I looked over the test questions again, and I focused on navigating each chain to see if there were any other kill zones. I also discovered that new links were revealed, when the candidates were killed. I also got practise using pointing pairs and triples as links. I think that these 3 things are worth mentioning in your future tutorials, and our collaboration.
9:27 "There is no kill zone at this point because the intersecting cell is between the two cells of the first strong link of the X-chain." I've no idea what you're talking about here. What do you mean by "the intersecting cell"? Why is R4C4 not in the kill zone (at this point) as it sees both the start and the end of the chain. This results in R6C6=9 and the outcome is the same your eventual conclusion.
Yes, your way of thinking about the logic works as well. In this section of the video I was trying to demonstrate what is known as a Nice Loop. But you are correct. You could have just stopped and kill the 9 in cell R4C4 which then opens up a Hidden Single with the 9 in cell R6C6. I'm surprised no one has ever made this comment before. This video is pretty old. Nice catch on your part!!
Mark 5:40 : We have a brush with a *closed x-chain* here! (Loop closing weak link: R2C9 -- R2C5.) Hence, we may open the sequence wherever a weak link occurs to apply a kill zone mechanism. Cells additionally to kill are: R5C3, R9C7, R5C6. Is this correct?
You are correct. You are now the teacher! I have to update my X-Chain videos to include any cell sharing a house with "on" and "off" cells. Because of the Either-Or links, the X-chains are bidirectional so this works with the cells you are targeting. I think when I was concentrating on the videos I was more focused on the building out of the chaining sequence. Good comment on your part!
There's a small mistake at the 3:04 mark in the video. For cell R5C5 the video shows cells R4C6 and R5C6 as the only two choices for the 3rd cell in the X-Chain sequence. Cells R5C1 and R5C3 should also be highlighted in dark green as possible choices for the 3rd cell. Neither R5C1 and R5C3 has a strong link to a 4th cell in the chain but they still should be highlighted in dark green at this point in the video.
@dxSudoku Channel Sudoku Swami says: re 'Continuous Loops' "all weak links become strong links" i.e conjugate pairs; so here other related 9's would be deleted ; e.g. the 9 in row 1 column 2; & row 4 col 2, row 3 col 4. Search RU-vid for Suduko Swami Continuous Loop
@@peterfairley1 I find Swami's explanations to be a little meaty. I'm trying to simplify it as much as I can. Sometimes I succeed. With my X-chain video I was trying to give the easiest way to find them in the puzzle.
I'm a bit confused by your definition of strong link. Can you give an example of a time when both candidates in a strong link can be true? edit: I just got to the part where you mention that both being true would violate sudoku rules. Since this is true, I think adding the qualifier that both can be true is confusing.
The definition of Strong Link just means one direction if false then the other is true. The definition doesn't preclude the possibility both can be true but the Sudoku rules do prevent it. Why I even made the point is because with Weak links the rule is if true the other is false. But both cells in a weak link can both be false meaning another cell in the house had the chosen candidate value. X-Chains are kind of hard to explain without using Strong Link in the definition. See if this explanation helps you: hodoku.sourceforge.net/en/tech_chains.php I thought this was interesting: "If two entities are strongly linked, they cannot be false at the same time. That means: If one of them is false, then the other has to be true (both true is only possible in very advanced types of links)." Although the Hodoku Wiki page says both true exists I've never seen it as of yet.
@@dxsudokuchannel, so a weak link means that a candidate value can be in a third location? Also, are you saying that you have never seen anybody give an example of an advanced strong link, where both are true?
Jason, I could be wrong, but from what I understand so far, a strong link allows us to look at 2 candidates in 1 cell, or 1 candidate in 2 cells, and then say, "If this is true, then that is false.", or "If this is false, then that is true.". A strong link is really something that a beginner can expect to understand without much explanation, but he'll get confused, because explainers don't do a good job. He can discover a big chain of strong links, and then start at either end and then try to say both things, and then start at the other end, and then say both things. This extreme flexibility makes solving easy, when it is available. The challenge is the weak link, which seems to be only useful for when 1 of the 2 cells is question is true, due to a third cell getting in the way. When going "forwards", it's fine, because the first cell encountered "eliminates" the other cells in the house. I think that it is easier to understand, if you look at the links as things that can be used in either direction and starting as true or starting as false: forward-true; forward-false; backward-true; backward-false. Both backwards uses might be unnecessary for most situations, since the first link is good enough to eliminate the kill zone candidates. If the forward-true can connect the chain, then that is all that we need.
@@eugenetswong Yes on the first question. Keep in mind the way the Strong Link works a false value or cell having candidate triggers the next cell in the chain to be true, that is, must be the value. Yes on the second question, I've never seen what the Hodoku Wiki page was saying, that is, the case when both cells of a Strong Link turn out to be true. I didn't think I should argue with the people who invented Hodoku! But it doesn't seem possible to me. I will keep my eye for it and let you know if see it!!! Fyi, I'm still learning many patterns myself. I know a lot of them. But there are so many. I don't know Finned Franken Swordfish or Forcing Chains. Maybe someday. I plan to do some videos on uniqueness patterns next. I'm not at the highest level yet so if I do make a mistake please point it out!
@@eugenetswong My response below this one was to your first set of questions. Remote Pair, 2-String Kite, and Skyscrapers are variations of X-Chains. Make sure you watch the video Remote Pairs. I talk about Strong links early in the video.
The kill zone seems to be applied only between the x-chain beginning and every end of added strong link. Why this limitation? I think the kill zone mechanism should be used between *each strong link start* (already in x-chain sequence) and just added strong link end. Is my conclusion correct?
I'm not sure it's a limitation. X-Chain means either the first is true, or the cell in the sequence is true. If any cell shares a house with the first cell, and a cell that is currently "on" or "true" in the chaining sequence, then it forms a kill-zone and the candidate is killed. 2-String Kites, Skyscrapers, Turbot Fish, and Empty Rectangles are all variants of the X-Chain having exactly four nodes in the chaining sequence. You conclusion is correct. The kill-zone is formed between the first cell in the chaining sequence, and the last cell. But intermediate cells in the changing sequence can also create kill-zones. Here's a neat video you might like since you've been group nodes. This is tutorial on the Remote Pair where the pairs are group-nodes within the cell, and the chaining sequence is exactly the same as an X-Chain: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-d9IJdbFJ38w.html This tutorial will help you see the kill-zone concept especially in second and third examples.
Regarding Test #7, i think that you need to explain chaining better. :( I don't understand how eliminated them. I think that you got into chaining too fast. It would be easier to understand, if we had a complete grasp of strong and weak relationships with positive and negative examples. Also, it might be easier with alternate terminology. I volunteer to be a test subject, if you'd like. I wish that writers would run things by people to see if the phrasing could be better.
I have too many questions! 1) "If 1 candidate is false, then the other candidate must be true.". Which candidate? There are 4 candidates among 2 cells! :( 2) How can both be true? You say that that would violate Sudoku rules. Therefore, how would they be true outside of Sudoku? :(
@@eugenetswong A Strong Link occurs between two cells within a house. Say the house is a row. So within a row there are only two locations a possible 1 candidate can occur. Say the first location is set to another value, then the second location becomes a Hidden Single. True or false in this context means choosing the possible candidate as the value of the cell. I apologize for assuming this is obvious. I tried very hard to spell it out clearly.
Chaining is just a sequence of values being picked. Take one side of an X-Wing with possible 3 candidates. The two cells are a sequence. If you pick once cell to have a value of 3 the other cannot be 3. If you pick one cell to have a value other than 3 then the other cell must be 3. What happens in one cell affects the other in a sequence.
Study this web page: hodoku.sourceforge.net/en/tech_chains.php "A chain is simply a stream of implications that lead from a premise (e.g. candidate x in cell y is not set) to a result. If a chain produces a contradiction (e.g. premise x is set in y leads to x is not set in y), then the original premise is proved to be false (if it was "if candidate x is set", x can be eliminated; if it was "if candidate x is not set", x can be placed immediately)." Let me know if there was something I could have said differently in the video to explain this better. This is not a simple topic.
@@dxsudokuchannel, hi. :) No apologies, please. :) Even though I feel a bit of frustration towards you, it's mostly people in general, because of the unnecessary terminology. It's such a logical hobby, that we use "true" & "false". Even though, I understood the basic definitions, I never really was able to apply them until I watched your videos, so thanks for helping me to step forward. I think that a lot of people also struggle to apply that.
Yes, there may be more than 1. But in the exercise I only did one. If you are interested in generating your own exercises, I did a video on how to do it: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-jPssW_W3iH8.html You also might find this video interesting: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-di1aM5X0h6Y.html And this one will take you skills to another level: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-QvqGjXyPrIU.html Make sure when you search for X-Chains you also include Group Nodes in the chaining sequence. It opens up all kinds of new candidate eliminations.
I'm trying to learn X-Chain with group nodes. Please consider the situation in puzzle at mark 3:05. I would like to build following x-chain (closed to a loop): R2C5 == R5C5 -- [R4,5C6] == [R8,9C6] -- R8C4 == [R2,3C4] -- R2C5 Would you say that described x-chain elements are linked correctly? (I noted: group nodes within square brackets, strong links with '==' and weak links with '--'.)
This one is wrong in the chaining sequence: [R2,3C4] -- R2C5. You don't know which cell is on or off in R23C4. So you can't assume there's a weak link to R2C5. Please check again. Maybe I'm reading this wrong. Sorry for the late replies. I've been dealing some health issues which have been making me exhausted. I'm starting to feel better but it's taking a long time.
@@dxsudokuchannel Hmm 🤔 R23C4 is acting as a group node. When one of these cells is ON, then R2C5 must be OFF. This looks like a weak link relation. There is exactly the same situation in my x-chain like within block #8. I cannot see any difference in the relations in block #2 and #8. PS. I'm very glad of your supporting answers. Do not worry about some delays... Mainly healthy and alive🙂
@@danielkoziarski8488 I was looking at C6. Okay, for block 2, I agree, you have R23C4 - R2C5. This becomes a Nice loop because you return back to starting cell R2C5 in the chaining sequence. Nice loops are bidirectional so any cell that shares a house with both an on-cell and off-cell can be removed. Did you look at my AIC videos yet?
Mark 12:22 : is it possible to eliminate the candidate 3 from R3C5 and then to *continue the chain:* weak link R8C5 - R2C5, strong link R2C5 - R1C6, which would allow further killing in R1C1 too?
@@dxsudokuchannel Yes. It is the cell you have highlighted in red (mark 12:22). After candidate 3 elimination from R3C5, there is a weak link from R8C5 to R2C5, followed by a strong link (within block/box 2) to R1C6. This further strong link allows to kill even more than in R1C1. I mean it is possible *also* to cross out the candidate 3 *from R1C9,* because it is a junction of R1C6 and R4C9. Explanation: R4C9 is a start of strong link in chain and R1C6 is an end of strong link in chain. So, both together give us additional opportunity to kill. I think each pair of kind: [start strong link] and [end cell of *other* strong link] in same x-chain produces *new* potential kill zone. I have verified the elimination logic and it seems to work...
@@danielkoziarski8488 Sorry for the late reply. I started a new job and I'm swamped. R1C1 is a nice kill! I agree, R4C9 as new chain kills R1C9. NICE WORK!!!
@@pascaltorvic6246 If something is not clear or confusing let me know. I did the #72 video on Skyscrapers after a conversation I had with someone to clarify something missing in the first video. If there's something odd with the X-Chain tutorial let me know.
@@dxsudokuchannel Sir, I think everything is in there, but I had to pause every second or so to get the essence of the thing, but those kind of things need our own effort..My only wish is if you can go slightly slower it would be perfect
@@pascaltorvic6246 There's a lot of skill that goes into making these videos. I think I might be getting better over time. See if this video has the right speed: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-di1aM5X0h6Y.html
