

[@Woofus1]

Ahh. Ok. Supposition only. I was hearing it as describing how both cases end up with no 3. By the way, digging your videos. Was stuck on an Expert lately (putting it away for a bit and revisiting it yet to be stuck again), BUT I used a chain for the first time today and got out of it. Maybe there was another way, but I wasn't seeing it. I have no issue now in recognizing the chains, but I am having trouble finding out what I want to do with them (where I SHOULD start)....vs. finding a target cell I want to try and eliminate from it and working out how to actually get to that point using the start/ends. Thanks for the series!

[@SudokuSwami]

It's a tricky thing, but it's always a good idea, as you are trying to construct a chain, to make sure there is a possible good result that may come of it. If you fail to consider that, you may end up constructing a valid chain, only to find that there is nothing to eliminate.

[@daleerwin7554]

No software I have ever tried has ever allowed me to access (read: color) individual candidates inside a cell, so I have never been able to run such a chain. Even three links is difficult for me to keep straight when using different candidates.

[@SudokuSwami]

For info on software, please write to me at [e-mail]

[@JoelHershberger]

Where can I get a good Sudoku computer program or one that is internet based? I can't seem to find one that has all the filters in it. By the way, I just found your channel by looking up X chains and I ended up starting at the beginning. This is all I have watched, so far, but intend to watch the rest of them. It is very interesting and is making a lot of sense to me. Thanks for all the hard work you have put into this.

[@SudokuSwami]

Hi Joel. I'm glad you found my Channel and are seemingly enjoying the Lessons. As a rule, I do not discuss software here in the Comments area. Please write to me at [e-mail] and I will be happy to answer all your questions. :-))

[@SudokuSwami]

"Crikey" ? Where you from? Australia? Stick with it, dude. You'll get it. :-) It's deep. But very cool. AIC's are a recurring concept. They are utilized in many of the solving techniques. Very important to understand.

[@ianjones6308]

UK :)

[@ianjones6308]

Agree that it is cool, however when starting out with an AIC type 2 how do you decide the starting point?

[@SudokuSwami]

Boy, that's a good question. One thing, is don't zoom in too hard with your eyes. Try to back away from the puzzle and see it as a whole. Then another thing to try, is to look for cells that might be potential endpoints, and then work the chain back from both ends toward the center, and try to piece it together like that. It takes quite a bit of trial and error, for sure. But like with anything else, the more you practice looking for them and stringing the links together, the better you will become at it. There will be another set of comprehensive videos on AICs Type I & II, later on in the Course, and we will talk about constructing them. So stay tuned for that! Good luck, and thanks for your interest.

[@jjpzebra9283]

Here's a question that, admittedly, you may already be covering later in the course. Simply, why can't you use already - solved numbers as part of a chain? For example, if 3 already is a given solution at the start of a puzzle, couldn't you use it as the beginning of a strong link? Likewise, if you already know 3 has been canceled out in a cell, couldn't you still use it by resurrecting it for a moment? The examples look like they use unsolved numbers. Maybe at times it would be easier to use a true number, or an eliminated one, to get where you need to go in a chain.

[@SudokuSwami]

If a Cell has already been definitely solved for Candidate X, I cannot think of any instance in which it could help you by using it in a Chain. The fact that it is a solved Cell will always be more beneficial all by itself than removing it temporarily to try and make other deductions. As to the second part of your question: If you have eliminated a Candidate from an unsolved Cell, but you discover that you could use it as a node in a Chain if you "resurrected" it, theoretically this should work, provided that nothing is preventing that Cell from containing that Candidate, and provided you strictly follow the rules of Alternating Inferences.

[@DocSardo]

A - B - C - D. If A is false then the dog ate your peanut butter and jelly sandwich. Got it!

[@nikimoore]

I find this very confusing. I understand the theory, but in practice I find it impossible to easily connect strong links with weak links. Either all the possible links are strong, or all the possible links are weak, so you end up with no-where to go - the links come to a dead end. I have now watched this video several times and I simply cannot get past that. Perhaps if I watch further videos it will become clear.

[@SudokuSwami]

You have apparently missed the point that a Strong Inference can provide a Weak Link. So if all your Links are Strong, just alternate the concepts of Strong-Weak-Strong in your mind.

[@nikimoore]

@@SudokuSwami Thanks so much for the prompt response. Yes, it is possible my attention wandered at a crucial point. I will watch the first few videos again. Just by the way, I do like your presenting style.

[@blahdiblah2169]

Another question Swami. Are all named solving techniques, such as x-wing, xy-wing, swordfish, jellyfish, etc, all variations (or composites) of AIC's? When I look at an x-wing, it seems that this is nothing more than 2x 3 link 4 pos AIC (SWS) which will give you eliminations on either side of the x-wing house.

[@SudokuSwami]

Yes, many techniques can be seen as AIC's, but not ALL of them. For instance, Unique Rectangles have nothing to do with Weak or Strong Links. For beginners, some of the techniques are more easily understood, by using alternate viewpoints. But if you can see them as AIC's, then you are one step ahead of the game.

[@blahdiblah2169]

@@SudokuSwami Thank you Swami. Even after watching Tut 4, I was able to make progress with some puzzles using just type 1 AIC's. Quite astonishing how it works, especially type 2s. Mind boggling really.

[@SudokuSwami]

It's just simple logic. My favorites are the Continuous and Discontinous Loops. They are usually very productive.

[@fubaralakbar6800]

19:30 That was one of the hardest Sudokus I have ever done.

[@CasaErwin]

I have been unable to practice the AIC type II because my software does not allow access to individual candidates. I can only color an entire cell. I guess I need to change my software. Any suggestions?

[@oumaroudia]

I was going to ask "where do you stop the chain? But I read your response to Ian Jones. So stopping is a matter of judgment; stop to a point where you can draw meaningful conclusions. Am I right?

[@SudokuSwami]

Exactly!

[@jlauby7777]

I see you making the chain with strong and weak links. What I don’t see is how to locate and identify the candidates to use in the chain. What draws to to a particular candidate to start?

[@SudokuSwami]

Ha. I am just putting the finishing touches on Tutorial #34, which includes a segment that addresses your exact question. But if you are currently watching and studying Tutorial #4, I HIGHLY recommend that you watch the Lessons in strict chronological order, and that you watch Videos #5 thru #33 before watching #34. :-)) Good luck.

[@mto0016]

How do you know where to start and end the chain or which strong and weak links to use?

[@SudokuSwami]

You cannot "know." You must search for them. Try making mini-chains of two and three links each, and then try to connect them. It just takes practice.

[@mto0016]

@@SudokuSwami okay thank you!! I get stuck on expert puzzles when I get to where there’s more than 2 candidates possible in each cell. I’m wondering if this is the key to “unlock” the puzzle without guessing.

[@cynthia4680]

My head is blowing up.

[@SudokuSwami]

Wow. Send photos!

[@mayyad1979]

What app is he using?

[@remyrat8961]

Regarding the AIC’s type II: I can see the inference very clear now. I have made some notes: 1. begins and ends with different-digit candidates 2. The cells containing the endpoints must SEE eachother. We can conclude that the digit that STARTS the chain can NOT be true in the end cell and the digit that ENDS the chain can NOT be true in the starting cell. TAKE NOTICE THAT: 1. Any link (weak or strong) between two same-digit candidates can ONLY be made within a house 2. Any link (weak or strong) between two different-digit candidates can ONLY be made within a single cell!!

[@SudokuSwami]

You have it exactly correct. Well Done!

[@krishnachaitanyakonduri9342]

Great explanation!! Could you please explain cannibalism a bit more detailed?

[@SudokuSwami]

Cannibalism occurs when a Candidate is proven to be false by the implications of the very Chain within which the particular Candidate is actually one of the nodes in the Chain. The term "Cannibalism" implies that the Chain is "eating itself."

[@us5634]

I'm still having a hard time with the logic of theAIC from your examples. I must be too dense.

[@SudokuSwami]

You are over-thinking it. It is really quite simple. If there are only TWO remaining instances of a particular Candidate in a House (Row, Column, or Block), then one of them must be True and the other must be False. This allows you conclude TWO things: 1. If one of them is True, then the other is False (Weak Inference) 2. If one of them is False, then the other is True (Strong Inference) If there are THREE or MORE instances of a particular Candidate in a House (Row, Column, or Block), then you can only make ONE conclusion: 1. If any one of those Candidates is True, then all the others are False (Weak Inference) If one of them is False, (in the case of three or more), then you cannot conclude anything about the other Candidates.

[@ramonbannister9498]

@21:57, I'm already confused, but I'll keep going. In the meantime, my logic says that if the 3 is false then that cell MUST be 4. That would eliminate the 4 in the cell immediately below. But you say due to the AIC rule, if 3 is false then the cell below it in this example is 4. But how could it be 4 if the 3 is false?

[@SudokuSwami]

The 3 in R7C8 is either True or False. Case 1.) If it is True, then the 4 in Cell R8C8 would have to be True. Case 2.) If the 3 in R7C8 is False, the logic of the Chain leads to the 4 in Cell R8C8 being True. Since the 4 in R8C8 is True EITHER WAY, then we know it must be True. It is a Verity, and you can safely enter 3 into Cell R7C8, and 4 into Cell R8C8,

[@KitJohnson9]

Mind blown.

[@Xzav1]

What is the name of the piano piece at the beginning of the lesson #4? I would like to learn it.

[@SudokuSwami]

It is J.S. Bach's Prelude to English Suite #3 in G minor. Good luck learning it. It is NOT easy. But just like Sudoku, it can be mastered with diligent practice. It is one of my favorite pieces by Bach. You have good taste! Good luck. :-))

[@ianjones6308]

Crikey this is hard to get the old head round

[@Ghost2T]

*_Your video are really amazing.🥰 I just don't understand what is "strong and weak" ? (Is the first hidden called "strong", followed by "weak" or not? and then "strong"). If the beginning & the end are both "strong", then the end is hidden, and if the beginning is "strong" and the end is "weak", it will be eliminated?. sorry my english is not good_*

[@SudokuSwami]

If you can say "If A is False, then B is True," it is a Strong Inference. If you can say, "If A is True, then B is False," it is a Weak Inference.

[@SudokuSwami]

And don't forget, a Strong Inference also has the properties of a Weak Inference, and can therefore be used as such, when constructing AIC's (Alternate Inference Chains).

[@twed57]

I just don't get the example at 19.34. If H7=3 then H8=4 C8=1, 3 or7 and C7=1, 4 or 7. If H7=4 then H8=3 C8=1, 4 or 7 and C7=1, 3 or 7 please help!

[@twed57]

Got it! Thanks.

[@SudokuSwami]

If the 3 in R7C7 is True, then the 4 in R8C7 would be True, If the 3 in R7C7 is False, then by virtue of the Chain, the 4 in R8C7 would be True again. Either way, R8C7 = 4. It is a Verity. Therefore R7C7 = 3 and R8C7 =4.

[@twed57]

@@SudokuSwami thank you!

[@abdullahhashmi5323]

hello! I am a bit confused with the aic type 2, the example in 21:33 , we see that if the r7c8 3 is true then the 4 in r9c8 is false because it there can only be that place for 4 but if the r7c8 3 is false, then it must be a 4 ultimately making the other cell a 3 using the same logic as I just wrote but it is not because due to the chain. My question is that why not use the chain logic in both cases? Why use it in one and not in the other? I know I'm missing something big here, I just recently started sudoku!

[@SudokuSwami]

Hello Abdullah. Ya know, I try so hard to make people understand thus stuff, that sometimes I am guilty of OVER-explaining it, which I believe is the case here. This example is very simple, and you only need to think of it ONE WAY. Consider this: A Strong Link begins by ASSUMING the first Candidate (or thing) is False, which implies another Candidate (or thing) is True. Apply that, to the 3 in R7C8. Start the Chain there, assuming that 3 is False and follow that Strong Link to the 3 in R7C3. Then follow the Chain around to the 4 in R8C8. If the first 3 is False, then the 4 in R8C8 must be True. But this is an impossible situation. If the 4 in R8C8 is True, the 4 in R7C8 must be False, and then R7C8 would be empty, because we assumed the 3 in R7C8 was False to begin with. When a Premise leads to a contradiction or an impossibility, we know that Premise must be INCORRECT. Therefore the 3 in R7C8 cannot be False and MUST be True. As soon as you enter that 3 into R7C8, as the solution to that Cell, then R8C8 can only be solved for 4. R7C8 = 3 & R8C8 = 4

[@abdullahhashmi5323]

@@SudokuSwami Thank so much for taking the time for explaining it to me. I get it now, I'm still new at this and it's a little hard for me to pick things up, thanks again for your help Sir!

[@fubaralakbar6800]

So basically, the endpoints of an AIC have an OR relationship, rather than the XOR of conventional strong links.

[@SudokuSwami]

If you have constructed an open-ended AIC correctly, i.e., beginning and ending with a Strong Link, alternating the Inferences (Strong-Weak-Strong, etc.), and the Chain has an odd # of Links, then at least ONE of the endpoints must be True, and it is even possible for BOTH endpoints to be True. But it impossible that both endpoints would be False.

[@dennistaylor6085]

OK, it appears that I am the only idiot here. I'm looking at the 9:30 diagram. I clearly see that Row 4 and Column 3 are the two entities that only have two 3s; therefore, they are strong links. However, I have no idea of why the blue cells are blue and the yellow cells are yellow. Could they be reversed and the "rules" would still be correct?

[@SudokuSwami]

Hello Dennis. Unfortunately, this Video was made before I had the ability to draw arrows on the screen. To mark the Inferences and the Links, we need to use two colors, to denote the alternating nature of the Chains. I use Blue and Yellow for this purpose. However, ANY two colors can be used. I am wondering if you had the audio turned on as you watched that part of the Video, because between 9:05 and 9:20 I clearly explain that I will use Blue to Yellow to denote a Strong Link, and Yellow to Blue to denote a Weak Link, as we move through the Chains. The Chain in the example you are referring to, begins in R2C3 and ends in R4C7. These two 3's are connected by the Weak Link between the 3's in R6C3 & R4C1. We could have started in R4C7 and ended in R2C3, going in the opposite direction. If we had done so, the colors would have been reversed. But either way, the outcome of the Chain is the same. The Inferences tell us that ONE of the Endpoints must be True, therefore a Candidate 3 in R2C7 would have to be False because it can see both Endpoints of the Chain. AICs can move in either direction. It is arbitrary which direction you choose.

[@dennistaylor6085]

@@SudokuSwami Thank you, Swami. You have confirmed one of my hypotheses: the colors could have been reversed. That answers a big question for me. I can easily understand why the two strong links were strong and why the weak link is weak. I just didn't understand why the colors (equivalent of arrows) pointed as it did. I may understand the bigger picture yet. Thanks, again.

[@SudokuSwami]

Great. Stick with it. You'll get it. Good luck!

[@dennistaylor6085]

Swami, I am now comfortable with the 9:00-9:30 region, knowing about how the strong-weak can be reversed. However, you have totally lost me in the 21:45 region. Here is why. Both r7c8 and r8c8 can be either a 3 or a 4. OK that is a "duh." You seem to say that if the 3 in r7c8 is true (which to me means that the value of r7c8 is a 3), r8c8 must have a value of 4. Again, to me that is a "duh." However, I think you are saying that if the 3 in r7c8 is false, the value of the cell must be a 3??? In my meager mind, if the 3 in r7c8 is false, the cell cannot be a 3 because true and false are opposites. Is it possible to slowly explain to me why the value of r7c8 is 3, regardless of whether candidate 3 in r7c8 is either true or false? Thanks, I'm sure I am missing something critical here.

[@SudokuSwami]

The 3 in R7C8 is either True or False, right? Let's examine both cases. Case 1: The 3 is True. This would mean that R8C8 would have to be a 4. Correct? Alright. Case 2. If we try to ASSUME the 3 in R7C8, is False, the CHAIN tells us that the 4 in R8C8 must be True. Since both Cases for the 3 in R7C8, lead to the conclusion that R8C8 is 4, we can now rest assured that R8C8 is definitely a 4. Once a 4 is placed in R8C8, the other Cell (R7C8) is solved for 3.

[@mouradtarzalt]

Can you please check back Sudoku Tutorial #4 / The Logic of AICs Example at Min 27:54 thr 32:16. Been confused by digits 5 & 7 beeing false and true

[@SudokuSwami]

Open-Ended Chains (like the one you are talking about) are SUPPOSITIONS. They are NOT facts. But what you DO KNOW, is that IF the first Candidate in the Chain is False, then the last Candidate has to be True. This is because of the alternating inferences, and because the Chain begins and ends with a Strong Link. So if you look at BOTH possibilities for the 5 in R1C1, it must be either True or False. Right? IF the 5 in R1C1 is False, then the 7 in R1C4 has to be True, because of the inferences in the Chain. (The 5 is not actually False, but you don't know that yet.) And IF the 5 in R1C1 is True, then again, the 7 in R1C4 has to be True, because it would turn into a Naked Single. So no matter whether the 5 in R1C1 is True or False, the inferences tell you that R1C4 turns out to be 7. Therefore, you can be CERTAIN that R1C4 is 7. Then by starting on R1C4, and running the Chain backwards, R1C1 is proven to be 5, by the same logic. But a time saving short-cut, is to know that when you have an AIC Type II that starts and ends with an identical Bi-Value Cell, you should immediately KNOW that the endpoint Candidates are the solutions to the Cells in which they lie. This was one of my first Videos, and my editing and production skills were very limited at that time. So, I apologize if I did not explain this as well and as succinctly as I could have, but everything I said was correct.

[@h0016911]

Understanding these AICs is not easy. Spotting these AIC (especially those 13-link long chain) looks very difficult

[@abscomm]

I had you up to this point, but this video makes no sense in my head. At 30:21 I cannot see how you determine which is right between the 5 and the 7 because they are the only two numbers left in the column and therefore if one is wrong then the other is right and vice versa. I´ll plod on and hope for a lightning AHA moment!

[@SudokuSwami]

The Chain starts with the 5 in R1C1. (You could also start with the 7 in R4C1 and go the other direction.) But starting with the 5 in R1C1, you begin by assuming the 5 is FALSE. If it is False, and you follow the inferences, it will lead to the 7 in R4C1 being True. The only other possibility for the 5 in R1C1, would be that it is True. If it is True, the 5 in R4C1 would have to be False, meaning the 7 in that Cell would have to be True, because it is the only other possibility. Therefore, the 7 in R4C1 must be True, which negates the 7 in R1C1, proving that the 5 in R1C1 must be True.

[@moisesweinstock313]

YOU HAVE A NEW PROGRAM THAT CAN MADE LINES WY YOU DONT RECONSTRUCT THE LESSON

[@alexwolf5547]

Hey :) i understand everything but my question is the logic behing the rules if b is true etc etc ... what i mean is how did the genius minds come up with those rules? Maybe i could understand it like really completely in the wholeness of the chain . Thx

[@SudokuSwami]

The "Rules" you are talking about are just basic logic. They are called Conditional Statements. This simply means that the True/False Value of something, is dependent on the T/F Value of something else. It is subject to certain "Conditions." The A's and the B's are variables, just like in Algebra. They can stand for ANYTHING you want. And with Strong Links and Weak Links in these Chains, A stands for the FIRST Candidate you are considering, and B stands for the SECOND Candidate you are considering. So the T/F Value of B is DEPENDENT on the T/F Value of A. In a Strong Link, you must be able to say with certainty that, IF A is False, THEN B MUST be True. And with a Weak Link you must be able to say, IF A is True, THEN B MUST be False. And notice that the Conditional Statement about Weak Links is also applicable to Strong Links. This is why a Strong Link can be used in the ROLE of a Weak Link (when needed), but NOT the other way around. Think about it over a glass of wine tonight. You'll get it. :-))

[@alexwolf5547]

Sudoku Swami thx :)!

[@alexwolf5547]

Sudoku Swami ok i had glass and thougjt about it ;-), my only question is . Why does it have to be strong link then weak link. Why cant there be weak link - weak link - weak link etc chains

[@SudokuSwami]

Because each subsequent Link (or Inference) in the Chain, must BEGIN with the Premise, that matches the Conclusion of the preceding Link. If the first Link implies, If A is False, then B is True, then the NEXT link must BEGIN with that B (which is the new A) being TRUE, because that was the conclusion of the preceding Link. This is the only way the Links can proceed in a logical way. They must ALTERNATE. Otherwise the Links would be totally unrelated and you could not make any logical deductions from them.

[@SudokuSwami]

Here. Read this article. sudokuswami.tumblr.com/post/187748849333/in-any-sudoku-aic-a-strong-link-can-always

[@jamiemer1109]

Sudoku Swami, I have the idea of the Idea of Strong and Weak links down at this point. However, I'm having trouble wrapping my head around the concept of the Type 2 AIC. In the example you show at 22:17 on the 3 and 4 in column 8, you're saying that the 3 in Row 8 Column 8 is false regardless if the 3 in Row 7 Column 8 is True or False. However, if they were both false then there would be no 3 at all in Column 8! So how exactly does the chain make the conclusion that Row 7 Column 8 is a 3 and Row 8 Column 8 is a 4?

[@SudokuSwami]

Someone asked me this same question a couple of days ago. Here is my answer to him: The 3 in R7C8 is either True or False, right? Let's examine both cases. Case 1: The 3 is True. This would mean that R8C8 would have to be a 4. Correct? Alright. Case 2. If we try to ASSUME the 3 in R7C8, is False, the CHAIN tells us that the 4 in R8C8 would again be True. Since both Cases for the 3 in R7C8, (T or F), lead to the conclusion that R8C8 is 4, we can now rest assured that R8C8 is definitely a 4. Once a 4 is placed in R8C8, the other Cell (R7C8) is solved for 3.

[@jamiemer1109]

Okay. I actually figured out that if the 3 in R7C8 is false then, R7C3 = 3, R8C3 = 1, R8C9 = 7, R8C7 = 9 and R8C1 = 3 which would eliminate the 3 in R8C8 and thus R8C8 = 4. But thank you anyway.

[@SudokuSwami]

Great. When using Conditional Statements, you have to be careful about what is actually being asserted. When you say, "If A is False, then B is True," it does not necessarily mean that A is truly False. You are only saying that IF A is False, then....something else would be XYZ or whatever. When you have multiple Conditional Statements, that all begin with different premises, and that all lead to the same conclusion, and you KNOW that at least ONE of the premises must be True, then you can be certain that the conclusion is True. This is called a Verity.

[@jjpzebra9283]

@@SudokuSwami Wait a minute! I agree that the technique works, though I'm having trouble getting it down in actual practice. However, your first assumption breaks down, no? That is, if you assume the 3 in row 7 column 8 is true, there is no assumption you can make about the 1 in row 7 column 3. Either 1 in column 3 might be true. Hence, no chain. There is a different reason for the 3 to be false in R8C8. In any event, two questions: first, some time ago you were asked about the software you used. Can I send you an email and ask the same thing? (If so, will you answer on point :-) ?) Second, can you recommend or note any software/app/program that can provide examples to try out? For example, is there some place where a program would tell you to find the AIC that starts at R7C* and eliminates one of the candidates? This would be good to practice things like almost locked candidates, for instance. Also, I share the reaction of someone who said they wished you are their accounting teacher. Only, my wish is for math. You make the principles crystal clear to understand. I wouldn't have become a lawyer if that had been true haha!

[@SudokuSwami]

@@jjpzebra9283 If the 3 in R7C8 is True, then the 4 in R8C8 would have to be True. This is NOT a Chain. To make a Chain, you must begin by assuming the 3 is False (Strong Link). Yes, for software recommendations, you can write to me at [e-mail]

[@daniloalegarves6021]

swami which sudoku app you are using, how can you draw a line or arrows in that sudoku app , if you draw a line you cannot be lost.

[@SudokuSwami]

Hello Danilo. Please check your email. :-))

[@madhusudananadiyodi1753]

Dear Swami, I appreciate the efforts taken by you to teach your special techniques . Can we solve an expert sudoku using AIC alone ?

[@Noogsie_47245]

I have a mental block. I have memorized when A is true then B is false. Easy enough. When A is false I get lost...

[@SudokuSwami]

This is an important concept, so I would spend some time locking it into your brain, if I were you. If there are many choices (possible instances of a single Candidate within a House), then if any one of them is True, then all the others must be False. But if there are only TWO choices, then if one of them is False then the other must be True, because there has to be one TRUE Candidate. These concepts help you to build Chains of Inferences.

[@Noogsie_47245]

@@SudokuSwami yes... I went back a couple of videos...

[@bradparker6156]

Hi Swami, Interesting things, these chains. Been trying my hand and struggling a bit, but to preempt your response to that, practise makes perfect, and I'm certainly in that phase of development. A question on something that may not even be possible. Suppose one were constructing a chain (perhaps I refer to an X chain) starting with candidate 8 of which there are 3 instaces in some row. The initial strong link would be to another row. If the chain construction led to a weak link to another candidate 8 in the original/starting row, can the final strong link be made to the remaining candidate 8? The links between any two of the 8s in the row are weak as there are more than 2 instances, but does the fact that the first 8 was part of the chain create a strong link between the remaining two candidates? If so, in the particular case described, I deduce the second last 8 in the chain could be eliminated?

[@SudokuSwami]

Good question. The answer is, "Absolutely NOT!" If there are three 8's in that Row, there can ONLY be a Weak Link between any two of them, even though one of them was used as the starting point to the Chain you described.

[@bradparker6156]

Just achieved my first 9 link type II AIC. Euphoria....

[@SudokuSwami]

Wow. That's great, Brad. Nice goin'. Another thing about your theoretical question above, you overlooked something that I did not mention earlier, because I did not want to unnecessarily confuse you. But what you had, without realizing it, was an AIC Type I. The Link immediately BEFORE your Weak Link leading back to the Row with three Candidate 8's could only be a Strong Link. Thus, you could have just stopped there, and eliminated the 8 that you wanted to make a Weak Link to, because it could see both of those endpoint 8's, one of which must be True.

[@bradparker6156]

Yes! Of course. That makes perfect sense. Thanks for the support and excellent training. I took some advice from one of your responses to one of my prevoius comments. Where you stated that the most difficult puzzles could be solved with loops and chains. I never liked these, purely as it felt too much like hit-and-hope. How does one know where to start a chain is the question i always asked myself. But your videos have gone long way to demystify these techniques. As you say, it can become fun once you get the hang of it. Not there yet, but will keep at it....

[@bradparker6156]

Hi Swami, Another question along similar lines to the first. Suppose one is constructing a chain and one uses a cell with candidates 1,4,7 linking to the 1 say and then linking out to another 1 in some other cell. After a few more links, one ends up trying to link to the 4 or 7 in the same cell. You're probably going to say that if you end up in such a position, the chain is going nowhere. But either way, is it a valid to link to one of the remaining candidates (4 or 7 in example) Apologies for the obscure questions. Problem for me is like with everything Sudoku, it's often difficult to spot a likely solution/strategy. Deciding on chain start points is a bit "hit-and-miss" at the moment and i'm often ending up doing a complete tour around the puzzle board before reaching an ultimate yes/No point, which has often led to a bit of a crow's nest. By the way, I've had to go up a level on my Sudoku app to see SDCs or AICs. Problem is, it's now throwing things like ALS and APE at me as well, which is making me feel like precisely that. Can't wait for your presentations on those techniques...

[@ashtonsmith1952]

I would have found it VERY instructive for your two AIC Type II demonstrations @20 and 28 minutes if you had presented a chain that didn't work. With the two 5/7 bi-value, I would have liked to see you start with the second 5 and end with first 7 to demonstrate that it does NOT work. As a learner, it is just as important to know what I am doing wrong as what I am doing right.

[@SudokuSwami]

Hello Ashton. Thank you for your interest in my Channel, and for your comment. All I can say, is that if you know the Rules for correctly constructing AICs of ANY kind, you should also know that violating those Rules, in any way, would result in an invalid Chain.

[@Jim_Fries]

The beginning introduction looks like the central coast of California...

[@SudokuSwami]

Good guess.......but incorrect. :-))

[@debbiestewart5944]

true this is a complete pain in my ass

[@SudokuSwami]

Nothing worthwhile is easy! :-))

[@elmofranklin4788]

Dude, I'm going to bail on your tutorials...they're like "drinking from a fire hose". I'll admit I'm rather a "newbie" at Sudoku, but your foray into "rules" and "nomenclature" takes the fun away from solving the puzzles. I'm sure you know Sudoku backwards, and forwards, but you're explaining nuclear fission to someone who is figuring out "firecrackers". Maybe somewhere down the road, they will make sense, but right now...have a good day.

[@SudokuSwami]

Okay, buddy. Thanks for letting me know! Ha ha. Good luck. (I will still be here when you decide to come back.) :-))

[@jwbakker5100]

He does not understand himself what he is doing. Terrible video .

[@SudokuSwami]

Hello. My intention is to help you. These Videos are free for you to watch. What is it that you do not understand?

[@pipster1891]

Wow. This seems a big jump from lesson 3!