A good solution to the puzzle

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A good solution to the puzzle

Postby AnotherLife » Sun Mar 28, 2021 6:31 pm

Can anyone offer a good solution to this not very hard sudoku? I mean, it should be human but not artificial computer-based (adieu Berthier, c'est fini).
Code: Select all
.1..5.628..6.........89..4....41.26.1.......5.62.85....7..28.........7..245.6..1.

Code: Select all
.----------------------.-------------------.-------------------.
| 3479    1      3479  | 37     5    347   | 6     2     8     |
| 345789  23589  6     | 1237   347  12347 | 1359  3579  1379  |
| 357     235    37    | 8      9    12367 | 135   4     137   |
:----------------------+-------------------+-------------------:
| 35789   3589   3789  | 4      1    379   | 2     6     379   |
| 1       389    34789 | 23679  37   23679 | 3489  3789  5     |
| 3479    6      2     | 379    8    5     | 1349  379   13479 |
:----------------------+-------------------+-------------------:
| 369     7      139   | 1359   2    8     | 3459  359   3469  |
| 3689    389    1389  | 1359   34   1349  | 7     3589  23469 |
| 2       4      5     | 379    6    379   | 389   1     39    |
'----------------------'-------------------'-------------------'
Last edited by AnotherLife on Sun Mar 28, 2021 8:45 pm, edited 1 time in total.
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Re: A good solution to the puzzle

Postby Hajime » Sun Mar 28, 2021 6:51 pm

AnotherLife wrote:Can anyone offer a good solution to this not very hard sudoku? I mean, it should be human but not artificial computer-based (adieu Bertier, c'est fini).
Code: Select all
.1..5.628..6.........89..4....41.26.1.......5.62.85....7..28.........7..245.6..1.

Pretty much different methods, so also pretty hard:
Code: Select all
Eliminated candidates per Method and per Sudoku

Method   \  Sudoku |   SER |     1
                   |-------|------
Not counted elims  |     0 |    68
Naked Singles      |   0.1 |    35
Hidden Singles     |   0.2 |    68
Naked Pair    [2]  |     3 |     4
Naked Triple  [3]  |   3.6 |     4
Naked Quad    [4]  |     5 |     1
Pointing/Claiming  |   2.8 |     6
WXYZ Wing     [4]  |   5.5 |     1
VWXYZ Wing    [5]  |   6.3 |     1
Turbot-fish   [4]  |   4.2 |     5
XY-Wing       [3]  |   4.1 |     2
                   |-------|------
Eliminated Cand's  |   195 |   195
Sum(SER * Cand's)  | 106.3 | 106.3


So 2 (VW)XYZ-Wings, 1 two-string-Kite, 3 Turbot-Cranes, and 2 XY-chains of length 3.
I could not solve this manually in 1 or 2 steps... Not what you hoped to hear, I think. :?
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Re: A good solution to the puzzle

Postby jco » Sun Mar 28, 2021 11:06 pm

Hello,

I found a solution in four easy steps.

After basics

Code: Select all
.-----------------------------------------------------.
| 349    1     39   |  37   5    347 | 6    2     8   |
| 3458   358   6    |  2    34   1   | 359  379   379 |
| 357    2     37   |  8    9    6   | 35   4     1   |
|-------------------+----------------+----------------|
| 35789  3589  3789 |  4    1   a39  | 2    6     79-3|
| 1      39    4    |  6    7    2   | 39   8     5   |
| 379    6     2    | b39   8    5   | 1    379   4   |
|-------------------+----------------+----------------|
| 39     7     139  |  15   2    8   | 4    359   6   |
| 6      389   1389 |  15   34   349 | 7    359   2   |
| 2      4     5    | c379  6    79-3| 8    1    d39  |
'-----------------------------------------------------'
1. W-Wing (3=9)r4c6-r6c4=r9c4-(9=3)r9c9 => -3 r4c9, r9c6

Code: Select all
.------------------------------------------------------.
| 349    1     39   |  37    5   347 | 6     2     8   |
| 3458   358   6    |  2    b34  1   | 359   379  c379 |
| 357    2     37   |  8     9   6   | 35    4     1   |
|-------------------+----------------+-----------------|
| 35789  3589  3789 |  4     1   39  | 2     6     79  |
| 1      39    4    |  6     7   2   | 39    8     5   |
| 379    6     2    |  39    8   5   | 1     379   4   |
|-------------------+----------------+-----------------|
| 39     7     139  |  15    2   8   | 4     359   6   |
| 6      389   1389 |  15   a34  349 | 7     59-3  2   |
| 2      4     5    |  79-3  6   79  | 8     1    d39  |
'------------------------------------------------------'
2. SS (3)r8c5=r2c5-r2c9=(3)r9c9 => -3 r8c8, r9c4 (+3 r9c9 & basics)

Code: Select all
.----------------------------------------------------.
|  349     1      39   |  37  5    347 | 6    2   8  |
|  3458    358    6    |  2   34   1   | 359  37  79 |
|  357     2      37   |  8   9    6   | 35   4   1  |
|----------------------+---------------+-------------|
|  5789-3  589-3  789-3|  4   1   d39  | 2    6   79 |
|  1      a39     4    |  6   7    2   | 39   8   5  |
| b379     6      2    | c39  8    5   | 1    37  4  |
|----------------------+---------------+-------------|
|  39      7      139  |  15  2    8   | 4    59  6  |
|  6       89     189  |  15  34   34  | 7    59  2  |
|  2       4      5    |  79  6    79  | 8    1   3  |
'----------------------------------------------------'
3. W-Wing (3=9)r5c2-r6c1=r6c4-(9=3)r4c6 => -3 r4c123 (& 11 placements)

Code: Select all
.--------------------------------------------.
|  4      1    9  | 3   5  7 |  6     2   8  |
|  358   b358  6  | 2   4  1 |  359  c37  79 |
|  357    2    37 | 8   9  6 |  35    4   1  |
|-----------------+----------+---------------|
|  5789   589  78 | 4   1  3 |  2     6   79 |
|  1     a39   4  | 6   7  2 |  9-3   8   5  |
|  7-3    6    2  | 9   8  5 |  1    d37  4  |
|-----------------+----------+---------------|
|  39     7    13 | 15  2  8 |  4     59  6  |
|  6      89   18 | 15  3  4 |  7     59  2  |
|  2      4    5  | 7   6  9 |  8     1   3  |
'--------------------------------------------'
4. SS (3)r5c2=r2c2-r2c8=(3)r6c8 => -3 r5c7, r6c1; ste

Regards,
jco
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Re: A good solution to the puzzle

Postby denis_berthier » Mon Mar 29, 2021 5:59 am

AnotherLife wrote:Can anyone offer a good solution to this not very hard sudoku? I mean, it should be human but not artificial computer-based (adieu Berthier, c'est fini).
Code: Select all
.1..5.628..6.........89..4....41.26.1.......5.62.85....7..28.........7..245.6..1.

Nobody on this forum decides who may answer a question or not. If you don't accept this policy, you'd better open your own private club, where only people venerating you are allowed to speak.
Almost everybody on this forum uses computer assistance in a way or another. Some say it, some prefer not to say it.
Computer analysis of a puzzle allows to see things that a manual solver is unlikely to find.

The puzzle (SER 6.3) is quite easy.
18 Singles and three whips[1] (pointing/claiming....):
Code: Select all
whip[1]: c7n5{r3 .} ==> r2c8 ≠ 5
whip[1]: r3n7{c3 .} ==> r2c1 ≠ 7, r1c1 ≠ 7, r1c3 ≠ 7
whip[1]: r1n9{c3 .} ==> r2c2 ≠ 9, r2c1 ≠ 9

lead to the following resolution state, which will be the starting point for the forthcoming solutions.
Code: Select all
   349       1         39        37        5         347       6         2         8         
   3458      358       6         2         34        1         359       379       379       
   357       2         37        8         9         6         35        4         1         
   35789     3589      3789      4         1         39        2         6         379       
   1         39        4         6         7         2         39        8         5         
   379       6         2         39        8         5         1         379       4         
   39        7         139       1359      2         8         4         359       6         
   6         389       1389      1359      34        349       7         359       2         
   2         4         5         379       6         379       8         1         39



1) Simplest-first solution, using only reversible patterns of size no more than 3: Show
hidden-pairs-in-a-column: c4{n1 n5}{r7 r8} ==> r8c4 ≠ 9, r8c4 ≠ 3, r7c4 ≠ 9, r7c4 ≠ 3
z-chain[2]: c4n9{r6 r9} - b9n9{r9c9 .} ==> r6c8 ≠ 9
z-chain[2]: r5n3{c2 c7} - r3n3{c7 .} ==> r2c2 ≠ 3
biv-chain[3]: r4c6{n3 n9} - c4n9{r6 r9} - b8n7{r9c4 r9c6} ==> r9c6 ≠ 3
biv-chain[2]: r9n3{c9 c4} - b5n3{r6c4 r4c6} ==> r4c9 ≠ 3
biv-chain[2]: c9n3{r9 r2} - c5n3{r2 r8} ==> r8c8 ≠ 3, r9c4 ≠ 3
hidden-single-in-a-row ==> r9c9 = 3
whip[1]: r7n3{c3 .} ==> r8c2 ≠ 3, r8c3 ≠ 3
whip[1]: c2n3{r5 .} ==> r4c1 ≠ 3, r4c3 ≠ 3, r6c1 ≠ 3
whip[1]: r9n9{c6 .} ==> r8c6 ≠ 9
whip[1]: b9n9{r8c8 .} ==> r2c8 ≠ 9
biv-chain[2]: c8n3{r2 r6} - c4n3{r6 r1} ==> r2c5 ≠ 3
singles ==> r2c5 = 4, r8c5 = 3, r8c6 = 4, r1c1 = 4, r1c3 = 9
biv-chain[3]: r6c8{n3 n7} - r4c9{n7 n9} - b5n9{r4c6 r6c4} ==> r6c4 ≠ 3
stte

It is likely that some of these steps can be skipped.


2) 1-step solution
There is no W1-anti-backdoor and therefore no solution with only one elimination.
(This doesn't mean there can't be any 1-step solution with a pattern making several eliminations at a time, but this restricts the possibilities.)


3) 2-step solutions
There are many 2-step solutions with whips, but they use whips that are absurdly long for such a simple puzzle. Two of the simplest ones are:
Code: Select all
whip[5]: r5n3{c2 c7} - r3n3{c7 c3} - c2n3{r2 r8} - c5n3{r8 r2} - b3n3{r2c7 .} ==> r6c1 ≠ 3
whip[7]: r1c4{n3 n7} - c6n7{r1 r9} - r9n3{c6 c9} - c8n3{r8 r2} - r2n7{c8 c9} - r4c9{n7 n9} - r4c6{n9 .} ==> r6c4 ≠ 3
stte

whip[5]: r5n3{c2 c7} - r3n3{c7 c3} - c2n3{r2 r8} - c5n3{r8 r2} - b3n3{r2c7 .} ==> r6c1 ≠ 3
whip[7]: r6c4{n9 n3} - r1c4{n3 n7} - c6n7{r1 r9} - r9n3{c6 c9} - c8n3{r8 r2} - r2n7{c8 c9} - c9n9{r2 .} ==> r4c6 ≠ 9
stte


Hajime wrote:I could not solve this manually in 1 or 2 steps

Considering the above results, it shouldn't be too surprising.

This puzzle is one more example that a 1- or 2- step requirement often leads to absurdly complex solutions. Puzzles with this requirement have to be designed specially for it, as has been the case for most of those proposed in this section of the forum.
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Re: A good solution to the puzzle

Postby AnotherLife » Mon Mar 29, 2021 9:39 am

jco wrote:I found a solution in four easy steps.

I see your human approach, and your four-step solution is similar to mine. Maybe someone will find a shorter one that is not too complicated.
Hajime wrote:
I could not solve this manually in 1 or 2 steps...

Code: Select all
.-------------------.--------------.---------------.
| 349    1     39   | 37   5   347 | 6    2    8   |
| 3458   358   6    | 2    34  1   | 359  379  379 |
| 357    2     37   | 8    9   6   | 35   4    1   |
:-------------------+--------------+---------------:
| 35789  3589  3789 | 4    1   39  | 2    6    379 |
| 1      39    4    | 6    7   2   | 39   8    5   |
| 379    6     2    | 39   8   5   | 1    379  4   |
:-------------------+--------------+---------------:
| 39     7     139  | 15   2   8   | 4    359  6   |
| 6      389   1389 | 15   34  349 | 7    359  2   |
| 2      4     5    | 379  6   379 | 8    1    39  |
'-------------------'--------------'---------------'

It is possible to prove that r2c9=9 and get a sste but we will need to construct a forcing net. Obviously, it is not a human solution and it does not meet my requirements. Moreover, I can hardly consider this as one step because we will need three branching chains starting from r6c1=3, r6c4=3, and r6c8=3.
This is the corresponding image from HoDoKu: https://disk.yandex.ru/i/CTt96SDyn3Ad3g
By the way, does anyone has problems with viewing and downloading my images from Yandex Disk?
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Re: A good solution to the puzzle

Postby pjb » Mon Mar 29, 2021 10:35 am

Avoiding ugly complicated chains:
Very occasionally, the "pattern overlay method" is useful, as it is here:

1) No pattern of 3 includes r2c29, r4c13, r6c1, r8c26, r9c4 so 3 can be deleted from these cells

2) Simple chain: (3=7)r1c4 - (7)r1c6 = (7-3)r9c6 = (3)r8c5 => -3 r2c5

(9s at r78c8 only ones in box => -9 r26c8)

3)Simple chain: (3=9)r4c6 - (9=7)r4c9 - (7=3)r6c8 => -3 r6c4; stte

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Re: A good solution to the puzzle

Postby 1to9only » Mon Mar 29, 2021 10:50 am

AnotherLife wrote:By the way, does anyone has problems with viewing and downloading my images from Yandex Disk?

The image is in webp image format, but it has a png extension - maybe this is confusing some browsers!
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Re: A good solution to the puzzle

Postby denis_berthier » Mon Mar 29, 2021 11:15 am

pjb wrote:Avoiding ugly complicated chains:
Very occasionally, the "pattern overlay method" is useful, as it is here:
1) No pattern of 3 includes r2c29, r4c13, r6c1, r8c26, r9c4

How do you prove this, apart from the ugly method of trying all the patterns of 3?
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Re: A good solution to the puzzle

Postby denis_berthier » Mon Mar 29, 2021 11:19 am

1to9only wrote:
AnotherLife wrote:By the way, does anyone has problems with viewing and downloading my images from Yandex Disk?

The image is in webp image format, but it has a png extension - maybe this is confusing some browsers!

If it is a .png image, it can be included as [img ]http://...../image_name.png[/img], without the space between "[img" and "]".
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Re: A good solution to the puzzle

Postby m_b_metcalf » Mon Mar 29, 2021 12:02 pm

AnotherLife wrote:Can anyone offer a good solution to this not very hard sudoku? I mean, it should be human but not artificial computer-based (adieu Berthier, c'est fini).
Code: Select all
.1..5.628..6.........89..4....41.26.1.......5.62.85....7..28.........7..245.6..1.


No, but it's a nice pattern that lends itself to the production of puzzles with symmetry of givens. An example is
Code: Select all
 . 8 . . 4 . 6 3 1
 . . 4 . . . . . .
 . . . 1 8 . . 5 .
 . . . 4 3 . 8 6 .
 4 . . . . . . . 5
 . 6 2 . 7 5 . . .
 . 4 . . 2 9 . . .
 . . . . . . 5 . .
 9 7 6 . 5 . . 2 .   Very hard, symmetry of givens.


A further bunch, all with symmetry of givens, is
Hidden Text: Show
Code: Select all
.1..2.345..4.........16..7....23.58.3.......9.42.95....7..16.........8..289.5..6.   ED=1.2/1.2/1.2   
.1..2.345..6.........47..6....58.42.5.......1.42.61....8..32.........8..127.4..5.   ED=1.5/1.2/1.2   
.1..2.345..5.........64..7....26.73.7.......2.62.37....2..83.........5..586.7..9.   ED=1.7/1.2/1.2   
.1..2.345..6.........71..6....24.71.8.......2.71.68....4..71.........4..569.8..7.   ED=2.0/1.2/1.2   
.1..2.345..6.........73..8....97.82.2.......9.97.82....7..48.........5..634.9..1.   ED=2.3/1.2/1.2   
.1..2.345..2.........13..6....34.75.3.......8.29.68....4..81.........5..268.5..1.   ED=2.5/1.2/1.2   
.1..2.345..2.........46..2....61.57.6.......8.31.58....9..84.........9..147.9..5.   ED=2.6/1.2/1.2   
.1..2.345..2.........36..7....71.85.9.......1.28.96....6..74.........5..234.5..9.   ED=2.8/1.2/1.2   
.1..2.345..2.........65..2....46.15.7.......3.81.92....4..89.........4..827.4..1.   ED=3.0/1.2/1.2   
.1..2.345..6.........75..6....51.62.1.......8.45.86....5..63.........5..627.4..8.   ED=3.2/1.2/1.2   
.1..2.345..6.........45..1....27.89.7.......1.68.14....7..32.........9..325.4..7.   ED=3.4/3.4/2.6   
.1..2.345..3.........61..7....23.81.3.......4.81.47....2..89.........4..534.7..8.   ED=3.6/1.2/1.2   
.1..2.345..6.........45..7....61.85.1.......9.68.95....3..62.........5..627.4..9.   ED=4.2/1.5/1.5   
.1..2.345..5.........63..1....27.16.1.......8.28.96....8..42.........5..534.6..8.   ED=4.4/1.2/1.2   
.1..2.345..2.........36..1....17.82.1.......6.58.46....6..19.........5..279.5..6.   ED=4.5/1.2/1.2   
.1..2.345..2.........16..2....63.51.3.......7.68.71....4..16.........4..827.4..6.   ED=5.6/1.2/1.2   
.1..2.345..6.........43..6....35.78.8.......3.31.68....5..82.........5..628.4..7.   ED=5.7/1.2/1.2   
.1..2.345..2.........64..2....57.26.8.......3.45.12....5..64.........5..268.5..7.   ED=6.6/1.2/1.2   
.1..2.345..6.........57..1....34.17.4.......6.38.67....8..35.........4..567.9..8.   ED=6.7/1.2/1.2   
.1..2.345..2.........16..2....73.89.8.......3.43.82....7..16.........7..598.7..6.   ED=7.1/2.3/2.3   
.1..2.345..6.........14..2....71.45.7.......2.68.92....7..89.........5..683.7..9.   ED=7.2/3.4/2.6   
.1..2.345..6.........17..6....54.27.4.......8.51.87....9..52.........9..783.1..2.   ED=7.3/1.5/1.5   
.1..2.345..2.........64..1....47.83.8.......4.34.18....7..89.........5..283.5..7.   ED=7.4/2.3/2.3   
.1..2.345..2.........65..2....54.78.4.......3.98.31....6..12.........6..134.6..5.   ED=7.6/1.2/1.2   
.1..2.345..6.........15..2....61.47.1.......8.92.85....4..68.........5..623.4..8.   ED=7.7/1.2/1.2   
.1..2.345..2.........16..7....65.48.5.......7.96.74....5..42.........1..763.1..2.   ED=7.8/1.2/1.2   
.1..2.345..6.........13..6....47.83.7.......6.48.63....7..45.........7..134.9..5.   ED=7.9/1.2/1.2   
.1..2.345..6.........14..7....78.13.7.......4.28.14....4..78.........5..672.3..8.   ED=8.2/1.2/1.2   
.1..2.345..6.........75..8....21.97.2.......3.91.73....5..87.........4..862.3..9.   ED=8.3/1.2/1.2   
.1..2.345..6.........37..1....58.12.1.......8.58.12....8..69.........7..249.5..8.   ED=8.4/2.3/2.3   
.1..2.345..6.........47..6....21.43.1.......8.23.84....9..52.........9..732.4..8.   ED=8.5/1.5/1.5   
.1..2.345..6.........57..1....16.85.1.......7.69.52....7..16.........5..623.4..7.   ED=8.6/1.2/1.2   
.1..2.345..2.........13..6....56.43.5.......2.74.82....8..79.........5..247.5..9.   ED=8.8/1.2/1.2   
.1..2.345..6.........74..8....39.45.3.......2.97.52....6..74.........8..972.3..1.   ED=8.9/1.5/1.5   
.1..2.345..4.........15..6....24.17.2.......6.48.76....2..98.........7..973.6..8.   ED=9.1/1.2/1.2   

All puzzles are minimal.

Regards,

Mike Metcalf
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Re: A good solution to the puzzle

Postby Cenoman » Mon Mar 29, 2021 6:42 pm

Solution to AnotherLife's puzzle:
Code: Select all
 +------------------------+-------------------+--------------------+
 |  349     1      39     |  37    5    347   |  6     2     8     |
 |  3458    358    6      |  2    D34   1     |  359   379   79-3  |
 |  357     2      37     |  8     9    6     |  35    4     1     |
 +------------------------+-------------------+--------------------+
 |  35789   3589   3789   |  4     1   d39    |  2     6     79-3  |
 |  1       39     4      |  6     7    2     |  39    8     5     |
 |  379     6      2      | c39    8    5     |  1     379   4     |
 +------------------------+-------------------+--------------------+
 |  39      7      139    |  15    2    8     |  4     359   6     |
 |  6       389    1389   |  15   C34   349   |  7     359   2     |
 |  2       4      5      |Bb379   6   B379   |  8     1   Aa39    |
 +------------------------+-------------------+--------------------+

1. W-wing (3=9)r9c9 - r9c4 = r6c4 - (9=3)r4c6 => -3 r4c9
2. Grouped kite (3)r9c9 = r9c46 - r8c5 = r2c5 => -3 r2c9; +3r9c9 and lcls
Code: Select all
 +------------------------+------------------+------------------+
 |  349     1      39     |  37   5    347   |  6     2    8    |
 |  3458    58-3   6      |  2    34   1     |  359   37*  79   |
 |  357     2      37     |  8    9    6     |  35    4    1    |
 +------------------------+------------------+------------------+
 |  35789   3589   3789   |  4    1    39    |  2     6    79   |
 |  1      c39*    4      |  6    7    2     | d39*   8    5    |
 | e37-9    6      2      |  39   8    5     |  1    d37*  4    |
 +------------------------+------------------+------------------+
 | a39      7      139^   |  15^  2    8     |  4     59^  6    |
 |  6      b89     189^   |  15^  34   34    |  7     59^  2    |
 |  2       4      5      |  79   6    79    |  8     1    3    |
 +------------------------+------------------+------------------+

3. Kite (3)r5c2 - r5c7 = r6c8 = r2c8 => -3 r2c2
4. DP(159)r78c348 using externals
(9)r7c1 == (9)r8c2 - (9=3)r5c2 - (37)b6p48 = (7)r6c1 => -9r6c1; ste
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Re: A good solution to the puzzle

Postby AnotherLife » Mon Mar 29, 2021 9:49 pm

Cenoman wrote:1. W-wing (3=9)r9c9 - r9c4 = r6c4 - (9=3)r4c6 => -3 r4c9
2. Grouped kite (3)r9c9 = r9c46 - r8c5 = r2c5 => -3 r2c9; +3r9c9 and lcls
3. Kite (3)r5c2 - r5c7 = r6c8 = r2c8 => -3 r2c2

After step 3 I used locked candidates in block 4 => -3 r4c1, -3 r6c1, -3 r4c3:
Code: Select all
---------------------.-------------.-------------.
| 349    1     39    | 37  5   347 | 6    2   8  |
| 3458   58    6     | 2   34  1   | 359  37  79 |
| 357    2     37    | 8   9   6   | 35   4   1  |
:--------------------+-------------+-------------:
| 5789-3 3589  789-3 | 4   1   39  | 2    6   79 |
| 1      39    4     | 6   7   2   | 39   8   5  |
| 79-3   6     2     | 39  8   5   | 1    37  4  |
:--------------------+-------------+-------------:
| 39     7     139   | 15  2   8   | 4    59  6  |
| 6      89    189   | 15  34  34  | 7    59  2  |
| 2      4     5     | 79  6   79  | 8    1   3  |
'--------------------'-------------'-------------'

Then a w-wing was available.
4. (7=9)r6c1 - r5c2 = r5c7 - (9=7)r4c9 => -7 r6c8; ste
Code: Select all
.-----------------.-------------.--------------.
| 349   1     39  | 37  5   347 | 6    2   8   |
| 3458  58    6   | 2   34  1   | 359  37  79  |
| 357   2     37  | 8   9   6   | 35   4   1   |
:-----------------+-------------+--------------:
| 5789  3589  789 | 4   1   39  | 2    6   d79 |
| 1     b39   4   | 6   7   2   | c39  8   5   |
| a79   6     2   | 39  8   5   | 1    3-7 4   |
:-----------------+-------------+--------------:
| 39    7     139 | 15  2   8   | 4    59  6   |
| 6     89    189 | 15  34  34  | 7    59  2   |
| 2     4     5   | 79  6   79  | 8    1   3   |
'-----------------'-------------'--------------'

I see that the human solvers have come to similar four-step solutions using simple chains.
Bogdan
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Re: A good solution to the puzzle

Postby eleven » Mon Mar 29, 2021 10:30 pm

Code: Select all
 *-----------------------------------------------------------------*
 |  349     1      39     |  3-7   5    347   |  6     2     8     |
 |  3458    358    6      |  2     34   1     |  359   379   379   |
 |  357     2      37     |  8     9    6     |  35    4     1     |
 |------------------------+-------------------+--------------------|
 |  35789   3589   3789   |  4     1   @39    |  2     6    @39+7  |
 |  1       39     4      |  6     7    2     |  39    8     5     |
 |  379     6      2      |@#39    8    5     |  1    #39+7  4     |
 |------------------------+-------------------+--------------------|
 |  39      7      139    |  15    2    8     |  4    #359   6     |
 |  6       389    1389   |  15    34   349   |  7    #359   2     |
 |  2       4      5      |@#39+7  6    39-7  |  8     1   @#39    |
 *-----------------------------------------------------------------*

There is a deadly pattern (2 digit oddagon) for 39 in the @ marked cells r4c69,r6c4,r9c49, so one of r4c9 or r9c4 must be 7.
And another one in the # marked cells r4c48,r78c8,r9c49), so one of r6c8 or r9c4 must be 7.
So wherever 7 is in box 6, r9c4 must be 7.

Still needs pair and skyscraper.
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Re: A good solution to the puzzle

Postby Cenoman » Tue Mar 30, 2021 8:48 am

Hi eleven,

Happy to read again your tricky solutions !
eleven wrote:There is a deadly pattern (2 digit oddagon) for 39 in the @ marked cells r4c69,r6c4,r9c49, so one of r4c9 or r9c4 must be 7.
And another one in the # marked cells r4c48,r78c8,r9c49), so one of r6c8 or r9c4 must be 7.
So wherever 7 is in box 6, r9c4 must be 7.

This step deserves huge applause !

eleven wrote:Still needs pair and skyscraper.
The kite (3)r5c27-r26c8 is enough for ste finish, but in the spirit of your first step, you can also finish with:
Hidden Text: Show
Code: Select all
 +--------------------+-----------------+------------------+
 |  4      1     9    |  3    5    7    |  6     2    8    |
 | #358   *58-3  6    |  2    4    1    | #359  *7-3  79   |
 |  357    2     37   |  8    9    6    |  35    4    1    |
 +--------------------+-----------------+------------------+
 |  5789   589   78   |  4    1    3    |  2     6    79   |
 |  1     *39    4    |  6    7    2    |  39    8    5    |
 | *37     6     2    |  9    8    5    |  1    *37   4    |
 +--------------------+-----------------+------------------+
 |  39     7     13   |  15   2    8    |  4     59   6    |
 |  6      89    18   |  15   3    4    |  7     59   2    |
 |  2      4     5    |  7    6    9    |  8     1    3    |
 +--------------------+-----------------+------------------+
5-link oddagon (3)r26, c28, b4, having two guardians +3 r2c17; ste (-3 r2c28)
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Re: A good solution to the puzzle

Postby AnotherLife » Tue Mar 30, 2021 10:23 am

eleven wrote:There is a deadly pattern (2 digit oddagon) for 39 in the @ marked cells r4c69,r6c4,r9c49, so one of r4c9 or r9c4 must be 7.
And another one in the # marked cells r4c48,r78c8,r9c49), so one of r6c8 or r9c4 must be 7.
So wherever 7 is in box 6, r9c4 must be 7.

Still needs pair and skyscraper.

Thank you, sir, for your non-standard human two-step solution to the puzzle. You get a prize for the best solution.

The humans win. Remember, Genisys is Skynet.
Bogdan
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