He Who Controls The Sπce (SER 7.1)

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He Who Controls The Sπce (SER 7.1)

Postby mith » Mon Apr 05, 2021 3:03 pm

Code: Select all
+-------+-------+-------+
| . . 3 | . . 1 | 4 . . |
| . . . | . . . | . 1 . |
| . . 5 | . . 9 | . . . |
+-------+-------+-------+
| 2 . . | . 6 . | . . 5 |
| 3 . . | 5 . 8 | . . 9 |
| 7 . . | . 9 . | . . 3 |
+-------+-------+-------+
| . . . | 2 . . | 3 . . |
| . 8 . | . . . | . . . |
| . . 4 | 6 . . | 2 . . |
+-------+-------+-------+
..3..14.........1...5..9...2...6...53..5.8..97...9...3...2..3...8.........46..2..
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Re: He Who Controls The Sπce (SER 7.1)

Postby Cenoman » Mon Apr 05, 2021 8:20 pm

Code: Select all
 +---------------------+-------------------+--------------------+
 |  689    69    3     |  78    27    1    |  4     5    267    |
 |  4      2     7     |  3     5     6    |  9     1    8      |
 | c168   b16    5     |  478   247   9    |  67    3    267    |
 +---------------------+-------------------+--------------------+
 |  2   xAa149  y189*  |  147   6     3    | z178*  4-7  5      |
 |  3     B146  B16*   |  5     47    8    |zB167*  2    9      |
 |  7      5     168*  |  14    9     2    |  168*  46   3      |
 +---------------------+-------------------+--------------------+
 |  1569   7     169   |  2     18    45   |  3     89   146    |
 | d16     8     2     |  9     3     47   |  5    d67   1467   |
 |  159    3     4     |  6     18    57   |  2     89   17     |
 +---------------------+-------------------+--------------------+

Kraken cell (149)r4c2 + DP (168)r456c37 (using internals)
(1)r4c2 - r3c2 = r3c1 - (1=67)r8c18
(4)r4c2 - (4=167)r5c237
(9)r4c2 - r4c3=DP=(7)r45c7
---------------
=> -7 r4c8; ste
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Re: He Who Controls The Sπce (SER 7.1)

Postby pjb » Tue Apr 06, 2021 12:22 am

Code: Select all
  689    b69      3      | 78     27     1      | 4      5      267   
  4       2       7      | 3      5      6      | 9      1      8     
 aB168   A16      5      | 478    247B   9      | 67a    3      267A   
-------------------------+----------------------+---------------------
  2       149     189    | 147D   6      3      | 178  eE47eE   5     
  3      c146    d16     | 5      47C    8      |d167b   2      9     
  7       5       168    | 14D    9      2      | 168b   46c    3     
-------------------------+----------------------+---------------------
  1569    7       169    | 2      18     45     | 3      89     146   
 C16      8       2      | 9      3      47     | 5     D67d    1467   
  159     3       4      | 6      18     57     | 2      89     17     

Kraken row r3c1279:
(6)r3c1 - r1c2 = r5c2 - (6=7)r5c37 - (7)r4c8
(6-1)r3c2 = r3c1 - (1=6)r8c1 - (6=7)r8c8 - (7)r4c8
(6)r3c7 - r56c7 = r6c8 - (6=7)r8c8 - (7)r4c8
(6-2)r3c9 = (2-4)r3c5 = (4)r5c5 - (4=7)r46c4 - (7)r4c8 => -7 r4c8; stte

Phil
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Re: He Who Controls The Sπce (SER 7.1)

Postby AnotherLife » Wed Apr 07, 2021 1:00 pm

After the lcls steps, I found manually a simple two-step solution without forcing chains.
1. W-wing
(7=4)r5c5-r6c4=r6c8-(4=7)r4c8 => -7 r4c4, r5c7
Code: Select all
.----------------.--------------.---------------.
| 689   69   3   | 78   27   1  | 4    5   267  |
| 4     2    7   | 3    5    6  | 9    1   8    |
| 168   16   5   | 478  247  9  | 67   3   267  |
:----------------+--------------+---------------:
| 2     149  189 | 14-7  6   3  | 178  d47 5    |
| 3     146  16  | 5    a47  8  | 16-7 2   9    |
| 7     5    168 | b14   9   2  | 168  c46 3    |
:----------------+--------------+---------------:
| 1569  7    169 | 2    18   45 | 3    89  146  |
| 16    8    2   | 9    3    47 | 5    67  1467 |
| 159   3    4   | 6    18   57 | 2    89  17   |
'----------------'--------------'---------------'

2. After 5 singles and some other lcls steps, there is an XY-Wing:
(4=6)r7c9-(6=7)r8c8-(7=4)r8c6 => -4 r7c6, r8c9; sste
Code: Select all
 .--------------.-------------.----------------.
| 89   69  3   | 78  2   1   | 4    5   67    |
| 4    2   7   | 3   5   6   | 9    1   8     |
| 18   16  5   | 78  4   9   | 67   3   2     |
:--------------+-------------+----------------:
| 2    19  189 | 14  6   3   | 178  47  5     |
| 3    4   16  | 5   7   8   | 16   2   9     |
| 7    5   168 | 14  9   2   | 168  46  3     |
:--------------+-------------+----------------:
| 56   7   19  | 2   18  5-4 | 3    89  a46   |
| 16   8   2   | 9   3   c47 | 5    b67 167-4 |
| 159  3   4   | 6   18  57  | 2    89  17    |
'--------------'-------------'----------------'

Actually, if we eliminate a digit or force a digit into a cell with a forcing chain (or a forcing net), we might need three of more chains, so is it better than a two-step solution with two chains described by standard patterns?
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Re: He Who Controls The Sπce (SER 7.1)

Postby jco » Wed Apr 07, 2021 1:38 pm

Hello AnotherLife,

AnotherLife wrote:(...)
Actually, if we eliminate a digit or force a digit into a cell with a forcing chain (or a forcing net), we might need three of more chains, so is it better than a two-step solution with two chains described by standard patterns?


I like the puzzle section because I can see a variety of solutions found by the players as they use their knowledge and creativity to propose interesting solutions different from the ones already posted. Many times I started studying the details of techniques previously unknown to me because I noticed the beauty, elegance and effectiveness of those techniques used by advanced players to solve puzzles.

Regards,
jco
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Re: He Who Controls The Sπce (SER 7.1)

Postby Hajime » Sun Apr 11, 2021 4:56 pm

Just 2 XY-chains, one of length 3 and one of length 5:

Solution Path:
Hidden Text: Show
Code: Select all
Singles towards
   +----'-----'----+---'----'---+---'-----'-----+ 
   | 689  2679   3 | 78  278  1 | 4    5    2678| 
   | 48   247   78 | 3    5   6 | 9    1    278 | 
   |1468 12467   5 |478 2478  9 |678   3    2678| 
   +----'-----'----+---'----'---+---'-----'-----+ 
   |  2   149   189|147   6   3 |178  478    5  | 
   |  3   146   16 | 5   147  8 |167   2     9  | 
   |  7    5    168| 14   9   2 |168  468    3  | 
   +----'-----'----+---'----'---+---'-----'-----+ 
   |1569  1679 1679| 2  1478 457| 3  46789 14678| 
   | 16    8     2 | 9    3   47| 5   467   1467| 
   | 159   3     4 | 6   178  57| 2   789   178 | 
   +----'-----'----'---'----'---'---'-----'-----+ 
                                                   
#1//B4
..3..145....35691...5..9.3.2...63..53..5.8.2975..92..3...2..3...8293.5...346..2..

Pointing, Claiming  | (8)c7b6 => (-8)r4c8 (-8)r6c8
Naked/Hidden Triplet | NSS (467)c8r468 => (-6)r7c8 (-7)r9c8
XY-chain [3]  |  (1=6)r8c1 (6=7)r8c8 (7=1)r9c9 => (-1)r8c9 (-1)r9c1
r2c3=7   Naked Single
r2c2=2   Naked Single
r2c9=8   Naked Single
r2c1=4   Naked Single
r7c2=7   Hidden Single In row 2
r8c1=1   Hidden Single In row 1
r3c2=1   Hidden Single In box 8
Naked/Hidden Triplet  | (457)b8e369 => (-4)r7c5 (-7)r9c5
Naked/Hidden Pair | (18)c5r79 => (-8)r1c5 (-8)r3c5 (-1)r5c5
Pointing, Claiming  | (6)b7r7 => (-6)r7c8 (-6)r7c9 | (8)c7b6 => (-8)r4c8 (-8)r6c8 | (4)b6c8 => (-4)r7c8 (-4)r8c8
Naked/Hidden Triplet  | (467)c8r468 => (-7)r9c8
XY-chain [5]  |  (7=4)r4c8 (4=9)r4c2 (9=6)r1c2 (6=4)r5c2 (4=7)r5c5 => (-7)r4c4 (-7)r5c7
stte
Summary used Methods
Hidden Text: Show
Code: Select all
Eliminated candidates per Method and per Sudoku

Method   \  Sudoku |   SER |     1
                   |-------|------
Not counted elims  |     0 |    84
Naked Singles      |   0.1 |    23
Hidden Singles     |   0.2 |   106
Naked Pair     [2] |     3 |     3
Naked Triple   [3] |   3.6 |     5
Pointing/Claiming  |   2.8 |    12
XY-Wing        [3] |   4.1 |     2
XY-chain       [5] |   5.1 |     2
                   |-------|------
Eliminated Cand's  |   237 |   237
Sum(SER * Cand's)  | 102.5 | 102.5

Initial Candidates :   237
Maximum SER rating :   5.1 <- Approach
Labour rating      : 102.5 <- Experimental rating
Time needed        : 00:00:00.369
SiSeSuSo Solver and Generator (version 2021-04b)
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