dxSudoku #62 Avoidable Rectangle Type 1

[@WindowsXP_YT]

1:47 Avoidable Rectangle (Type 1) If this square was 8, then these squares would be interchangeable and the puzzle would have two solutions. One solution where this square was 8 and another where it was 9. Therefore, you can eliminate 8 from this square.

[@dxsudokuchannel]

Yes, this is correct. It is the potential for ambiguity we are eliminating.

[@finecutpost]

I can see that you have put a lot of work into all your video's thank you very much for sharing your knowledge

[@dxsudokuchannel]

You are very welcome

[@headslmmer33]

In solution number 5 is the 7 and 1 in the 2nd and 7th rows also an avoidable rectangle by this same logic?

[@dxsudokuchannel]

Hi, I'm assuming you are talking about the 2-4 in columns 1&2 of rows 2 and 7, and at the 5:13 mark in the video. If so, here is the problem with the 2-4, the 2-4 in row 2 are givens. All the uniqueness techniques are about having more than one solution. Or a situation where you have to make a guess to solve the puzzle. Since the 2-4 in row 2 are givens, there is only one choice with the 2-4 in row 7. Since there's no guessing required to solve the puzzle, this is not an Avoidable Rectangle. I hope I got the right question.

[@headslmmer33]

@@dxsudokuchannel No, I was talking about the 7-1s in rows 2 and 7 but I totally missed the 2x2x2 rule so I see why it would be that now

[@dxsudokuchannel]

@@headslmmer33 I once had a huge argument with someone about the 2-2-2 rule. I was trying to convince them if it were not 2-2-2 it could not be ambiguous. I could see it intuitive but I don't think I was able to convince them with a proof or with language. At some point I may spend more time on this idea. At some point you need to take a look at AICs. AICs are somewhat like a universal puzzle-solving technique and they get past the UR type techniques. I still do UR Type 1s and 2s because they are so easy to find.

[@johnsonken1947]

I may be missing something but in Solution # 1 why is cell in Row 1 , 8 not a # 2. You have a 9 and 8 in row 9.

[@dxsudokuchannel]

This is a good question. The reason is, when givens are involved, that is, that 9 and 8 in row 9, you can't have a uniqueness situation. Uniqueness problems only occur when the four cells are values chosen by us solving the puzzle. Here's my favorite wiki page on uniqueness techniques: hodoku.sourceforge.net/en/tech_ur.php Take a closer look at this sentence: "A "Unique Rectangle" (UR) consists of four cells that occupy exactly two rows, two columns, and two boxes. All four cells have the same two candidates left..." The key thing here is "candidates" not "givens." Once givens are involved, the uniqueness problem doesn't happen. I hope this helps. Let me know and I will try to explain it further. But these are advanced Sudoku solving concepts that are tricky to explain.

[@an9431]

Thanks a lot for the extensive work. I have a major problem as many times this technique work and in quite few it doesn’t work. Possibly a caveat is there which I miss. I stick to the principles of 3 cells must have have been sorted and the fourth cell has more than one candidate besides the one in question. Also explain please what you mean by a “given”. Thanks a lot again

[@an9431]

And please on basis you made the colours blue and black.

[@an9431]

On what basis? Thanks

[@dxsudokuchannel]

If any of the four cells has a given then it's not a uniqueness box. I talk about the definition of "given" in this video: kzbin.info/www/bejne/Y33Vgaudl75-gpY Also, here's a really good wiki page on the uniqueness techniques: hodoku.sourceforge.net/en/tech_ur.php Many of the videos on my channel come from the techniques featured on the wiki pages I just referenced.

[@dxsudokuchannel]

Also, here's a better explanation of the logic behind all uniqueness techniques: kzbin.info/www/bejne/iILQmH2orqiUY8U The logic works as follows, we first assume our puzzle has only one solution. So the all the uniqueness techniques work on the idea of preventing the possibility of having two solutions because we are banking on the fact our puzzle only has one solution.

[@dxsudokuchannel]

@@an9431 I use Hodoku for most of my videos. Black means it's a given. Blue means it's a value set by us as we solve the puzzle.

[@jasonleonardchen756]

Hello, I have a serious problem to find the type 1, because I don´t have a clue how the search works.... I search and search, but mostly no results.... I am only successful in 3 excersices.... Can you please help me??? Thank you so much!!!....

[@dxsudokuchannel]

First, make sure for Avoidable Rectangle Type 1 you only concentrate on cells where you set the values. Do not consider any cell having a "given" as part of the pattern. So you are looking for pairs of cells sharing the same house having values set. If the two cells line up horizontally, you search down then up for a match. If the cells line up vertically, you search right then left for a match. A match is where one cell has one of the two values and the other cell as the other matching value as a possible candidate. The problem is once these values are set (not givens), you have situation where a puzzle has two solutions. In order to master finding these buggers, I would suggest you keep practicing until you've mastered the search algorithm. I would use Hodoku's "Learning Mode". I go into detail on how to use Hodoku's Learning mode in this video: kzbin.info/www/bejne/oIHWpIqVjJicfpo And this video: kzbin.info/www/bejne/Y5e3hnmAls-bidU Hodoku's Learning Mode is identical to the practice exercises I present in this video. So you will be able to create more practice exercises on your own as many as you need until you master the search algorithm. This is what I do when I am learning a new technique or prepping for one of my videos. Many times when I do 20 or so practice exercises I develop many new insights which I share in my videos.

[@prabhoochandshiboo8390]

In 2nd test I found in row 4 that is 5 and 6, and in row 9 that is 6 and 5/8. Is it ok sir ?.thank for the tecnic

[@dxsudokuchannel]

The Avoidable Rectangle Type I only work with the blue numbers not the numbers in black. The numbers in black are the original "givens". The blue numbers are the "values" which we set in each cell as we solve the puzzle. The reason the blue numbers matter is because we can interchange blue numbers if there is the possibility of ambiguity. The numbers in black are set in stone because the numbers in black define the solution path for the puzzle. I hope this helps. Please comment again and I will try to explain further if I am not making this clear.

[@an9431]

I got it now, this technique only apply for the numbers you introduce, not those “ given”. As with given the rule is not applicable as this allows the formidable crossing e.g. 4, 8,4,8.

[@dxsudokuchannel]

Hi, yes, that is correct. I talk about the definition of "given" in this video: kzbin.info/www/bejne/Y33Vgaudl75-gpY Also, here's a really good wiki page on the uniqueness techniques: hodoku.sourceforge.net/en/tech_ur.php Many of the videos on my channel come from the techniques featured on the wiki pages I just referenced.

[@_Pike]

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[@dxsudokuchannel]

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