X-Chain (Old Faithful!) / Sudoku Tutorial #27
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- Опубликовано: 22 авг 2024
- Explanation and demonstration of an AIC Type I that employs the same-digit candidate throughout, known as an X-Chain. Numerous examples, plus a Bonus Section on Continuous Loops!
24:56 Thank you for the tips! Understanding the logic you taught us about chains it's very easy to follow the examples as you show them, but finding them by ourselves is far more challenging.
Very useful rule clearly explained. Love the way you teach the eliminating candidates
Great instruction. I started to understand the concept about halfway through the examples. What helped me and what I think would help others in coming up with the chains is after I start with a strong link, I take a moment and determine which of the connecting weak links (or surrogate) will lead me to another strong link, then go from there.
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X-Chain at 19:16
1. A link is a line connecting two notes together. In a weak link the two notes cannot both be correct at the same time. In a strong link one of the two notes must be correct.
2. Connecting strong and weak links, in an alternating fashion, creates a "chain". Chains must always start and end with strong links.
3. Notice the chain of 2's.
4. Case 1: Imagine placing 2 on this end of the chain. Then, these notes cannot be correct.
5. Case 2: Now imagine erasing 2 from that same end of the chain. Again, these notes cannot be correct.
6. In either case, these squares cannot contain 2.
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Had a chance to make an x-chain in a recent puzzle after this video. Had to think beyond the three link variety but once you look hard it will appear. Really knocked the Sudoku down. Thanks for the video.
Wow this is awesome! I didn't know continuous loop before. And I can finally explain X-wing with strong and weak link!!
I'm glad you enjoyed the video. Thank you for your comment.
Very well explained, thank you very much !
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Great series! I just used an X-chain to solve a live puzzle. Thanks for this!
This is new to me. Very fascinating.
1:17 What a statement! I feel like there is plenty of people who avoid chains with a large arc. So what about a new episode of random tips and tricks where you pull out your skills and show us how to solve a difficult puzzle only by using those chains. It would definitely open our eyes :)
This is a great video, and a must-know technique as it contains by itself some other techniques as X wing or swordfish..
Im working on solver. I just noticed - Yes - you can shorthand x-cycles and eliminate many values. But if you leave them as an x-chains, multiple other x-chains later will give the same results, as x-cycles.
I'm glad that you are back!And you answer my question I would like to ask you. How to find...Very good and awaited video.Thank you Swami
Hello Mirek. Thanks for your continual support. Conjugate Pairs are the key to forming X-Chains. Just try to find as many Conjugate Pairs as you can, on each Candidate, one at a time, and then look for ways to connect them. It's as simple as that! You can also pick two potential endpoints, and then work backwards from each one, and try to connect them in the middle. Good luck!
ha ha. I know it is a piece of cake when you are a master. But I'm working on this.
Thank you for all your videos. Past, present and the future ones ;-)
As long as you keep working, you will become a Master. Practice makes perfect. :-))
Mark 24:42 : Why you do NOT *also eliminate* the x-chain candidate *from R4C5* ? (It's in sight of R4C3 and R6C5.)
What is the reason of focus limitation to the ends of a x-chaining sequence?
I would like to claim: it is possible to eliminate the x-chain candidate from cells which are in sight of both: a strong link end and other strong link start when both strong links belongs to the sequence.
You are correct. You can sometimes find smaller X-Chains that are contained within a Larger X-Chain.
@@SudokuSwami Thank you for a quick and clear response!
Do you have a video with x-chains containing also group nodes and/or group links?
No, sorry. I am no longer making Sudoku Videos. What you see, is all there is, or will be. If that status ever changes, I will post a notice. Thanks for your interest.
Nice video, interesting examples with the canibalistic X chains. Perhaps these canibalistic chains are discontinuous loops? (I don't really understand discontinuoud loops so I'm not too sure myself) I am looking forward to your video on discontinuous loops as I would like to fully understand what's going on and various different cases you can run into.
I'm hoping after this video I should be able to spot more x-chains (or continuous loops) within puzzles.
Continuous Loops are the best ones to find, because they can lead to multiple Candidate eliminations. And as I said in the Video, Loops can be made using different-digit Candidates, and the Links can be between the Cells, and also within Cells. You just need to follow the rules for Links.
There are three generally accepted types of Discontinuous Loops. But I will debunk this, and prove that there is really only ONE type, as the other two can be expressed in simpler ways, that can actually be more productive. Unfortunately, I have several Tutorials to make before I get to this, as I am following a planned Outline for my Complete Course. So, please be patient. We'll get there. :-)
And by the way, the concept of Cannibalism is not synonymous with Discontinuous Loops.
Sudoku Swami Thanks for your reply, I have found a continuous loop (specificially one that isn't just an xwing...) once within a puzzle but I don't know if it's something I can feasibly (timewise) look for (although if I happen to spot one whilst looking for other things like smaller xchains then great). It's nice to understand why it works though which you proved crystal clear in the video.
I'm back!
These are hard to spot, but a more interesting problem is in my opinion when and why one starts trying it. Do you just think that OK there are several conjugate pairs so let us see what I can make of them. Or do you rather think tactically, like: I'd need to get rid of that particular candidate, so let us see if I can't build a chain to do it with?
Yes.
@@SudokuSwami I take it you mean "yes" to the latter option, no?
I was trying to be funny, but what my answer means is BOTH. You could think of it either way.
@@SudokuSwami Crossed my mind but wanted to check. Both methods work of course, but I was wondering how for example those who compete use this. Maybe both ways they, too.
In competition you have to fill in Candidates by hand, so it is impractical to use my techniques. It would take too long.
24:55 Helpful tip!
Why can't the base sets be the 3's in row 1 and row 9? That would lead to different eliminations.
So I guess you think I am psychic and know exactly which diagram you are talking about from a 43 minute Video??
Good morning. How do you decide two end points? In every puzzle you say these are the two end points. I don’t get it. Please explain.
I know where the Endpoints are, because I have already found the Chain. You don't KNOW where the Endpoints are, at first. You must search for the Chain, by connecting Strong and Weak Links, and see where it leads. It takes practice,
You always say this is the start point and this is the end point but how do you know that
Good question. You only know that, AFTER you have found the Chain. I indicate the start and end points, to give you a "heads up" of where the Chain will be going. Finding Chains takes a combination of skill and art, which can only be achieved with lots of practice. The more puzzles you solve, the better you will get at it. I give tips on what to look for, in later Tutorials. There are key "ingredients" that can help you, like Conjugate Pairs, Bi-Value Cells, and shorter patterns that you can try to connect together. Stick with it. You'll get it.
Is this a sudoku software you are using?
Yes.
@@SudokuSwami What is a sudoku software you're used?
What if the length of cycle is 5 nodes?
In order to employ the logical deductions of Open-Ended AIC's (of all kinds), they must start and end with a Strong Inference, the Inferences must alternate, Strong-Weak-Strong, etc., and there must be an ODD number of Links and and EVEN number of Nodes.
That was really helpfull. Is it possible that you show how to start build these links
Hello Mourad. Thank you for your comment. Conjugate Pairs are the key to forming X-Chains. Just try to find as many Conjugate Pairs as you can, on each Candidate, one at a time, and then look for ways to connect them. It's as simple as that! You can also pick two potential endpoints, and then work backwards from each one, and try to connect them in the middle. Good luck!
An other one. When is it interesting to go for X Chains? When remain 4, 5, 6, 7, or 8 digits a candidate
When you see a lot of Conjugate Pairs on one particular Candidate, there is very likely an X- Chain to be found. I am sorry, but I do not understand the second half of your question.
I mean, for digit 1, let's say. When it is interesting to look for X-Chains? is it when there is still 5 ones to find, 4 or six etc
There is no guarantee that you will ever find an X-Chain. It is only MORE LIKELY that you will find one, when there are three or more Conjugate Pairs. The number of instances of a Candidate "left to find" is not important.
What's the best Sudoku puzzle book?
I don’t know anything about puzzle books. I would go to a large bookstore and ask someone to help you, or search on Amazon.com.