Question about this puzzle

Post the puzzle or solving technique that's causing you trouble and someone will help

Question about this puzzle

Postby Pupp » Sun Aug 30, 2020 10:34 pm

[Edit: fixed an issue of a wrong digit and added clarifications.]

Starting position no pencilmarks
Code: Select all
. 8 .|7 . .|. . .
. 7 .|8 . 4|. 6 2
. . 3|. 5 .|7 . .
-----+-----+-----
. 3 .|4 8 7|. 1 6
. . 4|2 . 1|8 . .
8 1 .|3 9 5|. 7 .
-----+-----+-----
. . 8|. 7 .|4 . .
3 6 .|5 . 2|. 8 .
. . .|. . 8|. 2 .


Starting Position with pencilmarks
Code: Select all
+----------------------+----------------------+----------------------+
| 124569 8      12569  | 7      1236   369    | 1359   3459   13459  |
| 159    7      159    | 8      13     4      | 1359   6      2      |
| 12469  249    3      | 169    5      69     | 7      49     1489   |
+----------------------+----------------------+----------------------+
| 259    3      259    | 4      8      7      | 259    1      6      |
| 5679   59     4      | 2      6      1      | 8      359    359    |
| 8      1      26     | 3      9      5      | 2      7      4      |
+----------------------+----------------------+----------------------+
| 1259   259    8      | 169    7      369    | 4      359    1359   |
| 3      6      179    | 5      14     2      | 19     8      179    |
| 14579  459    1579   | 169    1346   8      | 13569  2      13579  |
+----------------------+----------------------+----------------------+


Point where I'm asking about.
Code: Select all
 *-----------*
 |.8.|7..|...|
 |.7.|8.4|.62|
 |..3|.5.|7..|
 |---+---+---|
 |.3.|487|.16|
 |..4|2.1|8..|
 |81.|395|.7.|
 |---+---+---|
 |..8|.7.|4..|
 |36.|5.2|.8.|
 |...|..8|.2.|
 *-----------*


 *-----------*
 |.8.|72.|...|
 |.7.|8.4|.62|
 |..3|.5.|7.8|
 |---+---+---|
 |.32|487|.16|
 |7.4|261|8..|
 |816|395|274|
 |---+---+---|
 |..8|.7.|4..|
 |36.|542|.8.|
 |...|..8|62.|
 *-----------*


 *--------------------------------------------------------------------*
 | 14569  8      159    | 7      2      369    | 1359   3459   1359   |
 | 159    7      159    | 8      13     4      | 1359   6      2      |
 | 12469  249    3      | 169    5      69     | 7      49     8      |
 *----------------------+----------------------+----------------------|
 | 59     3      2      | 4      8      7      | 59     1      6      |
 | 7      59     4      | 2      6      1      | 8      359    359    |
 | 8      1      6      | 3      9      5      | 2      7      4      |
 *----------------------+----------------------+----------------------|
 | 1259   259    8      | 169    7      369    | 4      359    1359   |
 | 3      6      179    | 5      4      2      | 19     8      179    |
 | 1459   459    1579   | 19     13     8      | 6      2      13579  |
 *--------------------------------------------------------------------*


According to SE, I didn't solve it anyway near it's solution.

looking at r3c4=pm169 then I looked at r7c4=pm169

Then I looked at r7c1=pm1259 and again at r7c4=pm169 and lastly at r7c9-pm1359

It seemed like there was a relationship to the bottom three squares, and discounting the numbers that don't apply to the middle cell (2's,3's and 5's), the odd digit out was "6" in r7c4 so I chose the "6", and the rest of the puzzle just whip by in the blur without any serious thought.

Did I use an actual technique or just get lucky? Seems like there was a relationship to the 3 cells [r7c1, r7c4,r7c9] on row 7 in some fashion.
Pupp
 
Posts: 128
Joined: 18 October 2019

Re: Question about this puzzle

Postby Leren » Mon Aug 31, 2020 5:01 am

A solution from your last position including basics :

Code: Select all
*--------------------------------------------------------------------------------*
| 46-159  8      #159      | 7       2       369      |*1359    459-3   159-3    |
|#159     7      #159      | 8       13      4        |*1359    6       2        |
| 246-19  24-9    3        | 169     5       69       | 7       49      8        |
|--------------------------+--------------------------+--------------------------|
| 59      3       2        | 4       8       7        | 59      1       6        |
| 7       59      4        | 2       6       1        | 8       359     359      |
| 8       1       6        | 3       9       5        | 2       7       4        |
|--------------------------+--------------------------+--------------------------|
| 1259    259     8        | 169     7       369      | 4       359     1359     |
| 3       6       179      | 5       4       2        | 19      8       179      |
| 1459    459     1579     | 19      13      8        | 6       2       13579    |
*--------------------------------------------------------------------------------*

1. Claiming Pair of 3's in Box 3 => - 3 r1c89 2. Naked Triple (159) Box 1 => -159 r1c1, - 19 r3c1, - 9 r3c2. Singles get you to here :

Code: Select all
*--------------------------------------------------------------------------------*
| 46      8      #159      | 7       2       69       | 3       459     159      |
| 19-5    7      #159      | 8       3       4        | 159     6       2        |
| 246     24      3        | 1       5       69       | 7       49      8        |
|--------------------------+--------------------------+--------------------------|
| 59      3       2        | 4       8       7        | 59      1       6        |
| 7       59      4        | 2       6       1        | 8       3       59       |
| 8       1       6        | 3       9       5        | 2       7       4        |
|--------------------------+--------------------------+--------------------------|
| 129-5   29-5    8        | 6       7       3        | 4      *59     *159      |
| 3       6       19       | 5       4       2        | 19      8       7        |
| 45      45      7        | 9       1       8        | 6       2       3        |
*--------------------------------------------------------------------------------*

1. Pointing Pair of 5's Box 9 => - 5 r7c12 2. Claiming pair of 5's Box 1 => - 5 r2c1

Code: Select all
*--------------------------------------------------------------------------------*
| 46      8      a159      | 7       2       69       | 3       459    b159      |
| 9-1     7       159      | 8       3       4        | 159     6       2        |
| 246     24      3        | 1       5       69       | 7       49      8        |
|--------------------------+--------------------------+--------------------------|
| 59      3       2        | 4       8       7        | 59      1       6        |
| 7       59      4        | 2       6       1        | 8       3       59       |
| 8       1       6        | 3       9       5        | 2       7       4        |
|--------------------------+--------------------------+--------------------------|
|d129     29      8        | 6       7       3        | 4       59     c159      |
| 3       6       9-1      | 5       4       2        | 19      8       7        |
| 45      45      7        | 9       1       8        | 6       2       3        |
*--------------------------------------------------------------------------------*

Skyscraper (1's) Cells a-b-c-d => - 1 r2c1, r8c3. Singles from there.

Leren
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Re: Question about this puzzle

Postby Pupp » Mon Aug 31, 2020 2:33 pm

Thanks, that makes sense.
I missed the naked triple in box 1. I did see the claiming 3's when I did the puzzle on my phone, but missed it when I was trying to recreate the position on my computer.

That being said, once you pointed out the triples in box 1, it's makes sense on how I should have solved the puzzle. :geek:

I'm not going to speculate anymore on how that "6" in r7c4 somehow short cut the rest of the puzzle. I prefer to solve puzzles in the correct sequence.
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Re: Question about this puzzle

Postby mith » Mon Aug 31, 2020 6:49 pm

There's a hidden rectangle that will eliminate 9r7c4, and an AIC that will eliminate 1r7c4. But it sounds like a lucky guess, and not one that should have made the puzzle much easier on its own (SE still needs the skyscraper if you fill in 6r7c4).
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Re: Question about this puzzle

Postby Pupp » Tue Sep 01, 2020 3:59 pm

I already solved the puzzle. I solved it before I posted the puzzle. I was just wondering why my solution wasn't the same as SE. (I'd missed the naked triple (at that point in the puzzle)), and guessed that one of the cells used a "6". I'm sure I found the naked triple after I filled in more cells in the puzzle.

Once I got the 6, I solved the rest of the puzzle pretty quickly, so I wasn't really looking for a complete breakdown of the puzzle.

It's all good. It's a learning experience. Even though I'm still on "Very Hard 1" section, the puzzles are getting a bit more complex. No so much in new techniques, as much as just having a greater variety of techniques to look for, and more of the intermediate techniques in the puzzles.

Also, Sudoku Explorer isn't the end-all for explaining puzzles. I can't remember if was that puzzle, or different puzzle I plugged in SE, but it said there was a swordfish in the puzzle, and I can quite honestly say I solved that puzzle without resorting to using a swordfish, and didn't use anything advanced to solve the puzzle either. There was a different puzzle a couple weeks ago that I ended up using the BUG technique to solve, but Sudoku Explorer solved the puzzle with different steps. -That being said, even in a couple weeks, I'm getting much better at solving puzzles in the intended sequence and not resorting to some more advance technique that feels like a Deuce Ex Machina move, or using some twisted logic that just happens to pick the correct number in a cell. So if a cell has 3 pencil mark numbers, my twisted logic had a 33.3% chance of working. :lol:

In any event, the Very Hard puzzles from Sudoku 1000 are very enjoyable to solve. It's the first level I got to where I really feel like the puzzles have enough difficulty and variety of techniques to make the puzzles feel like something worthy of solving. Of course, eventually I'll be solving puzzles much harder. I guess my intermediate goal is to be able to solve puzzles in the 7.0 to 8.0 range. I can't put a timeline on that, since there are 250 puzzles per section in Sudoku 10000, and at this point, I might solve all 250 puzzles in a section for enjoyment purposes.
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Re: Question about this puzzle

Postby mith » Tue Sep 01, 2020 5:58 pm

Also, Sudoku Explorer isn't the end-all for explaining puzzles. I can't remember if was that puzzle, or different puzzle I plugged in SE, but it said there was a swordfish in the puzzle, and I can quite honestly say I solved that puzzle without resorting to using a swordfish, and didn't use anything advanced to solve the puzzle either.


SE will find swordfish before hidden triplets (unless using the new ordering) and naked/hidden quads. There will be puzzles that SE will use a swordfish on, and Hodoku will use a hidden triplet instead. There are often many paths to a solution, all rating programs can do is give you the solution they find based on the order of techniques they are programmed with.
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Re: Question about this puzzle

Postby Pupp » Tue Sep 01, 2020 6:29 pm

mith wrote:
Also, Sudoku Explorer isn't the end-all for explaining puzzles. I can't remember if was that puzzle, or different puzzle I plugged in SE, but it said there was a swordfish in the puzzle, and I can quite honestly say I solved that puzzle without resorting to using a swordfish, and didn't use anything advanced to solve the puzzle either.


SE will find swordfish before hidden triplets (unless using the new ordering) and naked/hidden quads. There will be puzzles that SE will use a swordfish on, and Hodoku will use a hidden triplet instead. There are often many paths to a solution, all rating programs can do is give you the solution they find based on the order of techniques they are programmed with.


Ahh, I didn't know that. That's very interesting, and helpful to know. For the most part, I only plug in a puzzle into SE or another solver out of curiosity, after I've already solved the puzzle. There was only a single puzzle since I started playing Sudoku, where I was genuinely stuck. I never really did figure out why I kept messing up, but with so many puzzles available, I just moved on to the next puzzle.
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Re: Question about this puzzle

Postby SteveG48 » Thu Sep 03, 2020 4:18 pm

Pupp wrote:Ahh, I didn't know that. That's very interesting, and helpful to know. For the most part, I only plug in a puzzle into SE or another solver out of curiosity, after I've already solved the puzzle. There was only a single puzzle since I started playing Sudoku, where I was genuinely stuck. I never really did figure out why I kept messing up, but with so many puzzles available, I just moved on to the next puzzle.


I haven't tried SE, but one reason that I like HoDoKu is that you can set it so that the program's solution path is not displayed while you work your own solution. When I reach the point where it's stte, I turn the program solver on and see what its approach was. You pick up on the sort of thing that Mith is talking about. I'll find moves in the solver that I missed, but more frequently I'll see that our approaches were merely different. For example, I always look for X-Y wings before looking for W wings. The program does it the other way around by default. That can make a big difference in the time that it takes to solve the puzzle- sometimes in my favor, sometimes not. It's a good way to learn.
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Re: Question about this puzzle

Postby Pupp » Thu Sep 03, 2020 6:37 pm

Here's another puzzle I need some input on. I switched Hard 5 on Sudoku 10000 Plus.
SE rated it 7.1

I was doing Hard 1 puzzles in under 10 minutes. It took me much longer to do Hard 5. The first puzzle I finished without guessing took nearly 40 minutes, but felt intellectually stimulating.

Here's the puzzle at the start.
Code: Select all
5 . .|2 . .|4 . .
. 7 .|. 5 6|8 . .
. . 2|9 . 7|. . .
-----+-----+-----
6 . 4|5 2 .|. . .
. 1 .|3 . .|2 9 .
. 2 8|. . .|3 4 .
-----+-----+-----
8 5 .|. 9 2|. . .
. . .|. 6 3|. . . r2c3
. . .|. . .|. . 4



Looks like it used a forcing chain at this point. It least seemed like I was using a forcing chain to figure out that "9" went in cell r2c3.
Code: Select all
 *--------------------------------------------------------------------*
 | 5      69     169    | 2      3      8      | 4      167    179    |
 | 4     7      39     | 1      5      6      | 8      23     239    |
 | 13     8      2      | 9      4      7      | 56     56     13     |
 *----------------------+----------------------+----------------------|
 | 6      3      4      | 5      2      9      | 17     178    178    |
 | 7      1      5      | 3      8      4      | 2      9      6      |
 | 9      2      8      | 6      7      1      | 3      4      5      |
 *----------------------+----------------------+----------------------|
 | 8      5      1367   | 4      9      2      | 167    1367   137    |
 | 12     4      179    | 78     6      3      | 1579   12578  1278   |
 | 23     69     3679   | 78     1      5      | 679    23678  4      |
 *--------------------------------------------------------------------*


The primary cells I looked at was r2c3, r3c1, and r3c9. But I looked at several other cells in order to make sure "9" was the only candidate that could go into the r2c3 cell. In particular, I had to look at cells r8c1 and r9c1, aside from the cells in rows 2 and 3.
I was staring at the board for at least 20 minutes, but at least 10 minutes or more at the 3 cells I mentioned, roving around trying to figure out if I could exclude either the "3" or "9" from cell r2c3. So I can't say what my exact thought process was last night. I looked at a bunch of cells other than the few I mentioned.

So I'm kind of flummoxed if did this correctly, or just got lucky. I was certain when I picked 9, it was the correct answer, but I can't seem to figure out how I came to that conclusion when I was working on the puzzle, looking at it the next day.
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Re: Question about this puzzle

Postby mith » Thu Sep 03, 2020 7:03 pm

SE finds an AIC using some of the cells you mentioned - and there are probably others - so you were likely in the right ballpark at least:

3r3c1 = (3-2)r9c1 = r9c8 - (2=3)r2c8 => -3r2c3

If there is a 3 in r3c1, there can't be a 3 in r2c3 (both in box 1).

If there is not a 3 in r3c1, there must be a 3 in r9c1 (only options in column 1).
If there is a 3 in r9c1, there cannot be a 2 in r9c1 (different digits, same cell).
If there is not a 2 in r9c1, there must be a 2 in r9c8 (only options in row 9).
If there is a 2 in r9c8, there cannot be a 2 in r2c8 (both in column 8)
If there is not a 2 in r2c8, there must be a 3 in r2c8 (only options in the cell)
If there is a 3 in r2c8, there cannot be a 3 in r2c3 (both in row 2)

Either way, there is not a 3 in r2c3, so 9c2c3 and stte.
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Re: Question about this puzzle

Postby Pupp » Thu Sep 03, 2020 8:06 pm

mith wrote:SE finds an AIC using some of the cells you mentioned - and there are probably others - so you were likely in the right ballpark at least:

3r3c1 = (3-2)r9c1 = r9c8 - (2=3)r2c8 => -3r2c3

If there is a 3 in r3c1, there can't be a 3 in r2c3 (both in box 1).

If there is not a 3 in r3c1, there must be a 3 in r9c1 (only options in column 1).
If there is a 3 in r9c1, there cannot be a 2 in r9c1 (different digits, same cell).
If there is not a 2 in r9c1, there must be a 2 in r9c8 (only options in row 9).
If there is a 2 in r9c8, there cannot be a 2 in r2c8 (both in column 8)
If there is not a 2 in r2c8, there must be a 3 in r2c8 (only options in the cell)
If there is a 3 in r2c8, there cannot be a 3 in r2c3 (both in row 2)

Either way, there is not a 3 in r2c3, so 9c2c3 and stte.


Ahh, thanks.
When I'm intently focusing on something for 10 minutes or more, it would be hard for me to remember all the different elements I'd looked at to come to a conclusion about something. At least, by the next morning. It's different, for me anyway, looking at a puzzle like this—after it's been solved, to recreate what I was thinking when I already know the answer.
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Re: Question about this puzzle

Postby denis_berthier » Sat Sep 05, 2020 4:47 am

Pupp wrote:Here's another puzzle I need some input on. I switched Hard 5 on Sudoku 10000 Plus.
SE rated it 7.1

Looks like it used a forcing chain at this point. It least seemed like I was using a forcing chain to figure out that "9" went in cell r2c3.
Code: Select all
 *--------------------------------------------------------------------*
 | 5      69     169    | 2      3      8      | 4      167    179    |
 | 4      7      39     | 1      5      6      | 8      23     239    |
 | 13     8      2      | 9      4      7      | 56     56     13     |
 *----------------------+----------------------+----------------------|
 | 6      3      4      | 5      2      9      | 17     178    178    |
 | 7      1      5      | 3      8      4      | 2      9      6      |
 | 9      2      8      | 6      7      1      | 3      4      5      |
 *----------------------+----------------------+----------------------|
 | 8      5      1367   | 4      9      2      | 167    1367   137    |
 | 12     4      179    | 78     6      3      | 1579   12578  1278   |
 | 23     69     3679   | 78     1      5      | 679    23678  4      |
 *--------------------------------------------------------------------*


Given to SudoRules as:

Code: Select all
(solve-sukaku-grid
    *--------------------------------------------------------------------*
    ! 5      69     169    ! 2      3      8      ! 4      167    179    !
    ! 4      7      39     ! 1      5      6      ! 8      23     239    !
    ! 13     8      2      ! 9      4      7      ! 56     56     13     !
    *----------------------+----------------------+----------------------!
    ! 6      3      4      ! 5      2      9      ! 17     178    178    !
    ! 7      1      5      ! 3      8      4      ! 2      9      6      !
    ! 9      2      8      ! 6      7      1      ! 3      4      5      !
    *----------------------+----------------------+----------------------!
    ! 8      5      1367   ! 4      9      2      ! 167    1367   137    !
    ! 12     4      179    ! 78     6      3      ! 1579   12578  1278   !
    ! 23     69     3679   ! 78     1      5      ! 679    23678  4      !
    *--------------------------------------------------------------------*
)


You need only a short (3D) bivalue-chain[3] (after a trivial whip[1]):

Code: Select all
***********************************************************************************************
***  SudoRules 20.1.s based on CSP-Rules 2.1.s, config = W+SFin
***  Using CLIPS 6.32-r770
***********************************************************************************************
86 candidates, 382 csp-links and 382 links. Density = 10.45%
whip[1]: r3n6{c8 .} ==> r1c8 ≠ 6
biv-chain[3]: r2c8{n2 n3} - b1n3{r2c3 r3c1} - r9c1{n3 n2} ==> r9c8 ≠ 2
stte
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Re: Question about this puzzle

Postby Pupp » Sat Sep 05, 2020 5:25 am

Thanks. I'm getting a feel for the technique. Not sure if it's a forcing chain or AIC, but it works really well. I identify pairs of cells with 2 numbers but not the same pair, and see if one of the cells is always a certain number, regardless if I plug in either number in the other cell. (It does involved following a chain of other cells). Although it's not the same pair, I'm not sure if there needs to be a common denominator, or if that even matters. I haven't done enough puzzles at this point.

Oddly enough, it's pretty easy to figure out if a pair of cells has no chance of being a candidate because it will just peter out and never become a loop, or if it does loop, will have major issues with breaking the puzzle. For example, forcing a number to be in the same row/column twice.
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Re: Question about this puzzle

Postby denis_berthier » Sat Sep 05, 2020 6:15 am

Pupp wrote:Thanks. I'm getting a feel for the technique. Not sure if it's a forcing chain or AIC, but it works really well.

Neither "forcing chain" nor "AIC" have ever had any precise definitions.
At the origin, "AICs" were only basic AICS (what I call bivalue-chains or 3D-bivalue-chains). But people started to add complications to them, such as including Subsets.
As for "forcing-chains", it's an expression used by SE, it is presented by SE in a very T&E-ish way as step-by-step conclusions based on some original hypothesis. It covers very different kinds of chains.

In the present situation, the only thing you have to find is a sequence of connected bivalue-cells in rc-space, as shown in my resolution path.
denis_berthier
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Location: Paris

Re: Question about this puzzle

Postby RSW » Sat Sep 05, 2020 9:45 am

Pupp wrote:Point where I'm asking about.
Code: Select all
 *-----------*
 |.8.|7..|...|
 |.7.|8.4|.62|
 |..3|.5.|7..|
 |---+---+---|
 |.3.|487|.16|
 |..4|2.1|8..|
 |81.|395|.7.|
 |---+---+---|
 |..8|.7.|4..|
 |36.|5.2|.8.|
 |...|..8|.2.|
 *-----------*


 *-----------*
 |.8.|72.|...|
 |.7.|8.4|.62|
 |..3|.5.|7.8|
 |---+---+---|
 |.32|487|.16|
 |7.4|261|8..|
 |816|395|274|
 |---+---+---|
 |..8|.7.|4..|
 |36.|542|.8.|
 |...|..8|62.|
 *-----------*


 *--------------------------------------------------------------------*
 | 14569  8      159    | 7      2      369    | 1359   3459   1359   |
 | 159    7      159    | 8      13     4      | 1359   6      2      |
 | 12469  249    3      | 169    5      69     | 7      49     8      |
 *----------------------+----------------------+----------------------|
 | 59     3      2      | 4      8      7      | 59     1      6      |
 | 7      59     4      | 2      6      1      | 8      359    359    |
 | 8      1      6      | 3      9      5      | 2      7      4      |
 *----------------------+----------------------+----------------------|
 | 1259   259    8      | 169    7      369    | 4      359    1359   |
 | 3      6      179    | 5      4      2      | 19     8      179    |
 | 1459   459    1579   | 19     13     8      | 6      2      13579  |
 *--------------------------------------------------------------------*


According to SE, I didn't solve it anyway near it's solution.

looking at r3c4=pm169 then I looked at r7c4=pm169

Then I looked at r7c1=pm1259 and again at r7c4=pm169 and lastly at r7c9-pm1359

It seemed like there was a relationship to the bottom three squares, and discounting the numbers that don't apply to the middle cell (2's,3's and 5's), the odd digit out was "6" in r7c4 so I chose the "6", and the rest of the puzzle just whip by in the blur without any serious thought.

Did I use an actual technique or just get lucky? Seems like there was a relationship to the 3 cells [r7c1, r7c4,r7c9] on row 7 in some fashion.


There are a number of valid ways of arriving at the same correct solution. Starting with your PM grid, this is the verbose output of my solver:
Hidden Text: Show
Code: Select all
+----------------+------------+-----------------+
 | 14569 8   159  | 7   2  369 | 1359 3459 1359  |
 | 159   7   159  | 8   13 4   | 1359 6    2     |
 | 12469 249 3    | 169 5  69  | 7    49   8     |
 +----------------+------------+-----------------+
 | 59    3   2    | 4   8  7   | 59   1    6     |
 | 7     59  4    | 2   6  1   | 8    359  359   |
 | 8     1   6    | 3   9  5   | 2    7    4     |
 +----------------+------------+-----------------+
 | 1259  259 8    | 169 7  369 | 4    359  1359  |
 | 3     6   179  | 5   4  2   | 19   8    179   |
 | 1459  459 1579 | 19  13 8   | 6    2    13579 |
 +----------------+------------+-----------------+

Naked triple: In block 1, r1c3 r2c1 r2c3 have identical candidates: 1 5 9
- Removing candidate 1 from r1c1 r3c1
- Removing candidate 5 from r1c1
- Removing candidate 9 from r1c1 r3c1 r3c2
Naked Quad: In row 3, the digits 2 4 6 9 must go in cells r3c1 r3c2 r3c6 r3c8 (unspecified order)
These digits can then be eliminated from the other cells in row 3
- Removing candidate(s) 6 9 from cell r3c4
* Cell r3c4 now has only one possible value: 1
- Removing candidate 1 from r7c4 r9c4 r2c5
* Cell r9c4 now has only one possible value: 9
- Removing candidate 9 from r7c4 r9c1 r9c2 r9c3 r9c9 r7c6
* Cell r7c4 now has only one possible value: 6
- Removing candidate 6 from r7c6
* Cell r7c6 now has only one possible value: 3
- Removing candidate 3 from r1c6 r7c8 r7c9 r9c5
* Cell r9c5 now has only one possible value: 1
- Removing candidate 1 from r9c1 r9c3 r9c9
* Cell r2c5 now has only one possible value: 3
- Removing candidate 3 from r2c7
Box/Line: In column 7, the only valid positions for digit 3 are r1c7
- Removing candidate 3 from block 3 r1c8 r1c9
Box/Line: In column 8, the only valid positions for digit 3 are r5c8
- Removing candidate 3 from block 6 r5c9
Naked pair: In row 5, r5c2 r5c9 have identical candidates: 5 9
- Removing candidate 5 from r5c8
- Removing candidate 9 from r5c8
Naked pair: In row 9, r9c1 r9c2 have identical candidates: 4 5
- Removing candidate 5 from r9c3 r9c9
Naked pair: In block 7, r9c1 r9c2 have identical candidates: 4 5
- Removing candidate 5 from r7c1 r7c2
* Cell r5c8 now has only one possible value: 3
* Cell r9c3 now has only one possible value: 7
- Removing candidate 7 from r8c3 r9c9
* Cell r9c9 now has only one possible value: 3
Naked Quint (Hidden Quad): In row 1, the digits 1 4 5 6 9 must go in cells r1c1 r1c3 r1c6 r1c8 r1c9 (unspecified order)
These digits can then be eliminated from the other cells in row 1
- Removing candidate(s) 1 5 9 from cell r1c7
Naked Triple: In column 9, the digits 1 5 9 must go in cells r1c9 r5c9 r7c9 (unspecified order)
These digits can then be eliminated from the other cells in column 9
- Removing candidate(s) 1 9 from cell r8c9
* Cell r1c7 now has only one possible value: 3
* Cell r8c9 now has only one possible value: 7
Box/Line: In column 3, the only valid positions for digit 5 are r1c3 r2c3
- Removing candidate 5 from block 1 r2c1
Code: Select all
   
 +------------+--------+-------------+
 | 46  8  159 | 7 2 69 | 3   459 159 |
 | 19  7  159 | 8 3 4  | 159 6   2   |
 | 246 24 3   | 1 5 69 | 7   49  8   |
 +------------+--------+-------------+
 | 59  3  2   | 4 8 7  | 59  1   6   |
 | 7   59 4   | 2 6 1  | 8   3   59  |
 | 8   1  6   | 3 9 5  | 2   7   4   |
 +------------+--------+-------------+
 | 129 29 8   | 6 7 3  | 4   59  159 |
 | 3   6  19  | 5 4 2  | 19  8   7   |
 | 45  45 7   | 9 1 8  | 6   2   3   |
 +------------+--------+-------------+


Finned 2-Fish (aka Finned-X-Wing): Digit 9 in rows 2 8 columns (1) 3 7, Fin: r2c1 => -9r1c3
If digit 9 is true in the fin, then it may be eliminated from all other cells in sight of the fin cell. If digit 9 is false in the fin, then the 2-Fish is valid, and digit 9 must go in columns 3 7, and candidate 9 would be invalid in all other cells in columns 3 7
Therefore digit 9 can be eliminated from all cells where it would have been eliminated in either case.

Box/Line: In block 1, the only valid positions for digit 9 are r2c1 r2c3
- Removing candidate 9 from row 2 r2c7

Code: Select all
 +------------+--------+------------+
 | 46  8  15  | 7 2 69 | 3  459 159 |
 | 19  7  159 | 8 3 4  | 15 6   2   |
 | 246 24 3   | 1 5 69 | 7  49  8   |
 +------------+--------+------------+
 | 59  3  2   | 4 8 7  | 59 1   6   |
 | 7   59 4   | 2 6 1  | 8  3   59  |
 | 8   1  6   | 3 9 5  | 2  7   4   |
 +------------+--------+------------+
 | 129 29 8   | 6 7 3  | 4  59  159 |
 | 3   6  19  | 5 4 2  | 19 8   7   |
 | 45  45 7   | 9 1 8  | 6  2   3   |
 +------------+--------+------------+


Sashimi 2-Fish (aka Sashimi-X-Wing): Digit 9 in rows 4 8 columns 1 (3) 7, Fin: r8c3 => -9r7c1
If digit 9 is true in the fin, then it may be eliminated from all other cells in sight of the fin cell. If digit 9 is false in the fin, then the 2-Fish is valid, and digit 9 must go in columns 1 7, and candidate 9 would be invalid in all other cells in columns 1 7
Therefore digit 9 can be eliminated from all cells where it would have been eliminated in either case.


Code: Select all
 +------------+--------+------------+
 | 46  8  15  | 7 2 69 | 3  459 159 |
 | 19  7  159 | 8 3 4  | 15 6   2   |
 | 246 24 3   | 1 5 69 | 7  49  8   |
 +------------+--------+------------+
 | 59  3  2   | 4 8 7  | 59 1   6   |
 | 7   59 4   | 2 6 1  | 8  3   59  |
 | 8   1  6   | 3 9 5  | 2  7   4   |
 +------------+--------+------------+
 | 12  29 8   | 6 7 3  | 4  59  159 |
 | 3   6  19  | 5 4 2  | 19 8   7   |
 | 45  45 7   | 9 1 8  | 6  2   3   |
 +------------+--------+------------+


Sashimi 2-Fish (aka Sashimi-X-Wing): Digit 1 in rows 1 7 columns (1) 3 9, Fin: r7c1 => -1r8c3
If digit 1 is true in the fin, then it may be eliminated from all other cells in sight of the fin cell. If digit 1 is false in the fin, then the 2-Fish is valid, and digit 1 must go in columns 3 9, and candidate 1 would be invalid in all other cells in columns 3 9
Therefore digit 1 can be eliminated from all cells where it would have been eliminated in either case.

Then singles to solution
RSW
 
Posts: 64
Joined: 01 December 2018
Location: Western Canada

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