Amazing! I can already anticipate some implications of these types of discontinuity, nevertheless I can hardly wait for Tutorial #42! Thank you very much, Swami!
When you just follow a strong-weak pattern, I always considered the type 3 as a type 1. Using propagation rules, however, it is easier to see the difference in the logic because there is a distinction made between standard strong/weak links and those within cells.
Right. In a Type 3, if you connect the two Candidates in the Cell of Discontinuity, you are ending up with a Type 1, except that one of the two Weak Links is coming from within the Cell, instead of from outside the Cell. I will cover this in Tutorial #44.
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Hi Swami! In trying to construct continuous loops using your previous videos, I keep finding that instead, my loops usually return to the starting candidate on a strong link, proving that the starting candidate must be true after all. After watching this video of yours, I now know that these are DL Type 2's. I've yet to run across either of the other types of DLs. Are there any statistics on which type of DL is most common? Since Type 2's are the most powerful it would be a cool thing if they were the most common type, but it could just be that I've been lucky.
Sorry, it just hit me that my question was stupid. Since I've always begun my chains with a strong link, it's a foregone conclusion that the only kind of DL I'd find is a Type 2.
Your question is not stupid. If you always start with a Strong Link, then you will never find a DL Type 1. BUT....you could find a Type 2 or a Type 3. (Remember that Chains can be analyzed in EITHER direction.) As far as the statistics go, I do not know the answer about the frequency of each Type. You'd have to look at a few billion puzzles, to figure it out. :-))
@@SudokuSwami Ah that's right! If I returned to a different digit in the same cell on a weak link, that would be a Type 3. But so far it hasn't happened, so it does have me wondering. Thanks for your answer.
@@SudokuSwami Actually to be honest, I DID find one Type 3 a few days ago. But the return weak link was a surrogate weak link, so redrawing it as a strong link made it into a Type 2, shifting the cell of discontinuity. What has me curious is that usually in Sudoku, the less powerful patterns are more common, so I'd expect to find loops that only allow a single candidate elimination more often than those that actually solve a cell.
In the situation you described above, it doesn't matter if the "returning" Link is a Surrogate Weak Link. If the Link preceding it was a Strong Link, the Surrogate Weak Link must be perceived as WEAK, to keep the Chain working properly, (i.e., that If A is True, then B is False). You cannot view it as a Strong Link. Thus, you would have a DL Type 3. In your Chain, let's call the Strongly-Linked Candidate, Candidate X, and let's call the Weakly-Linked Candidate, Candidate Y. So you would have two cases: Either the Cell is a Bi-Value Cell, or it has three or more Candidates. If it is a Bi-Value Cell, you could make a Strong Link from Y to X, and thus you would have a Type 2, with X being the solution. If it is NOT a Bi-Value Cell, then you can make a Weak Link from Y to X, and thus you would have a Type 1 with Candidate Y being eliminated. Either way, Candidate Y is FALSE. But you can simply view it as a DL Type 3, even though you are imagining the Chain is starting on the Strong Link.
One general question about AICs. Do they have to follow a clockwise or anti-clockwise pattern? Or is that just a general pattern and the only restriction is you can't use the same candidate twice? What are the explicit restrictions in this case?
Hi Jon. ALL AIC's can move in either direction, and if they are constructed correctly, they will be valid and make sense either way. The inferences will be reversed, depending on which way you envision it, (one direction or the other), but the RESULTS will be exactly the same, no matter which direction you go.
And you are right. You CANNOT string the Chain through a specific Candidate that has already been used. The only way you can use a Candidate twice, is if you are returning to it, to connect a Loop. But even then, you are not really using it twice, because after the Loop is connected that Candidate will only appear ONCE in the completed Loop.
@@SudokuSwami By overlapping I mean cutting back through the same cells, while using different candidates. You usually don't see this is solver when they draw the lines for strong and weak links because the lines would be over top of each other. I've only seen one example that really did this. Maybe if I allowed chains to have, say 30 links I'd see more of this. Then I could really understand if there are any restrictions. Here is that example. gyazo.com/989e94b939fb302d3fbedd0411ad0bb8gyazo.com/989e94b939fb302d3fbedd0411ad0bb8
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Amazing! I can already anticipate some implications of these types of discontinuity, nevertheless I can hardly wait for Tutorial #42! Thank you very much, Swami!
Cheers, AT. Good to hear from you. I appreciate your appreciation. :-))
Bravo on the Chopin
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When you just follow a strong-weak pattern, I always considered the type 3 as a type 1. Using propagation rules, however, it is easier to see the difference in the logic because there is a distinction made between standard strong/weak links and those within cells.
Right. In a Type 3, if you connect the two Candidates in the Cell of Discontinuity, you are ending up with a Type 1, except that one of the two Weak Links is coming from within the Cell, instead of from outside the Cell. I will cover this in Tutorial #44.
Hi Swami, a big portion of theory. Now is the time for practice video ;-)
For Beautiful Custom T-Shirts & Coffee Mugs featuring the Swami Logo and other Sudoku Phrases, 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
Hi Swami! In trying to construct continuous loops using your previous videos, I keep finding that instead, my loops usually return to the starting candidate on a strong link, proving that the starting candidate must be true after all. After watching this video of yours, I now know that these are DL Type 2's. I've yet to run across either of the other types of DLs. Are there any statistics on which type of DL is most common? Since Type 2's are the most powerful it would be a cool thing if they were the most common type, but it could just be that I've been lucky.
Sorry, it just hit me that my question was stupid. Since I've always begun my chains with a strong link, it's a foregone conclusion that the only kind of DL I'd find is a Type 2.
Your question is not stupid. If you always start with a Strong Link, then you will never find a DL Type 1. BUT....you could find a Type 2 or a Type 3. (Remember that Chains can be analyzed in EITHER direction.) As far as the statistics go, I do not know the answer about the frequency of each Type. You'd have to look at a few billion puzzles, to figure it out. :-))
@@SudokuSwami Ah that's right! If I returned to a different digit in the same cell on a weak link, that would be a Type 3. But so far it hasn't happened, so it does have me wondering. Thanks for your answer.
@@SudokuSwami Actually to be honest, I DID find one Type 3 a few days ago. But the return weak link was a surrogate weak link, so redrawing it as a strong link made it into a Type 2, shifting the cell of discontinuity. What has me curious is that usually in Sudoku, the less powerful patterns are more common, so I'd expect to find loops that only allow a single candidate elimination more often than those that actually solve a cell.
In the situation you described above, it doesn't matter if the "returning" Link is a Surrogate Weak Link. If the Link preceding it was a Strong Link, the Surrogate Weak Link must be perceived as WEAK, to keep the Chain working properly, (i.e., that If A is True, then B is False). You cannot view it as a Strong Link. Thus, you would have a DL Type 3.
In your Chain, let's call the Strongly-Linked Candidate, Candidate X, and let's call the Weakly-Linked Candidate, Candidate Y. So you would have two cases: Either the Cell is a Bi-Value Cell, or it has three or more Candidates. If it is a Bi-Value Cell, you could make a Strong Link from Y to X, and thus you would have a Type 2, with X being the solution. If it is NOT a Bi-Value Cell, then you can make a Weak Link from Y to X, and thus you would have a Type 1 with Candidate Y being eliminated. Either way, Candidate Y is FALSE. But you can simply view it as a DL Type 3, even though you are imagining the Chain is starting on the Strong Link.
What happened to video #42? I tried to get back to it but can not.
There was a section I decided to redo. So I took it down. The revised version should be up soon. Thanks for watching!!
One general question about AICs. Do they have to follow a clockwise or anti-clockwise pattern? Or is that just a general pattern and the only restriction is you can't use the same candidate twice? What are the explicit restrictions in this case?
Hi Jon. ALL AIC's can move in either direction, and if they are constructed correctly, they will be valid and make sense either way. The inferences will be reversed, depending on which way you envision it, (one direction or the other), but the RESULTS will be exactly the same, no matter which direction you go.
@@SudokuSwami So I can overlap my lines, cutting back and forth and zig-zig throughout the puzzle as much as I want?
And you are right. You CANNOT string the Chain through a specific Candidate that has already been used. The only way you can use a Candidate twice, is if you are returning to it, to connect a Loop. But even then, you are not really using it twice, because after the Loop is connected that Candidate will only appear ONCE in the completed Loop.
What exactly do you mean by "overlap" ?
@@SudokuSwami By overlapping I mean cutting back through the same cells, while using different candidates. You usually don't see this is solver when they draw the lines for strong and weak links because the lines would be over top of each other. I've only seen one example that really did this. Maybe if I allowed chains to have, say 30 links I'd see more of this. Then I could really understand if there are any restrictions. Here is that example.
gyazo.com/989e94b939fb302d3fbedd0411ad0bb8gyazo.com/989e94b939fb302d3fbedd0411ad0bb8