Thank you for the nice comment! If you need more practice exercises try Hodoku's Learning Mode. It's very good. Also, Empty Rectangle is a variant of the X-Chain. But take your time. Get good with Empty Rectangle's first. You should also learn 2-String Kites and Skyscrapers. Especially Skyscrapers because they are very common.
Although the explanation was still a bit fuzzy (my fault, I'm sure), I got the general idea. It was the exercises that really brought it home. And not just 1 or 2, but 10! Excellent job. Thanks!
Me too! Many times on these techniques is was act of looking for the same technique 10 times in row that really made me understand it. If you want to generate your own practice exercises, take a look at this video: ua-cam.com/video/jPssW_W3iH8/v-deo.html Once you go down the path of doing exercises you skills are going to improve dramatically. Keep me posted on your progress. I'm grad you stuck with the video an extracted all the value out of it!
The exercises really help a lot I have found for myself. Another way of looking at the A-B switch is by using what is call a Group Node. Take a look at this video on how to find X-Chains having Group Node links: ua-cam.com/video/FXMcfqmriNQ/v-deo.html
Thank you for the nice comment! When I did video #29 I purposely tried to keep the terminology to a minimum. To really understand the Empty Rectangle you need to understand the terminology around Sudoku Links. A Sudoku Link is just a fancy term for a relationship between two things in a Sudoku puzzle. I am currently working on redoing the 2-String Kite video but using the Sudoku Link terminology. After the 2-String Kite, my plan is to do a new Empty Rectangle tutorial but using the more advanced Sudoku Link terminology. It turns out, the Empty Rectangle is really a special type of X-Chain. If you are able understand this video at some point in your future you need to master X-Chains. X-Chains are the gateway to the most advanced puzzle solving techniques. Generally, I no longer look for Empty Rectangles. I just look for X-Chains and the Empty Rectangles get found in the process. The A-B switch terminology is still valid, but a more mainstream common terminology is to call the A and B part Group-Nodes and between them is a Group Link. Here is an Empty Rectangle pattern but diagrammed using Sudoku Links: imgur.com/Diaro3W Don't worry if you don't understand it right away. For now, just look at the diagram and think about it. It will become much clearer over time. Also, here is a really good wiki page on Chaining and Sudoku Links: hodoku.sourceforge.net/en/tech_chains.php This wiki page is probably a little more dense than my tutorials but I follow this set of wiki pages for most of my terminology I used in my videos. btw, here is a link to my first book if you are interested: www.amazon.com/dp/1736452606?ref_=pe_3052080_397514860 Sorry for the shameless plug on the book. But if you only knew the insane amount of work that went into the book you would instantly forgive me! Also, I am currently working on my second book which will include material on the Empty Rectangle and all the single-digit puzzle solving patterns. I will probably get my second book published by March 2022.
This is a fantastic tutorial - will be checking out other videos for other techniques on your channel. Thank you! At 13:08 I believe I found another empty rectangle using the same conjugate pair - there's another AB switch in block 6, meaning the 2 in r6c4 can also be removed.
Yes on the 13:08 removing 2 in r6c4. Nice catch! Thanks for the compliment. When I did this video I was trying to keep it simple. There's a more advanced version of this video if you are interested: ua-cam.com/video/FXMcfqmriNQ/v-deo.html
The AB-switch idea was another way of not getting too bogged down in terminology. My preferred way of thinking about Empty Rectangles is they are X-Chains having a Group Node. What is a Group Node is explained in this video: ua-cam.com/video/cVwV3MXXx5c/v-deo.html Once you learn what a group node is, then when you search for Empty Rectangles you will also find Finned X-Wings and Sashimi X-Wings at the same time.
Minor error at the 7:48 mark. We missed the first half of an x-wing in column 7. There was no AB switch in blocks 1,2 and blocks 4,5 so there was no Empty Rectangle Rectangle anyway. Also, very interesting enough at the 10:19 mark the puzzle shown has two different Empty Rectangles. The one shown the AB switch is found in block 5. But there is a second valid Empty Rectangle pattern using the same two conjugate pairs on row 8 with the AB switch in block 6. We used the second AB switch to solve the puzzle and what happens is a set of locked candidates occurs in block 5 which results in the same non-possible candidate being removed as the first Empty Rectangle. It's interesting to see two Empty Rectangles using the same first half of an x-wing in the same puzzle this way.
At the 1:00 minute mark in the video it explains how it works. As with all puzzle solving technique you have to visually confirm the logic. The AB switch terminology is just to help you begin to understand how the logic works. The AB switch part is not the whole story. But the trigger on the other side determines which cells are active in the block having the AB switch is the important concept I was trying to convey. Here's link to the Hodoku Wiki page on Empty Rectangles. Maybe this explanation will work better for you: hodoku.sourceforge.net/en/tech_sdp.php#er What is really useful in understanding how these work is by looking at several examples. At the 11:44 mark of the video the practice exercises begin. You can pause the video and try to find the ER yourself. And then resume the video to see the answer. After seeing the pattern several times hopefully it will help you understand it. When the trigger is false, the other corner of the Strong Link is active which kills the target candidate. When the Trigger is true or on, then the B part of the AB switch kills the target candidate. I tried really hard to make this easy to visualize with the graphics. You really need to convince yourself by running test scenarios with possible values.
Excellent explanation of the empty rectangle concept. The key is to look for the first half of the x-wing and the A-B switch and then hunt for the kill zone. So from the examples it looks like the “A-B switch” does not necessarily have to be three cells containing a naked triple. It could be four cells (example # 7). Is this correct? Thank you very much.
I think he missed your question. You're right, the AB switch doesn't need to be a naked triple, it can be four cells (or five, or even two). A-B switch happens when a digit's candidates lie exclusively in one row and one column (two axes) of a block. One axis (row or column) points at one of the X-Wing cells, then the other axis points at a potential elimination candidate. The elimination candidate must then line up with the opposite X-Wing cell. If everything lines up, you can remove that elimination candidate from the cell.
Thanks for the video, At 12:34, couldn't there be an empty rectangle with the same first half of xwing candidates, but with the AB switch being in box 9?
Great catch! Yes, this is definitely another Empty Rectangle: imgur.com/wKzshUV It's kind of cool example having both ends of a Strong Link connecting to AB switches this way! Great comment!
@@TylerHumphrey05 Yes, you can remove both. I've come a long way in my thinking about Empty Rectangles since I did video #29. At this point, I don't search for them. What I do is when I search for X-Chains I look for Group-Nodes in any direction. Finned X-Wings, Sashimi X-Wings, and Empty Rectangles are all types of X-Chains having Group Nodes and Group Links. Here's a later video on Empty Rectangles showing my current way of thinking about them and searching for them: ua-cam.com/video/FXMcfqmriNQ/v-deo.html Chaining becomes very important when solving the more difficult puzzles.
In the AB pattern, is it true that it doesn't matter if A exists? If A does not exists, it's a locked candidate; if A exist, it's an empty rectangle. Either way, The intersection of B and C2 cannot have the current number.
I'm not sure what you mean by A not existing. An Empty Rectangle is a type of X-chain having Group Nodes. Take look at this video: ua-cam.com/video/di1aM5X0h6Y/v-deo.htmlsi=0uA1UnXq02x98rSA
Sorry I was not clear. I mean that in the exmple, two cells are marked 'A'. It does not matter if these 'A' cell contains the current number. Either way, the number can be removed from the cell that sees both 'B' cell(s) and the second cell of the 'first half of x-wing'
The Empty Rectangle, Turbo Fish, 2-String Kite, and Skyscraper are all variants of the X-Chain. If you get good at X-Chains there are even a few other variants that show up not having any names but the concepts are the same as with Empty Rectangle. Here's the X-Chain tutorial: "dxSudoku #41 X-Chain Puzzle Solving Technique". Andoku 3s "Hard" level is really good for practicing X-Chains.
Here's a more advanced faster paced video on the Empty Rectangle puzzle-solving technique: ua-cam.com/video/FXMcfqmriNQ/v-deo.html I normally don't even search for Empty Rectangles when I do puzzles. The Empty Rectangle is a variant of the X-Chain using a one or two Group Nodes. So when I look for X-Chains, I just include Group-Nodes as part of my search. Here's a tutorial I did on the X-Chain if you are interested: ua-cam.com/video/di1aM5X0h6Y/v-deo.html X-Chains are very common and really good to know.
With an Empty Rectangle you start on the one side which is the first half of an X-Wing (aka, a Strong Link), from the two corner points, you move left or right to an adjacent block. Inside the block there are 2 to 5 cells which create a situation where some cells are force off because the end-point of the X-Wing half is set too a value. The only way to really understand it is to look at the logic shown in the video of the way the values can be set. But to find the AB switch all you have to do is move along the row or column to one of the adjacent blocks. I gave a longer more detailed explanation on Reddit.
Finally a clear empty rectangle tutorial with practice problems. Thank you!
Thank you for the nice comment! If you need more practice exercises try Hodoku's Learning Mode. It's very good. Also, Empty Rectangle is a variant of the X-Chain. But take your time. Get good with Empty Rectangle's first. You should also learn 2-String Kites and Skyscrapers. Especially Skyscrapers because they are very common.
Although the explanation was still a bit fuzzy (my fault, I'm sure), I got the general idea. It was the exercises that really brought it home. And not just 1 or 2, but 10! Excellent job. Thanks!
Me too! Many times on these techniques is was act of looking for the same technique 10 times in row that really made me understand it. If you want to generate your own practice exercises, take a look at this video:
ua-cam.com/video/jPssW_W3iH8/v-deo.html
Once you go down the path of doing exercises you skills are going to improve dramatically. Keep me posted on your progress. I'm grad you stuck with the video an extracted all the value out of it!
Thank you!!!!!!! I'm still a little lost on the A-B switch, but all of the tests really helped me understand it better!
The exercises really help a lot I have found for myself. Another way of looking at the A-B switch is by using what is call a Group Node. Take a look at this video on how to find X-Chains having Group Node links:
ua-cam.com/video/FXMcfqmriNQ/v-deo.html
Love this video. Finally a tutorial that clearly states the rules and systematically illustrates the technique for executing defined rules. Great job!
Thank you for the nice comment! When I did video #29 I purposely tried to keep the terminology to a minimum. To really understand the Empty Rectangle you need to understand the terminology around Sudoku Links. A Sudoku Link is just a fancy term for a relationship between two things in a Sudoku puzzle. I am currently working on redoing the 2-String Kite video but using the Sudoku Link terminology. After the 2-String Kite, my plan is to do a new Empty Rectangle tutorial but using the more advanced Sudoku Link terminology. It turns out, the Empty Rectangle is really a special type of X-Chain. If you are able understand this video at some point in your future you need to master X-Chains. X-Chains are the gateway to the most advanced puzzle solving techniques. Generally, I no longer look for Empty Rectangles. I just look for X-Chains and the Empty Rectangles get found in the process. The A-B switch terminology is still valid, but a more mainstream common terminology is to call the A and B part Group-Nodes and between them is a Group Link. Here is an Empty Rectangle pattern but diagrammed using Sudoku Links:
imgur.com/Diaro3W
Don't worry if you don't understand it right away. For now, just look at the diagram and think about it. It will become much clearer over time. Also, here is a really good wiki page on Chaining and Sudoku Links:
hodoku.sourceforge.net/en/tech_chains.php
This wiki page is probably a little more dense than my tutorials but I follow this set of wiki pages for most of my terminology I used in my videos.
btw, here is a link to my first book if you are interested:
www.amazon.com/dp/1736452606?ref_=pe_3052080_397514860
Sorry for the shameless plug on the book. But if you only knew the insane amount of work that went into the book you would instantly forgive me! Also, I am currently working on my second book which will include material on the Empty Rectangle and all the single-digit puzzle solving patterns. I will probably get my second book published by March 2022.
This is a fantastic tutorial - will be checking out other videos for other techniques on your channel. Thank you!
At 13:08 I believe I found another empty rectangle using the same conjugate pair - there's another AB switch in block 6, meaning the 2 in r6c4 can also be removed.
Yes on the 13:08 removing 2 in r6c4. Nice catch! Thanks for the compliment. When I did this video I was trying to keep it simple. There's a more advanced version of this video if you are interested:
ua-cam.com/video/FXMcfqmriNQ/v-deo.html
"Jason T" adds a really good AB-switch definition. Don't miss this chunk of crucial knowledge and see his reply to a question by Thomas Wilke!
The AB-switch idea was another way of not getting too bogged down in terminology. My preferred way of thinking about Empty Rectangles is they are X-Chains having a Group Node. What is a Group Node is explained in this video:
ua-cam.com/video/cVwV3MXXx5c/v-deo.html
Once you learn what a group node is, then when you search for Empty Rectangles you will also find Finned X-Wings and Sashimi X-Wings at the same time.
@@dxsudokuchannel Useful advise! Your support is quick and reliable, as usual! 😎
@@danielkoziarski8488 Thank you for your support of my channel. It's very much appreciated.
Minor error at the 7:48 mark. We missed the first half of an x-wing in column 7. There was no AB switch in blocks 1,2 and blocks 4,5 so there was no Empty Rectangle Rectangle anyway. Also, very interesting enough at the 10:19 mark the puzzle shown has two different Empty Rectangles. The one shown the AB switch is found in block 5. But there is a second valid Empty Rectangle pattern using the same two conjugate pairs on row 8 with the AB switch in block 6. We used the second AB switch to solve the puzzle and what happens is a set of locked candidates occurs in block 5 which results in the same non-possible candidate being removed as the first Empty Rectangle. It's interesting to see two Empty Rectangles using the same first half of an x-wing in the same puzzle this way.
I still don't understand how I know what is an AB switch and what is not
At the 1:00 minute mark in the video it explains how it works. As with all puzzle solving technique you have to visually confirm the logic. The AB switch terminology is just to help you begin to understand how the logic works. The AB switch part is not the whole story. But the trigger on the other side determines which cells are active in the block having the AB switch is the important concept I was trying to convey.
Here's link to the Hodoku Wiki page on Empty Rectangles. Maybe this explanation will work better for you:
hodoku.sourceforge.net/en/tech_sdp.php#er
What is really useful in understanding how these work is by looking at several examples. At the 11:44 mark of the video the practice exercises begin. You can pause the video and try to find the ER yourself. And then resume the video to see the answer. After seeing the pattern several times hopefully it will help you understand it.
When the trigger is false, the other corner of the Strong Link is active which kills the target candidate. When the Trigger is true or on, then the B part of the AB switch kills the target candidate. I tried really hard to make this easy to visualize with the graphics. You really need to convince yourself by running test scenarios with possible values.
Excellent explanation of the empty rectangle concept. The key is to look for the first half of the x-wing and the A-B switch and then hunt for the kill zone.
So from the examples it looks like the “A-B switch” does not necessarily have to be three cells containing a naked triple. It could be four cells (example # 7). Is this correct?
Thank you very much.
Thanks for the nice feedback! I'm currently working on the X-Chain video. It's very close to done.
I think he missed your question. You're right, the AB switch doesn't need to be a naked triple, it can be four cells (or five, or even two).
A-B switch happens when a digit's candidates lie exclusively in one row and one column (two axes) of a block. One axis (row or column) points at one of the X-Wing cells, then the other axis points at a potential elimination candidate. The elimination candidate must then line up with the opposite X-Wing cell. If everything lines up, you can remove that elimination candidate from the cell.
@@jrtomsic You are right. I did not understand the question. As you said, the AB can be 2 to 5 cells.
Jason T thank you very much for the explanation. I really appreciate you taking the time to answer my question
@@jrtomsic Very clean definition of AB-switch, that I was missing in the dxsudoku's video #29.
Thanks for the video,
At 12:34, couldn't there be an empty rectangle with the same first half of xwing candidates, but with the AB switch being in box 9?
Great catch! Yes, this is definitely another Empty Rectangle:
imgur.com/wKzshUV
It's kind of cool example having both ends of a Strong Link connecting to AB switches this way! Great comment!
@@dxsudokuchannel this is the one k found initially. I guess you can remove both of these?
@@TylerHumphrey05 Yes, you can remove both. I've come a long way in my thinking about Empty Rectangles since I did video #29. At this point, I don't search for them. What I do is when I search for X-Chains I look for Group-Nodes in any direction. Finned X-Wings, Sashimi X-Wings, and Empty Rectangles are all types of X-Chains having Group Nodes and Group Links. Here's a later video on Empty Rectangles showing my current way of thinking about them and searching for them:
ua-cam.com/video/FXMcfqmriNQ/v-deo.html
Chaining becomes very important when solving the more difficult puzzles.
In the AB pattern, is it true that it doesn't matter if A exists? If A does not exists, it's a locked candidate; if A exist, it's an empty rectangle. Either way, The intersection of B and C2 cannot have the current number.
I'm not sure what you mean by A not existing. An Empty Rectangle is a type of X-chain having Group Nodes. Take look at this video: ua-cam.com/video/di1aM5X0h6Y/v-deo.htmlsi=0uA1UnXq02x98rSA
Sorry I was not clear. I mean that in the exmple, two cells are marked 'A'. It does not matter if these 'A' cell contains the current number. Either way, the number can be removed from the cell that sees both 'B' cell(s) and the second cell of the 'first half of x-wing'
@@jasony001 This is the definition of a Group Node in a chaining sequence.
Great tutorial, thanks!
The Empty Rectangle, Turbo Fish, 2-String Kite, and Skyscraper are all variants of the X-Chain. If you get good at X-Chains there are even a few other variants that show up not having any names but the concepts are the same as with Empty Rectangle. Here's the X-Chain tutorial: "dxSudoku #41 X-Chain Puzzle Solving Technique". Andoku 3s "Hard" level is really good for practicing X-Chains.
Too much redundancy in the communication. You could speed it up a little.
Here's a more advanced faster paced video on the Empty Rectangle puzzle-solving technique:
ua-cam.com/video/FXMcfqmriNQ/v-deo.html
I normally don't even search for Empty Rectangles when I do puzzles. The Empty Rectangle is a variant of the X-Chain using a one or two Group Nodes. So when I look for X-Chains, I just include Group-Nodes as part of my search. Here's a tutorial I did on the X-Chain if you are interested:
ua-cam.com/video/di1aM5X0h6Y/v-deo.html
X-Chains are very common and really good to know.
Came from reddit, what is AB switch?
With an Empty Rectangle you start on the one side which is the first half of an X-Wing (aka, a Strong Link), from the two corner points, you move left or right to an adjacent block. Inside the block there are 2 to 5 cells which create a situation where some cells are force off because the end-point of the X-Wing half is set too a value. The only way to really understand it is to look at the logic shown in the video of the way the values can be set. But to find the AB switch all you have to do is move along the row or column to one of the adjacent blocks. I gave a longer more detailed explanation on Reddit.