From 7Sudoku graded very difficult

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From 7Sudoku graded very difficult

Postby swaatacba » Sun Sep 06, 2020 11:17 am

This is a puzzle published earlier this year by 7Sudoku, but it is no longer on the site.

Despite several attempts, I have failed to proceed beyond this point. Help please.
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Re: From 7Sudoku graded very difficult

Postby rjamil » Sun Sep 06, 2020 3:18 pm

Hi swaatacba,

Am not an expert, but try to help you at my level:

Code: Select all
...74...1.71..59..5.9.....8.9.61.4.............5.82.3.4.....7.5..73..81.8...74...
+---------------+------------+--------------+
| 236  8    23  | 7   4   9  | 5    26  1   |
| 26   7    1   | 8   36  5  | 9    4   236 |
| 5    4    9   | 2   36  1  | 36   7   8   |
+---------------+------------+--------------+
| 23   9    8   | 6   1   37 | 4    5   27  |
| 1    23   4   | 59  59  37 | 26   8   267 |
| 7    6    5   | 4   8   2  | 1    3   9   |
+---------------+------------+--------------+
| 4    123  236 | 19  29  8  | 7    26  5   |
| 9    25   7   | 3   25  6  | 8    1   4   |
| 8    15   26  | 15  7   4  | 236  9   236 |
+---------------+------------+--------------+

Above mentioned is the original puzzle and your solved pencilmark state in text form.

There are lot of moves exist after above mentioned pencilmark. However, few of them that solves the puzzle with singles to the end are as follows:

1) Grouped Skyscraper: Base cells 2 @ r5c27 Target cells 2 @ r78c2 and 2 @ r9c7 => -2 @ r9c3; or
Code: Select all
+-----------------+------------+----------------+
| 236  8      23  | 7   4   9  | 5      26  1   |
| 26   7      1   | 8   36  5  | 9      4   236 |
| 5    4      9   | 2   36  1  | 36     7   8   |
+-----------------+------------+----------------+
| 23   9      8   | 6   1   37 | 4      5   27  |
| 1    (2)3   4   | 59  59  37 | (2)6   8   267 |
| 7    6      5   | 4   8   2  | 1      3   9   |
+-----------------+------------+----------------+
| 4    1(2)3  236 | 19  29  8  | 7      26  5   |
| 9    (2)5   7   | 3   25  6  | 8      1   4   |
| 8    15     6-2 | 15  7   4  | (2)36  9   236 |
+-----------------+------------+----------------+

2) Grouped 2 String Kite: Base cells 2 @ r7c8 and 2 @ r9c79 Target cells 2 @ r1c8 and 2 @ r9c3 => -2 @ r1c3; or
Code: Select all
+----------------+------------+--------------------+
| 236  8    3-2  | 7   4   9  | 5      (2)6  1     |
| 26   7    1    | 8   36  5  | 9      4     236   |
| 5    4    9    | 2   36  1  | 36     7     8     |
+----------------+------------+--------------------+
| 23   9    8    | 6   1   37 | 4      5     27    |
| 1    23   4    | 59  59  37 | 26     8     267   |
| 7    6    5    | 4   8   2  | 1      3     9     |
+----------------+------------+--------------------+
| 4    123  236  | 19  29  8  | 7      (2)6  5     |
| 9    25   7    | 3   25  6  | 8      1     4     |
| 8    15   (2)6 | 15  7   4  | (2)36  9     (2)36 |
+----------------+------------+--------------------+

3) W-Wing: 26 @ r1c8 r9c3 Strong Link 6 @ r7c38 => -2 @ r1c3.
Code: Select all
+-----------------+------------+----------------+
| 236  8    3-2   | 7   4   9  | 5    (26)  1   |
| 26   7    1     | 8   36  5  | 9    4     236 |
| 5    4    9     | 2   36  1  | 36   7     8   |
+-----------------+------------+----------------+
| 23   9    8     | 6   1   37 | 4    5     27  |
| 1    23   4     | 59  59  37 | 26   8     267 |
| 7    6    5     | 4   8   2  | 1    3     9   |
+-----------------+------------+----------------+
| 4    123  23(6) | 19  29  8  | 7    2(6)  5   |
| 9    25   7     | 3   25  6  | 8    1     4   |
| 8    15   (26)  | 15  7   4  | 236  9     236 |
+-----------------+------------+----------------+


R. Jamil
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Re: From 7Sudoku graded very difficult

Postby Leren » Sun Sep 06, 2020 9:36 pm

Code: Select all
*---------------------------------------*
| 236 8    3-2 | 7  4  9  | 5   d26 1   |
| 26  7    1   | 8  36 5  | 9    4  236 |
| 5   4    9   | 2  36 1  | 36   7  8   |
|--------------+----------+-------------|
| 23  9    8   | 6  1  37 | 4    5  27  |
| 1   23   4   | 59 59 37 | 26   8  267 |
| 7   6    5   | 4  8  2  | 1    3  9   |
|--------------+----------+-------------|
| 4   123 b236 | 19 29 8  | 7   c26 5   |
| 9   25   7   | 3  25 6  | 8    1  4   |
| 8   15  a26  | 15 7  4  | 236  9  236 |
*---------------------------------------*

(2=6) r9c3 - r7c3 = r7c8 - (6=2) r1c8 => - 2 r1c3; stte

Leren
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Re: From 7Sudoku graded very difficult

Postby denis_berthier » Mon Sep 07, 2020 4:08 am

Starting from your PM:
Code: Select all
(solve-sudoku-grid
   +---------------+------------+--------------+
   ! 236  8    23  ! 7   4   9  ! 5    26  1   !
   ! 26   7    1   ! 8   36  5  ! 9    4   236 !
   ! 5    4    9   ! 2   36  1  ! 36   7   8   !
   +---------------+------------+--------------+
   ! 23   9    8   ! 6   1   37 ! 4    5   27  !
   ! 1    23   4   ! 59  59  37 ! 26   8   267 !
   ! 7    6    5   ! 4   8   2  ! 1    3   9   !
   +---------------+------------+--------------+
   ! 4    123  236 ! 19  29  8  ! 7    26  5   !
   ! 9    25   7   ! 3   25  6  ! 8    1   4   !
   ! 8    15   26  ! 15  7   4  ! 236  9   236 !
   +---------------+------------+--------------+
)


a few simple rules give the solution:

Code: Select all
***********************************************************************************************
***  SudoRules 20.1.s based on CSP-Rules 2.1.s, config = W+SFin
***  Using CLIPS 6.32-r770
***********************************************************************************************
71 candidates, 230 csp-links and 230 links. Density = 9.26%
whip[1]: r7n3{c3 .} ==> r9c3 ≠ 3, r9c2 ≠ 3
whip[1]: c6n3{r5 .} ==> r5c5 ≠ 3
whip[1]: c1n6{r2 .} ==> r1c3 ≠ 6
whip[1]: r1n3{c3 .} ==> r2c1 ≠ 3
hidden-pairs-in-a-row: r9{n1 n5}{c2 c4} ==> r9c2 ≠ 2
x-wing-in-rows: n2{r2 r4}{c1 c9} ==> r9c9 ≠ 2, r5c9 ≠ 2, r1c1 ≠ 2
finned-x-wing-in-rows: n2{r5 r9}{c7 c2} ==> r8c2 ≠ 2, r7c2 ≠ 2
stte
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Re: From 7Sudoku graded very difficult

Postby swaatacba » Mon Sep 07, 2020 1:14 pm

Leren wrote:(2=6) r9c3 - r7c3 = r7c8 - (6=2) r1c8 => - 2 r1c3; stte


I have followed Leren's instructions and it generates a valid solution.

I suspect that all the proposed solutions are correct, but need to take a while to understand the logic. The long term aim is to mimic the logic in Excel.

Thank you, Stephen
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Re: From 7Sudoku graded very difficult

Postby Hajime » Mon Sep 07, 2020 2:29 pm

swaatacba wrote:The long term aim is to mimic the logic in Excel.

In Excel VBA ? I have published some methods in VBA. You can investigate that...
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Re: From 7Sudoku graded very difficult

Postby SpAce » Mon Sep 07, 2020 2:55 pm

swaatacba wrote:
Leren wrote:(2=6) r9c3 - r7c3 = r7c8 - (6=2) r1c8 => - 2 r1c3; stte

I have followed Leren's instructions and it generates a valid solution.

It's the same as rjamil's W-Wing, just written explicitly as an AIC (which is better).

I suspect that all the proposed solutions are correct, but need to take a while to understand the logic.

They're all correct. If it helps, here are some alternate presentations for them.

rjamil's three solutions presented as AICs:

Code: Select all
Grouped Skyscraper:    (2)r78c2 = r5c2 - r5c7 = (2)r9c7    => -2 r9c3; stte
Grouped 2-String Kite: (2)r9c3 = r9c79 - r7c8 = (2)r1c8    => -2 r1c3; stte
W-Wing:                (2=6)r9c3 - r7c3 = r7c8 - (6=2)r1c8 => -2 r1c3; stte

Note: the Grouped Skyscraper is also:

Code: Select all
Finned Sashimi X-Wing: (2)c27\r59b7 => -2 r9c3; stte

Any of those is enough by itself. Denis' solution needs two non-basic steps:

Code: Select all
1. X-Wing:                (2)r24\c19   => -2 r1c1,r59c9
2. Finned Sashimi X-Wing: (2)r59\c27b7 => -2 r78c2; stte

The latter is also (and usually presented as):

Code: Select all
2. Skyscraper: (2)r5c2 = r5c7 - r9c7 = (2)r9c3 => -2 r78c2; stte
-SpAce-: Show
Code: Select all
   *             |    |               |    |    *
        *        |=()=|    /  _  \    |=()=|               *
            *    |    |   |-=( )=-|   |    |      *
     *                     \  ¯  /                   *   

"If one is to understand the great mystery, one must study all its aspects, not just the dogmatic narrow view of the Jedi."
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Re: From 7Sudoku graded very difficult

Postby swaatacba » Mon Sep 07, 2020 4:32 pm

Hajime wrote:In Excel VBA ? I have published some methods in VBA. You can investigate that...


Thank you. The crucial point about employing Excel's user interface rather than VBA, is that it exposes the logic and methodology to the user.

I avoid, for the most part, hiding any part of the worksheet(s). Users are free to use the auditing processes to expose the methods and the formulae. Some of the worksheets are protected, but there are no passwords.

You may be interesting to look at this example. https://drive.google.com/file/d/10FfLrMrFcyzGkZkmKM2HiRsgMwmciljz/view?usp=sharing

Stephen
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