The New Sudoku Players' Forum

[FairyTailed]

Hey everyone!

I decided to finally make an account here after lurking for a while. A puzzle was posted to another internet forum - you can find a picture of it here: https://imgur.com/a/XhyBZEX.

Upon looking through the comments, I read that people were solving this puzzle with Skyscrapers and Finned Swordfishes. Great techniques! The former usually forgotten about, the latter quite hard to spot. Myself I also spotted an Empty Rectangle and a 2-String Kite. Seems like an ordinary puzzle with a strong finish? Well... I reconsidered the state of the puzzle. Every single row, column or box has each candidate appear exactly twice. EXCEPT for the cells r679c3. This made me think: is this a case of BUG+3? I have never encountered a BUG bigger than 1 in my own solving - only seen a few examples of more on this forum.

If this IS a case of BUG applying, we have to look for a common digit they all force. Luckily, not too hard to find:

If r6c3 = 7 --> r3c3 = 3;
If r9c3 = 7 --> r3c3 = 3;
If r7c3 = 9 --> r8c3 = 7 --> r3c3 = 3.

QED!

The same digit will be achieved using other strategies.

Happy on finding this, I consulted SudokuWiki and Hodoku to check if this solve is correct. I put the puzzles in the exact same state and in both cases I banned every strategy that wasn't BUG. To my surprise, both solvers resorted to using Bowman's Bingo. They did no recognize this as a BUG.

This leaves my question to you: "Is this a case of BUG and are solvers not adapted to higher variants of BUG, or am I overlooking something?"

Cool thing: if BUG+3 is usable here, it puts the puzzle in a state where you can use BUG+1 to truely solve it until the end: https://imgur.com/a/e8Obpep. What a buggy puzzle.

I look forward to hearing from you!

[SpAce]

Hey everyone!

I decided to finally make an account here after lurking for a while.

Hello, and welcome to the forum. Looks like no one's picked up your question before.

This made me think: is this a case of BUG+3? I have never encountered a BUG bigger than 1 in my own solving - only seen a few examples of more on this forum.

Yes, it's BUG+3:

Code: Select all

.--------------.------------.------------.
| 4   9   6    | 7   5   12 | 8   12  3  |
| 2   1   8    | 6   9   3  | 7   5   4  |
| 37  5   37   | 4   8   12 | 12  6   9  |
:--------------+------------+------------:
| 35  27  4    | 8   12  9  | 35  17  6  |
| 1   8   35   | 35  6   7  | 4   9   2  |
| 79  6   29+7 | 35  12  4  | 35  8   17 |
:--------------+------------+------------:
| 59  3   15+9 | 2   7   6  | 19  4   8  |
| 6   4   79   | 1   3   8  | 29  27  5  |
| 8   27  12+7 | 9   4   5  | 6   3   17 |
'--------------'------------'------------'

........3......75..5.48......4..9...1...67..2.6.....8..3.2...4..4.1....58....56..

Btw, please post a similar text-based grid or at least the puzzle string next time, so it can be copy-pasted into a solver for analysis. They're easy to generate from either Hodoku or SudokuWiki which you seem to be using anyway.

If this IS a case of BUG applying, we have to look for a common digit they all force. Luckily, not too hard to find:

If r6c3 = 7 --> r3c3 = 3;
If r9c3 = 7 --> r3c3 = 3;
If r7c3 = 9 --> r8c3 = 7 --> r3c3 = 3.

Correct. A bit more complicated forcing chain would solve the whole puzzle:

7r9c3 -> 2r9c2
7r6c3 -> 7r8c8 -> 7r4c2 -> 2r9c2
9r7c3 -> 1r7c7 -> 7r9c9 -> 2r9c2
=> +2 r9c2

...but that's of course available more simply with any Turbot Fish variant (Skyscraper, Kite, Crane) as well as a Grouped Turbot Crane (i.e. Empty Rectangle) and others. I actually prefer your two-stepper (BUG+3 and BUG+1) here.

This leaves my question to you: "Is this a case of BUG and are solvers not adapted to higher variants of BUG, or am I overlooking something?"

Both Hodoku and SudokuWiki are capable of dealing with BUG+1 only. They can't find any higher variants.

Cool thing: if BUG+3 is usable here, it puts the puzzle in a state where you can use BUG+1 to truely solve it until the end

Yes, that works too.

[FairyTailed]

Btw, please post a similar text-based grid or at least the puzzle string next time, so it can be copy-pasted into a solver for analysis. They're easy to generate from either Hodoku or SudokuWiki which you seem to be using anyway.

I'm sorry, I will do this from now on! I'm not exactly sure how to do a text-based grid, so I'll paste strings for now.

...but that's of course available more simply with any Turbot Fish variant (Skyscraper, Kite, Crane) as well as a Grouped Turbot Crane(i.e. Empty Rectangle) and others. I actually prefer your two-stepper (BUG+3 and BUG+1) here.

I'm interested in the Crane you mention. I know Turbot Fish, 2-String-Kite and Skyscraper. However, I've never heard of a Crane. I've always been told that 2-String-Kites and Skyscrapers are variants of what is called a Turbot Fish. For long I believed these were the only two variants. Until I hit this puzzle - of which you can see the state here: https://i.imgur.com/uGDkwmu.png. Alternatively here is a string between the brackets: "1.....7.374.3.....8...5.496....6..85...4.5.6.561....749...7.53.......6.961...9..7".

As you can see by the image, we have a Turbot Fish on 1's. At least, it matches what is commonly described as one. However, it's not a Skyscraper, nor a normal 2-String-Kite. Is this the Crane you speak off? I've been looking on Google but I cannot seem to find anything about Cranes in Sudoku.

You also speak about Empty Rectangle's as Grouped Turbot Cranes. I'm interested to see why exactly that is once I know what a crane is.

Personally I used uniqueness r34c46 to remove the 1's from r4c46 to solve the puzzle, but I find it helpful and educative to try multiple endings and thus to look at different patterns.

Both Hodoku and SudokuWiki are capable of dealing with BUG+1 only. They can't find any higher variants.

Cool, I did not know. But I guess it makes sense? Else we could be running into puzzles where the computer applies BUG+N where N is extremely high, only because as a computer it's so efficient at finding the common digit. For a human, finding the common digit of a BUG+23 will at least be very time inefficient.

Big thank you, SpAce.

[SpAce]

I'm sorry, I will do this from now on! I'm not exactly sure how to do a text-based grid, so I'll paste strings for now.

Great! In Hodoku you can get the pencil mark grid from the menu "Edit::Copy Candidates", and in SudokuWiki by clicking "Email This Board". Then you can paste it into a text editor if you want to edit it or add some mark-up (use fixed font). When you paste it into a post, put it inside a "Code" block to keep the font fixed.

I'm interested in the Crane you mention. I know Turbot Fish, 2-String-Kite and Skyscraper. However, I've never heard of a Crane.

I would have been surprised if you had! I'm glad you asked -- and actually figured it out already:

I've always been told that 2-String-Kites and Skyscrapers are variants of what is called a Turbot Fish. For long I believed these were the only two variants. Until I hit this puzzle - of which you can see the state here: https://i.imgur.com/uGDkwmu.png. Alternatively here is a string between the brackets: "1.....7.374.3.....8...5.496....6..85...4.5.6.561....749...7.53.......6.961...9..7".

As you can see by the image, we have a Turbot Fish on 1's. At least, it matches what is commonly described as one. However, it's not a Skyscraper, nor a normal 2-String-Kite. Is this the Crane you speak off? I've been looking on Google but I cannot seem to find anything about Cranes in Sudoku.

You deduced it correctly! Turbot Crane is what's been traditionally called "Turbot Fish" (as a specific pattern). Your example would be:

Code: Select all

.--------------------.---------------------.------------------.
| 1    59     569    | 2689   2489   2468  | 7      25    3   |
| 7    4      569    | 3      29     26    | 128    125   128 |
| 8    23     23     | 17     5      17    | 4      9     6   |
:--------------------+---------------------+------------------:
| 234  239    2349   | 127    6      1237  | 123    8     5   |
| 23   78     78     | 4     *1239   5     | 1239   6     2-1 |
| 5    6      1      | 289    2389   238   | 239    7     4   |
:--------------------+---------------------+------------------:
| 9    28     248    | 1268   7      12468 | 5      3    *128 |
| 234  23578  234578 | 1258  *12348  12348 | 6     *124   9   |
| 6    1      23458  | 258    2348   9     | 28     24    7   |
'--------------------'---------------------'------------------'

Turbot Crane: (1)r5c5 = r8c5 - r8c8 = (1)r7c9 => -1 r5c9

The original name "Turbot Fish" was ambiguous because it's also the family name, which makes accurate communication impossible. If you say a pattern is a Turbot Fish, there's no way to know if you mean Skyscraper, 2-String Kite, or the specific Turbot Fish pattern -- because they're all Turbot Fishes.

You can see the practical problem in Hodoku, for example, because there's no way to look for that particular pattern specifically. If you filter Turbot Fishes, you'll get all three kinds. Only Skyscrapers and Kites can be filtered as specific patterns but not the third one. It can also be found under Empty Rectangles if you turn on "Allow ERs with two candidates", but then it gets mixed with all the normal ERs. So, there's no way around the problem, and it's because the original naming of these patterns wasn't very well thought through.

That's why we (or I) came up with the new unambiguous name Turbot Crane, giving it an equal footing with the other two Turbot Fishes. The name is roughly related to the shape of the pattern. You can find the original discussion here. I don't know if the name will ever catch on, but at least it's now been adopted by tarek in the Sukaku Explainer. That gives me hope.

You also speak about Empty Rectangle's as Grouped Turbot Cranes. I'm interested to see why exactly that is once I know what a crane is.

All three Turbot Fishes have grouped counterparts, meaning that the pattern contains at least one group link (as opposed to just simple links). We have Grouped Skyscrapers (same as Finned/Sashimi X-Wing), Grouped 2-String Kites, and now also Grouped Turbot Cranes. Traditionally the last one has been called "Empty Rectangle", but it's another ambiguous name because it's been used to mean either the full pattern or just a hinge strong link in a box (and not even necessarily a grouped one). In this discussion it was eventually agreed that to avoid the ambiguity, we should use "Grouped Turbot Crane" for the full pattern (in line with the other two Grouped Turbot Fishes), and "Empty mini-Rectangle" (EmR) for the other use.

In other words, we now have these two logical family trees which include all six kinds of Turbot Fishes:

Code: Select all

                                 AICs
                                   |
                               X-Chains                   
                                   |                     
                             Turbot Fishes               
                                   |                     
           -----------------------------------------------   
          |                        |                      |
     [Skyscraper]           [2-String Kite]         [Turbot Crane]

Code: Select all

                                 AICs
                                   |
                           Grouped X-Chains
                                   |
                         Grouped Turbot Fishes
                                   |
           -------------------------------------------------
          |                        |                        |
[Grouped Skyscraper]    [Grouped 2-String Kite]    [Grouped Turbot Crane]

Here are some examples of Turbot Cranes from your original puzzle (a treasure trove of Turbot Fishes in general):

Turbot Cranes + Grouped Turbot Cranes: Show

Code: Select all

.---------------.------------.--------------.
| 4    9    6   | 7   5   12 | 8    12   3  |
| 2    1    8   | 6   9   3  | 7    5    4  |
| 37   5    37  | 4   8   12 | 12   6    9  |
:---------------+------------+--------------:
| 35  *27   4   | 8   12  9  | 35  *17   6  |
| 1    8    35  | 35  6   7  | 4    9    2  |
| 79   6    279 | 35  12  4  | 35   8    17 |
:---------------+------------+--------------:
| 59   3    159 | 2   7   6  | 19   4    8  |
| 6    4    79  | 1   3   8  | 29  *27   5  |
| 8    2-7  127 | 9   4   5  | 6    3   *17 |
'---------------'------------'--------------'

Turbot Crane: (7)r4c2 = r4c8 - r8c8 = (7)r9c9 => -7 r9c2

Code: Select all

.--------------.------------.---------------.
| 4    9   6   | 7   5   12 | 8    12   3   |
| 2    1   8   | 6   9   3  | 7    5    4   |
| 37   5   37  | 4   8   12 | 12   6    9   |
:--------------+------------+---------------:
| 35  *27  4   | 8   12  9  | 35  *17   6   |
| 1    8   35  | 35  6   7  | 4    9    2   |
| 79   6   279 | 35  12  4  | 35   8   *17  |
:--------------+------------+---------------:
| 59   3   159 | 2   7   6  | 19   4    8   |
| 6    4   79  | 1   3   8  | 29   27   5   |
| 8   *27  127 | 9   4   5  | 6    3    1-7 |
'--------------'------------'---------------'

Turbot Crane: (7)r9c2 = r4c2 - r4c8 = (7)r6c9 => -7 r9c9

Code: Select all

.--------------.------------.---------------.
| 4    9   6   | 7   5   12 | 8    12    3  |
| 2    1   8   | 6   9   3  | 7    5     4  |
| 37   5   37  | 4   8   12 | 12   6     9  |
:--------------+------------+---------------:
| 35  *27  4   | 8   12  9  | 35   1-7   6  |
| 1    8   35  | 35  6   7  | 4    9     2  |
| 79   6   279 | 35  12  4  | 35   8     17 |
:--------------+------------+---------------:
| 59   3   159 | 2   7   6  | 19   4     8  |
| 6    4   79  | 1   3   8  | 29  *27    5  |
| 8   *27  127 | 9   4   5  | 6    3    *17 |
'--------------'------------'---------------'

Turbot Crane: (7)r4c2 = r9c2 - r9c9 = (7)r8c8 => -7 r4c8

Code: Select all

.---------------.------------.--------------.
| 4   9    6    | 7   5   12 | 8    12   3  |
| 2   1    8    | 6   9   3  | 7    5    4  |
| 37  5    37   | 4   8   12 | 12   6    9  |
:---------------+------------+--------------:
| 35  27   4    | 8   12  9  | 35  *17   6  |
| 1   8    35   | 35  6   7  | 4    9    2  |
| 79  6    29-7 | 35  12  4  | 35   8   *17 |
:---------------+------------+--------------:
| 59  3    159  | 2   7   6  | 19   4    8  |
| 6   4   *79   | 1   3   8  | 29  *27   5  |
| 8   27   127  | 9   4   5  | 6    3    17 |
'---------------'------------'--------------'

Turbot Crane: (7)r8c3 = r8c8 - r4c8 = (7)r6c9 => -7 r6c3

Code: Select all

.----------------.------------.-------------.
| 4    9    6    | 7   5   12 | 8   12   3  |
| 2    1    8    | 6   9   3  | 7   5    4  |
| 37   5    37   | 4   8   12 | 12  6    9  |
:----------------+------------+-------------:
| 35   27   4    | 8   12  9  | 35  17   6  |
| 1    8    35   | 35  6   7  | 4   9    2  |
| 79   6    29-7 | 35  12  4  | 35  8   *17 |
:----------------+------------+-------------:
| 59   3    159  | 2   7   6  | 19  4    8  |
| 6    4   *79   | 1   3   8  | 29  27   5  |
| 8   *27  *127  | 9   4   5  | 6   3   *17 |
'----------------'------------'-------------'

Grouped Turbot Crane: (7)r6c9 = r9c9 - r9c23 = (7)r8c3 => -7 r6c3

Code: Select all

.----------------.------------.-------------.
|  4    9    6   | 7   5   12 | 8   12   3  |
|  2    1    8   | 6   9   3  | 7   5    4  |
|  37   5    37  | 4   8   12 | 12  6    9  |
:----------------+------------+-------------:
|  35  *27   4   | 8   12  9  | 35  17   6  |
|  1    8    35  | 35  6   7  | 4   9    2  |
| *79   6   *279 | 35  12  4  | 35  8   *17 |
:----------------+------------+-------------:
|  59   3    159 | 2   7   6  | 19  4    8  |
|  6    4    79  | 1   3   8  | 29  27   5  |
|  8    2-7  127 | 9   4   5  | 6   3   *17 |
'----------------'------------'-------------'

Grouped Turbot Crane: (7)r9c9 = r6c9 - r6c13 = (7)r4c2 => -7 r9c2

Personally I used uniqueness r34c46 to remove the 1's from r4c46 to solve the puzzle, but I find it helpful and educative to try multiple endings and thus to look at different patterns.

Yes, that's always a good idea! You learn much more if you're not satisfied with the first pattern you find.

Both Hodoku and SudokuWiki are capable of dealing with BUG+1 only. They can't find any higher variants.

Cool, I did not know. But I guess it makes sense? Else we could be running into puzzles where the computer applies BUG+N where N is extremely high, only because as a computer it's so efficient at finding the common digit.

It makes sense for very high Ns, but low Ns (like 1..5) are actually often very easy for humans. The fact that most software solvers don't use anything but +1 is a weakness, because it means they can't solve some puzzles as easily or elegantly as skilled humans.

For a human, finding the common digit of a BUG+23 will at least be very time inefficient.

Exactly. But it can be an educational exercise!

Big thank you, SpAce.

No problem! I hope you'll stay active. You seem to have the right attitude for learning. I'm glad if we can encourage that.

[FairyTailed]

Great! In Hodoku you can get the pencil mark grid from the menu "Edit::Copy Candidates", and in SudokuWiki by clicking "Email This Board". Then you can paste it into a text editor if you want to edit it or add some mark-up (use fixed font). When you paste it into a post, put it inside a "Code" block to keep the font fixed.

Thank you! Easier than I thought it would be.

I would have been surprised if you had! I'm glad you asked -- and actually figured it out already: (...) You deduced it correctly! Turbot Crane is what's been traditionally called "Turbot Fish" (as a specific pattern). (...)

The original name "Turbot Fish" was ambiguous because it's also the family name, which makes accurate communication impossible. If you say a pattern is a Turbot Fish, there's no way to know if you mean Skyscraper, 2-String Kite, or the specific Turbot Fish pattern -- because they're all Turbot Fishes.

You can see the practical problem in Hodoku, for example, because there's no way to look for that particular pattern specifically. If you filter Turbot Fishes, you'll get all three kinds. Only Skyscrapers and Kites can be filtered as specific patterns but not the third one. It can also be found under Empty Rectangles if you turn on "Allow ERs with two candidates", but then it gets mixed with all the normal ERs. So, there's no way around the problem, and it's because the original naming of these patterns wasn't very well thought through.

That's why we (or I) came up with the new unambiguous name Turbot Crane, giving it an equal footing with the other two Turbot Fishes. The name is roughly related to the shape of the pattern. You can find the original discussion here. I don't know if the name will ever catch on, but at least it's now been adopted by tarek in the Sukaku Explainer. That gives me hope.

Glad I was able to solve that then! On a serious note: the idea of a Crane specifically popped the puzzle I provided above into my mind - I really like that name. It does visually look like one. And I obviously entirely agree with the semantic value here. It frustrated me that there was a Turbo Fish that wasn't a Skyscraper or 2-String-Kite without a proper name in itself. Frankly I think the name "Turbot Fish" on its own can potentially be confusing because the "Fish" does not match up to what a Fish is usually used for (Swordfish, Jellyfish, ...). Although, visually we can recognize it as looking like a turbot. I prefer names that have visual recognition of the pattern involved. That's why I like your Crane and that's why I prefer using Bent Triple, Bent Quadruple (and higher) over XY(Z)-Wing and Sue de Coq. I think visual representation makes it easier for newer people to learn the patterns - both understanding and finding them.

It's good to know that Turbot Fish can now ultimately be subdivised into three categories. If any puzzle pops up on other internet fora where this situation applies, I will describe the technique as a Crane and make the distinction from other Turbot Fish. I will also provide with useful links to your comments.

On the note of a Crane being a 2-candidate ER, I think we can also state the following: "If an ER is situated on a candidate limited to two cells, it might as well not be an ER. Because while the premise that the candidate should occupy exactly one row and column is true, we cannot determine for which row and column this is true (there's 2 possibilities) regardless of the Strong Link indicating where it is." A visual representation will look like this: https://imgur.com/a/LGesQPc. The Strong Link on 1's in column 5 (orange cells) indicates that the ER is formed on r8c9 where the 9 is situated (red cell). Whereas, when we look at box 9 in itself, we cannot logically determine whether the ER is formed on r8c9 or r7c8 where the 3 is situated (green cell). Therefore, we either have 2 ER's on the exact same cells or no ER at all. Even if we accept there are 2, it doesn't really go by standard ER rules because while both ER instances are located in one row and column, they are not the same row and column. Let me know what you think about this!

All three Turbot Fishes have grouped counterparts, meaning that the pattern contains at least one group link (as opposed to just simple links). We have Grouped Skyscrapers (same as Finned/Sashimi X-Wing), Grouped 2-String Kites, and now also Grouped Turbot Cranes. Traditionally the last one has been called "Empty Rectangle", but it's another ambiguous name because it's been used to mean either the full pattern or just a hinge strong link in a box (and not even necessarily a grouped one). In this discussion it was eventually agreed that to avoid the ambiguity, we should use "Grouped Turbot Crane" for the full pattern (in line with the other two Grouped Turbot Fishes), and "Empty mini-Rectangle" (EmR) for the other use.

I don't think I'm quite understanding the logic behind it. Although admittedly, I've not yet checked out the links as I'm writing this comment - I will. It's safe to say though that when it will come to mathematical/logical determination, I have to admit defeat. I'm not sure if these threads will contain comments that require a certain mathematical insight or level, but I have not had true math courses since High School. I had 8 hours of maths a week, but I've been a Law Student for 5 years now. I've read multiple threads about Sudoku on this forum where the maths/logic just went straight over my head at first few glances. Of course I won't let this stop me from reading onwards, but I guess it's a precaution I have to give .

Edit: What I'm trying to say is: I don't immediately see the difference on the Grouped Crane vs ER.

Here are some examples of Turbot Cranes from your original puzzle (a treasure trove of Turbot Fishes in general)

Glad I managed to provide you with that glorious puzzle then!

Personally I used uniqueness r34c46 to remove the 1's from r4c46 to solve the puzzle, but I find it helpful and educative to try multiple endings and thus to look at different patterns.

Yes, that's always a good idea! You learn much more if you're not satisfied with the first pattern you find.

Frankly, I really enjoy solving puzzle with uniqueness technique. It's the mixed (not really mixed, but yeah) sentiment on "puzzles having a unique solution" that in the end made me look for seconds in case people don't like to use those strategies.

It makes sense for very high Ns, but low Ns (like 1..5) are actually often very easy for humans. The fact that most software solvers don't use anything but +1 is a weakness, because it means they can't solve some puzzles as easily or elegantly as skilled humans.

For a human, finding the common digit of a BUG+23 will at least be very time inefficient.

Exactly. But it can be an educational exercise!

Humans reign supreme! I'm aware that thread of BUG+23 existed, hence I specifically went for that number!

No problem! I hope you'll stay active. You seem to have the right attitude for learning. I'm glad if we can encourage that.

I will try to stay active! Thank you for that nice comment. Although, I'm far from perfect. To provide an example: I'm not a big fan of AIC, Loops and long XY-chains. When these strategies occupy more than 3 boxes, I usually arrive the point where I have trouble keeping track of them in my brain. Furthermore, I'd only use them if I simply could not find pattern logic. This leaves me in a situation where I'm most-likely going to have to colour or note on a different piece of paper. One can get satisfaction from this because it can solve literally any puzzle. Personally I don't get too much satisfaction from it because I think the intellectual capacity required to apply, understand and find these long chains is rather low. This is not meant as a dent towards people using these techniques, but to the techniques themselves. Frankly colouring to me is too simple for how effective it is - which puts it in the "I don't like this too much"-bracket for me, together with Bowman's Bingo. I'm willing to change my view on this, but I would still never resort to colouring before checking off every pattern logic we know. However, I've never really been convinced by anyone.

Have a nice day!

[FairyTailed]

https://imgur.com/a/pRA5Ukq. Another Interesting puzzle. I found this looking something up.

Code: Select all

.--------------.---------------.--------------.
| 7   28   89  | 236   5    4  | 39   1    68 |
| 19  6    3   | 8     7    19 | 4    2    5  |
| 5   128  4   | 1236  136  69 | 7    39   68 |
:--------------+---------------+--------------:
| 2   7   *56  | 4     36   58 | 389  369  1  |
| 4  13  *156  | 9     2    58 | 38   36   7  |
|*69  38   89  |13-6   136  7  | 5    4    2  |
:--------------+---------------+--------------:
| 8   5    2   |*16    4    3  | 16   7    9  |
| 3   9    16  | 7     8    2  | 16   5    4  |
|*16  4    7   | 5     9   *16 | 2    8    3  |
'--------------'---------------'--------------'


The website of HoDoKu lists this as an Empty Rectangle (http://hodoku.sourceforge.net/en/tech_sdp.php). This seems to be entirely wrong. Not just because we consider this to be a Crane, but also because they didn't actually use the Empty Rectangle.

I assume the logic applied is that, since r6c1 {69} is bivalue, the ER can be looked at from both cases of that cell. Either it's a 6 and r6c4 is not {13-6} or it is a 9, in which case the Strong Link on {16} in r9 forces r7c4 to be a 6 {6-1} and thus r6c4 is not a 6. While this is a totally valid technique (it's a Crane), it doesn't use the logic of the Empty Rectangle. Rather than actually using the opposing row/column of 6's, it uses the case where r6c1 is not a 6 simply because it is bivalue.

I find it strange the writer of the article would consider this to be an Empty Rectangle. Even more so because there's actually a real Empty Rectangle there which they do not use. Furthermore HoDoKu recognizes this as a Turbo Fish (which means it's what we consider to be a Crane) and not as an Empty Rectangle.

Code: Select all

.--------------.---------------.--------------.
| 7   28   89  | 236   5    4  | 39   1    68 |
| 19  6    3   | 8     7    19 | 4    2    5  |
| 5   128  4   | 1236  136  69 | 7    39   68 |
:--------------+---------------+--------------:
| 2   7   *56  | 4     36   58 | 389  369  1  |
| 4   13  *156 | 9     2    58 | 38   36   7  |
|*69  38   89  | 13-6 136  7   | 5    4    2  |
:--------------+---------------+--------------:
| 8   5    2   |*16    4    3  |*16   7    9  |
| 3   9   *16  | 7     8    2  |*16   5    4  |
| 16  4    7   | 5     9    16 | 2    8    3  |
'--------------'---------------'--------------'


The case of the Empty Rectangle itself is actually very interesting. Would this be what we call a "Grouped Empty Rectangle"? Traditionally an Empty Rectangle has a strong link on at least conjugate pairs (but usually on locked pairs, like here). Here however, there's a link on 3 pairs. r8c3 {16} ---> r8c7 {16} ---> r8c6 {16} ---> r6c4 {16}.

At least this is a Grouped Link or Double Link. I'm not sure on what terminology is appropriate here.

Hope my formatting works out fine.

Thoughts?

[FairyTailed]

I'm sorry for a third reply - but at the same time I'm not. Someone posted a puzzle they generated on Reddit and it is just absolutely gorgeous. Not only does it look like a beetle
and is it fully semitrical (https://imgur.com/a/qq23ibI), code: "..5.9.1..3.......5.82...94..4.5.9.6...6.1.4...3..6..5.5..1.4..21..678..4.........", it is literally filled with Cranes, Empty Rectangles, Skyscrapers, 2-String-Kites and everything else you'd like. Entre Autres, I found an ER that interacts with a Turbot Crane as its Strong Link for a double elimination. Just wow.

To not clutter myself with redundant work, I will refer to my comment on Reddit to give you my journey and the way the solver goes about the puzzle in this link: https://www.reddit.com/r/sudoku/comments/elgofg/diabolical_puzzle/fdi85x5/

If posting such link is against the rules of the forum, please let me know and I will remove it.

[SpAce]

Hi FairyTailed,

I'll reply to the other stuff later when I have more time, but first this.

Someone posted a puzzle they generated on Reddit and it is just absolutely gorgeous. Not only does it look like a beetle
and is it fully semitrical (https://imgur.com/a/qq23ibI), code: "..5.9.1..3.......5.82...94..4.5.9.6...6.1.4...3..6..5.5..1.4..21..678..4.........", it is literally filled with Cranes, Empty Rectangles, Skyscrapers, 2-String-Kites and everything else you'd like. Entre Autres, I found an ER that interacts with a Turbot Crane as its Strong Link for a double elimination. Just wow.

A fun puzzle. I've been taking a break from solving puzzles, but I made an exception for this. If you're interested, below you'll find my three-step solution which was found completely without pencil marks (although shown in the steps for clarity). I normally start puzzles like that and then add pencil marks if I get stuck, but this was easy enough to solve all the way without them. In fact, I find obvious deadly patterns and single digit patterns about as easy to see that way, and they were enough to crack this.

my solution: Show

Step 1.

Code: Select all

.-------------------.------------.------------------.
|   4     c67+  5   | 278  9  27 | 1    3    b6+8-7 |
|   3      1    9   | 78   4  6  | 278  278   5     |
|  d67+    8    2   | 3    5  1  | 9    4     67+   |
:-------------------+------------+------------------:
|   27     4    17  | 5    8  9  | 237  6     137   |
|   2789   5    6   | 27   1  3  | 4    278   789   |
|   2789   3    178 | 4    6  27 | 278  5     1789  |
:-------------------+------------+------------------:
|   5      9    78  | 1    3  4  | 6    78    2     |
|   1      2    3   | 6    7  8  | 5    9     4     |
| ae6+8-7  67+  4   | 9    2  5  | 378  1     37-8  |
'-------------------'------------'------------------'

BUG-Lite(67)+2 r139,c129,b137:

8r9c1 == (8-6)r1c9 = r1c2 - r3c1 = 6r9c1 - loop => -8 r9c9, -7 r1c9,r9c1

Step 2.

Code: Select all

.----------------.------------.------------------.
|  4    c67  5   | 278  9  27 | 1    3      68   |
|  3     1   9   | 78   4  6  | 278  28-7   5    |
| b67    8   2   | 3    5  1  | 9    4     a67   |
:----------------+------------+------------------:
|  27    4   17  | 5    8  9  | 237  6      137  |
|  2789  5   6   | 27   1  3  | 4    278    789  |
|  2789  3   178 | 4    6  27 | 278  5      1789 |
:----------------+------------+------------------:
|  5     9  e78  | 1    3  4  | 6   f78     2    |
|  1     2   3   | 6    7  8  | 5    9      4    |
|  68   d67  4   | 9    2  5  | 378  1      3-7  |
'----------------'------------'------------------'

L1-Wing:

7r3c9 = r3c1 - r1c2 = r9c2 - r7c3 = 7r7c8 => -7 r2c8,r9c9

Step 3.

Code: Select all

.--------------.------------.-------------------.
| 4    67  5   | 278  9  27 | 1     3      68   |
| 3    1   9   | 78   4  6  | 278   28     5    |
| 67   8   2   | 3    5  1  | 9     4      67   |
:--------------+------------+-------------------:
| 2    4  b17  | 5    8  9  | 3     6     a17   |
| 789  5   6   | 27   1  3  | 4     28-7   789  |
| 789  3   178 | 4    6  27 | 278   5      1789 |
:--------------+------------+-------------------:
| 5    9  c78  | 1    3  4  | 6    d78     2    |
| 1    2   3   | 6    7  8  | 5     9      4    |
| 68   67  4   | 9    2  5  | 78    1      3    |
'--------------'------------'-------------------'

Skyscraper:

7r4c9 = r4c3 - r7c3 = 7r7c8 => -7 r5c8; stte

To not clutter myself with redundant work, I will refer to my comment on Reddit to give you my journey and the way the solver goes about the puzzle in this link: [url]https://www.reddit.com/r/sudoku/comments/elgofg/diabolical_puzzle/fdi85x5/

If posting such link is against the rules of the forum, please let me know and I will remove it.

I don't think there are such rules (though can't know for sure). Personally I find it interesting and beneficial for all if different forums get glances of each others' discussions. Seems like there's a relatively active sudoku community on reddit. I wasn't aware of it until recently when someone from there joined our forum (but unfortunately disappeared soon). (Btw, thanks for making the Crane known there! Glad to see it got a good reception.)

[oldenumber77]

Absolutely. Yes. Here is a graphical explanation. https://imgur.com/a/BsCe7sv