dxSudoku #29 Empty Rectangle Puzzle Solving Technique 

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.

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.

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: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-jPssW_W3iH8.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: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-FXMcfqmriNQ.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: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-cVwV3MXXx5c.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.

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: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-FXMcfqmriNQ.html

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.

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.

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: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-FXMcfqmriNQ.html Chaining becomes very important when solving the more difficult puzzles.

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.

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.

Here's a more advanced faster paced video on the Empty Rectangle puzzle-solving technique: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-FXMcfqmriNQ.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: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-di1aM5X0h6Y.html X-Chains are very common and really good to know.