## Hinge (ER) doesn't work?

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### Hinge (ER) doesn't work?

..16...7.6...798..4..82..6....9...367.4.8.19239.....8..4..1...7..329...8.....89..
Normally when I look at a Hinge the elimination is obvious once you have confirmed that you have a true case, but not here. Have I missed something? This comes from the October18 posting and is the position reached by SpAce.
The Box Analysis of the puzzle at this point confirms that there are possible eliminations in candidate 3. We do have a Conjugate Pair in 3s in column 5 and there is a Hinge or ER cornered at r9c9 which can see into one end of this CP. Therefore it should be all go to eliminate 3 at r1c9, but is it?
Obviously if 3r1c5 then r1c9 <> 3, BUT 3r9c5 => 3r7c7, which does not definitely rule out 3 from r1c9. The final solution does not have 3 at r1c9, and even if I had assumed the Hinge Elimination to be true it probably would not have helped much at that time. However, I would be interested in comments about why this case does seem to fit the criteria but does not seem to be true in both cases of the CP.
Yogi
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### Re: Hinge (ER) doesn't work?

Yogi wrote:We do have a Conjugate Pair in 3s in column 5 and there is a Hinge or ER cornered at r9c9 which can see into one end of this CP. Therefore it should be all go to eliminate 3 at r1c9, but is it?

No. It seems that you've misunderstood something about the workings of the "Hinge". In general, it has two strong links (like any other Turbot Fish) -- one in a line (in this case column 5) and one in a box (in this case box 9), connected by a weak link in a line (in this case row 9). That pattern proves that at least one of the end points of the formed chain must be true. Here the end points are 3r1c5 and 3r7c7 (not 3r9c9). Thus you can eliminate 3r1c7 (not 3r1c9).

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`.-------------------.-----------------.---------------------.| 2589  2358   1    | 6   a(3)5   345 |  245-3   7     3459 || 6     235    25   | 14    7     9   |  8       1245  1345 || 4     357    579  | 8     2     135 |  35      6     1359 |:-------------------+-----------------+---------------------:| 1258  1258   258  | 9     45    27  |  457     3     6    || 7     56     4    | 35    8     356 |  1       9     2    || 3     9      256  | 17    456   127 |  457     8     45   |:-------------------+-----------------+---------------------:| 89    4      89   | 35    1     356 | d2(3)56  25    7    || 15    1567   3    | 2     9     47  |  456     145   8    || 125   12567  2567 | 47   b356   8   |  9       145  c1345 |'-------------------'-----------------'---------------------'`

(3)r1c5 = r9c5 - r9c9 = (3)r7c7 => -3 r1c7

As a diagram:

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`c5       c7  c9o . . . . x       r1|         .|         .|         .|         .|         o       r7|          \|           \|            \o . . . . . . o   r9`

Note, that if the weak link line were row 7 (instead of row 9), then we'd have this:

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`c5       c7  c9    o . . . . . . x   r1|             .|             .|             .|             .o . . . . o   .   r7           \  .            \ .             \.              o   r9`

That would eliminate 3r1c9.

The other two possible variants of the pattern would be:

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`c5       c7  c9o . . . . . . x   r1|             .|             .|             .|             .|             o   r7|            /|           / |          /   o . . . . o       r9`

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`c5       c7  c9o . . . . x       r1|         .    |         .    |         .    |         .    o . . . . . . o   r7          .  /          . /           ./             o       r9`

Btw, about that term "Hinge". Do you use that specifically for minimal ERs like this (or for all ERs)? If so, is that a generally accepted name for such cases, and where does it originate from? I'm asking because that would make my question here moot. I thought there was no specific name for the minimal-ER Turbot Fishes.

Added: I googled a bit, and it seems that the term "Hinge" has too much baggage to be used specifically for this purpose only. Therefore, I would still advocate adopting a new term, such as "Crane", or "Loader Crane" or "Turbot Crane" (as discussed in the other thread), so we could have a completely named Turbot Fish Family without any ambiguity. What do you think, Yogi? I'd value your opinion since you're an avid user of Turbot Fishes.
-SpAce-: Show
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`   *             |    |               |    |    *        *        |=()=|    /  _  \    |=()=|               *            *    |    |   |-=( )=-|   |    |      *     *                     \  ¯  /                   *    `

"If one is to understand the great mystery, one must study all its aspects, not just the dogmatic narrow view of the Jedi."

SpAce

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### Re: Hinge (ER) doesn't work?

http://www.sudocue.net/guide.php#EmptyRectange
In Science and Sudoku, great discoveries are sometimes made simultaneously and independently by different people. The Empty Rectangle strategy is a perfect example. On December 25, 2005. Rod Hagglund wrote this topic in the Eureka forum, introducing his “Hinge” method. The next day, Håvard started a thread in the Pappocom forum, introducing his “Skyscraper” and “2-String Kite” methods. The thread continued for a long time, drifting on and off topic, but February 11, 2006, Håvard wrote this post about his “Empty Rectangle” observations. Even though his discovery was of a later date, the name Empty Rectangle was brought to a larger audience, and this name, including the convenient ER acronym, is now used by most players, except for a few die-hards in the Eureka forum.

The key feature of an Empty Rectangle is a 3x3 box in which 4 cells in a rectangular formation do not contain a candidate for the digit we are inspecting, leaving an L, T or + shaped candidate pattern, known as the hinge. This is one of the few strategies that uses absent candidates. The 4 cells can be empty with only candidates for other digits, but may also contain other digits. It is important, however, that the box does not yet contain the digit we’re looking for.

I thought there was no specific name for the minimal-ER Turbot Fishes.
there isn't, hinge and er are explains both max -> min conditions of an empty rectangle intersections. 2 different creators similar relative time frame. {because they only look at 4 cells "empty" of candidates in a square shape and not the constructs digit count.
Some do, some teach, the rest look it up.

StrmCkr

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Joined: 05 September 2006

### Re: Hinge (ER) doesn't work?

StrmCkr wrote:
SpAce wrote:I thought there was no specific name for the minimal-ER Turbot Fishes.
there isn't, hinge and er are explains both max -> min conditions of an empty rectangle intersections. 2 different creators similar relative time frame. {because they only look at 4 cells "empty" of candidates in a square shape and not the constructs digit count.

Thanks for the clarification, StrmCkr! If "Hinge" and "ER" are indeed synonyms (as I kind of suspected), in that case I would discourage the use of the slightly confusing "Hinge" term, as "ER" is better known. Apparently we still need a new name for the minimal ER then.

SpAce

Posts: 2584
Joined: 22 May 2017

### Hinge (ER) doesn't work?

Thanx. Yeah I screwed up again, this time by losing track of the corners. With 3 only possible at r7c7 or r9c9, there are two 3Hinges (or ERs) in Box9. One is cornered at r7c9 and the other is cornered at r9c7, and it's the latter one which can see into r9c5 and thus eliminates 3 from r1c7.
You can perhaps now understand why I prefer the term Hinge, which relates directly to how they work and what they do, rather than the admittedly more common Empty Rectangle or ER, which focusses on something that is missing, but doesn't say much about how they work. It's the corner or Hinge cell that does the work.
Yogi
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Location: New Zealand

### Re: Hinge (ER) doesn't work?

Not really a corner more of the apex center cell(s) in the construct box where the used row/col intersect aka the empty rectangle intersection.

Er dosent focus on the empty cells to build it it uses them to aid in identifying a box that houses a row /col intersection that acts as a grouped weak/strong link between digits with a direction change. The 4 empty cells narrow it Down to 1 row and 1 Colum to look for a bilocal row or column (or another eri) to perform eliminations if said strong links end points see the opposites directions peer cells.

A hinge focused it's topic to identifying the cells to build a row and column in a box with 4 cells off so that the box holds potential truths for row or column calling it a hinge due to one critical cell acting as a pivit point forgetting that a minimal eri of 2 candidates actually has 2 hinges and 4 potential directing changes.
Altogether its the Same effect and outcome as above but more confusion when you dissect the name and implied hinge means.

Hence why Er is used more frequently coupled with this forum held more audience then the long dead. Org site.

Clear as mud.?
Some do, some teach, the rest look it up.

StrmCkr

Posts: 1178
Joined: 05 September 2006

### Re: Hinge (ER) doesn't work?

Yogi wrote:You can perhaps now understand why I prefer the term Hinge, which relates directly to how they work and what they do, rather than the admittedly more common Empty Rectangle or ER, which focusses on something that is missing, but doesn't say much about how they work.

Yes. I've never liked the name Empty Rectangle, and would also have preferred Hinge had I been around when things got named. That being said, I don't think it's helpful to use terms that no one else uses, even if they're more logical. Since Hinge and ER appear to be full synonyms, I think we all should use ER to avoid confusion and drop Hinge once and for all.

I can share from my own relatively recent (and on-going) newbie experience that your use of the term Hinge actually confused me when I was studying older posts. I would have known what ER meant but I'd never seen Hinge mentioned anywhere else, and even google didn't help. I suspected but couldn't know for sure if they were the same thing. Now I know they mean the same thing, but then I didn't, and I wondered if I'd missed something. So, if you don't want to confuse more newbies, please don't use that term anymore.

And all that being said, I still do think that the minimal ER (such as this) should have its own name. (Hinge doesn't work for that purpose either since it's a historical synonym for all ERs and not just that.)

Yogi wrote:It's the corner or Hinge cell that does the work.

Not really. The corner cell, or ERI, doesn't actually do anything -- it's just the pivot point between two strongly linked groups (or two candidates) in the box. It's those groups or candidates that do the work. In the case of the "normal" ER, the strong link is between two groups -- one pointing in the direction of a column and the other of a row -- and there's only one pivot point. In the case of the minimal ER, such as this, the strong link is within a conjugate pair which makes it different from other ERs, because there are two potential pivot points. That's one reason why it should have its own name.

StrmCkr wrote:Er dosent focus on the empty cells to build it it uses them to aid in identifying a box that houses a row /col intersection that acts as a grouped weak/strong link between digits with a direction change. The 4 empty cells narrow it Down to 1 row and 1 Colum to look for a bilocal row or column (or another eri) to perform eliminations if said strong links end points see the opposites directions peer cells.

Does someone actually use those empty cells to identify an ER? I don't and never have. It's much easier to see the candidates that form the L, T or + -shaped pattern directly. Hence Yogi is right about the name not being very descriptive, imho.

SpAce

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Joined: 22 May 2017

### Re: Hinge (ER) doesn't work?

Does someone actually use those empty cells to identify an ER? I don't and never have. It's much easier to see the candidates that form the L, T or + -shaped pattern directly. Hence Yogi is right about the name not being very descriptive, imho.

Yes some look at what's off to see what space is still on.

An easy example.
blr reduction for a mini row in a box too see that the mini row is the only truth the other two boxes mini rows are off. .

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` XXX|///|///XXX|... |...XXX|... |... `
Some do, some teach, the rest look it up.

StrmCkr

Posts: 1178
Joined: 05 September 2006

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