The New Sudoku Players' Forum

[Cenoman]

Weekly Extreme of this week:

Code: Select all

+---+---+---+
|...|...|...|
|7..|.6.|8.5|
|.93|.7.|24.|
+---+---+---+
|...|..6|5.1|
|...|...|..9|
|1.5|9.4|...|
+---+---+---+
|.86|.5.|12.|
|3.2|.8.|..7|
|...|...|...|
+---+---+---+

.........7...6.8.5.93.7.24......65.1........91.59.4....86.5.12.3.2.8...7.........

Source: www.sudoku.org.uk

[SteveG48]

Code: Select all

 *--------------------------------------------------------------------*
 | 26     12456  148    | 2458  a49     2589   | 7-9  ab179    3      |
 | 7     f124   f14     |f234    6      239    | 8   abf19     5      |
 | 58     9      3      | 158    7      158    | 2      4      6      |
 *----------------------+----------------------+----------------------|
 |d48     347    9      |e78     2      6      | 5     b37     1      |
 | 26     236    78     | 578    1      578    | 4     b36     9      |
 | 1      67     5      | 9      3      4      | 67     8      2      |
 *----------------------+----------------------+----------------------|
 | 9      8      6      |e37     5      37     | 1      2      4      |
 | 3      145    2      | 146    8      19     | 69     569    7      |
 |c45     1457   147    | 1246  b49     129    | 3     c569    8      |
 *--------------------------------------------------------------------*


9r1c58,r2c8 = 9r9c5&(1376)r1245c8 - (6|9=54)r9c18 - (4=8)r4c1 - (8=73)r47c4 - (3=1249)r2c2348 => -9 r1c7 ; ste

[jco]

Two steps for me. After basics,

Code: Select all

,--------------------------------------------------------------------,
| 26     12456  148    |#2458   49    #2589   | 79     179    3      |
| 7      124    14     | 234*   6      239    | 8      19     5      |
| 58     9      3      | 158    7      158    | 2      4      6      |
|----------------------+----------------------+----------------------|
| 48     347    9      | 78     2      6      | 5      37     1      |
| 26     236    8-7    |#578    1     #578    | 4      36     9      |
| 1      67     5      | 9      3      4      | 67     8      2      |
|----------------------+----------------------+----------------------|
| 9      8      6      | 37     5      37     | 1      2      4      |
| 3      145    2      | 146    8      19     | 69     569    7      |
| 45     1457   147    | 1246   49     129    | 3      569    8      |
'--------------------------------------------------------------------'

1. UR(58)r15c46 using internals with extended ALS Y-wing => -7 r5c3 [& 14 placements]
||(7)r5c46
||(4)r1c4 - (4=97)r1c57 - r6c7 = r6c2
||(9)r1c6 - (9=7)r1c7 - r6c7 = r6c2
||(2)r1c46 - (2)r2c4 = [(7)r6c2 = r6c7 - (7=9)r1c7 - (9=143)r2c348 - (3=7)r7c4 - r4c4 = r5c46]
----

Code: Select all

,--------------------------------------------------,
| 6    5    14   | 2    49   8    | 79   179  3    |
| 7    2    14   | 34   6   *39   | 8   *19   5    |
| 8    9    3    | 15   7    15   | 2    4    6    |
|----------------+----------------+----------------|
| 4    37   9    | 8    2    6    | 5    37   1    |
| 2    36   8    | 57   1    57   | 4    36   9    |
| 1    67   5    | 9    3    4    | 67   8    2    |
|----------------+----------------+----------------|
| 9    8    6    | 37   5    37   | 1    2    4    |
| 3    14   2    | 146  8   *19   |*69   5    7    |
| 5    14   7    | 146  49   2    | 3    69   8    |
'--------------------------------------------------'

2. Skyscraper (9) r2c8 = r2c6 - r8c6 = r8c7 => -9 r9c8, r1c7; ste

[rjamil]

Upto triple-digit POM moves solution (after 13 singleton moves):

Code: Select all

 +-------------------+------------------+------------+
 | 24568  12456  148 | 12458  49  12589 | 79  179  3 |
 | 7      124    14  | 1234   6   1239  | 8   19   5 |
 | 58     9      3   | 158    7   158   | 2   4    6 |
 +-------------------+------------------+------------+
 | 48     347    9   | 78     2   6     | 5   37   1 |
 | 268    2367   78  | 578    1   578   | 4   367  9 |
 | 1      67     5   | 9      3   4     | 67  8    2 |
 +-------------------+------------------+------------+
 | 9      8      6   | 37     5   37    | 1   2    4 |
 | 3      145    2   | 146    8   19    | 69  569  7 |
 | 45     1457   147 | 12467  49  1279  | 3   569  8 |
 +-------------------+------------------+------------+

1) #VT: (12 6 4 6 10 5 7 5 4)
Single-digit POM: .111.1.1..111.1.1....1.1...........1....1....1..............1...1.1.1....111.1...
Digit 1 not in 12 Templates => -1 @ r1c4 r1c6 r2c4 r2c6

Single-digit POM: 44444.....444............4.44.............4.......4...........4.4.4.....44444....
Digit 4 not in 6 Templates => -4 @ r1c1 r1c2

Single-digit POM: ......77.7............7.....7.7...7..777.7.7..7....7.....7.7...........7.777.7...
Digit 7 not in 7 Templates => -7 @ r9c4 r9c6

Single-digit POM: 8.88.8.........8..8..8.8...8..8.....8.88.8..........8..8...........8............8
Digit 8 not in 5 Templates => -8 @ r1c4

Single-digit POM: ....9999......9.9..9.........9..............9...9.....9.............999.....99.9.
Digit 9 not in 4 Templates => -9 @ r8c6 r9c8

Code: Select all

 +-----------------+---------------+------------+
 | 2568  1256  148 | 245  49  2589 | 79  179  3 |
 | 7     124   14  | 234  6   239  | 8   19   5 |
 | 58    9     3   | 1    7   58   | 2   4    6 |
 +-----------------+---------------+------------+
 | 48    347   9   | 78   2   6    | 5   37   1 |
 | 268   2367  78  | 578  1   578  | 4   367  9 |
 | 1     67    5   | 9    3   4    | 67  8    2 |
 +-----------------+---------------+------------+
 | 9     8     6   | 37   5   37   | 1   2    4 |
 | 3     45    2   | 46   8   1    | 69  569  7 |
 | 45    1457  147 | 246  49  29   | 3   56   8 |
 +-----------------+---------------+------------+

2) #VT: (4 6 4 6 7 5 7 4 4)
Single-digit POM: 8.8..8.........8..8....8...8..8.....8.88.8..........8..8...........8............8
Digit 8 not in 4 Templates => -8 @ r5c6

Code: Select all

 +-----------------+---------------+------------+
 | 2568  1256  148 | 245  49  2589 | 79  179  3 |
 | 7     124   14  | 234  6   239  | 8   19   5 |
 | 58    9     3   | 1    7   58   | 2   4    6 |
 +-----------------+---------------+------------+
 | 48    347   9   | 78   2   6    | 5   37   1 |
 | 268   2367  78  | 578  1   57   | 4   367  9 |
 | 1     67    5   | 9    3   4    | 67  8    2 |
 +-----------------+---------------+------------+
 | 9     8     6   | 37   5   37   | 1   2    4 |
 | 3     45    2   | 46   8   1    | 69  569  7 |
 | 45    1457  147 | 246  49  29   | 3   56   8 |
 +-----------------+---------------+------------+

3) #VT: (4 6 4 6 7 5 7 4 4)
Double-digit POM: .11....1..11....1....1.............1....1....1..............1.......1....11......
and POM: ......77.7............7.....7.7...7..777.7.7..7....7.....7.7...........7.77......
Digit 1 not in 3 Templates => -1 @ r2c2

Code: Select all

 +-----------------+---------------+------------+
 | 2568  1256  148 | 245  49  2589 | 79  179  3 |
 | 7     24    14  | 234  6   239  | 8   19   5 |
 | 58    9     3   | 1    7   58   | 2   4    6 |
 +-----------------+---------------+------------+
 | 48    347   9   | 78   2   6    | 5   37   1 |
 | 268   2367  78  | 578  1   57   | 4   367  9 |
 | 1     67    5   | 9    3   4    | 67  8    2 |
 +-----------------+---------------+------------+
 | 9     8     6   | 37   5   37   | 1   2    4 |
 | 3     45    2   | 46   8   1    | 69  569  7 |
 | 45    1457  147 | 246  49  29   | 3   56   8 |
 +-----------------+---------------+------------+

4) #VT: (3 6 4 6 7 5 7 4 4)
Triple-digit POM: .11....1...1....1....1.............1....1....1..............1.......1....11......
and POM: 22.2.2....2.2.2.........2......2....22...............2.......2...2.........2.2...
and POM: 66...........6............6.....6...66.....6..6....6....6.........6..66....6...6.
Digit 1 not in 2 Templates => -1 @ r1c2 r9c3
Digit 1 in all 2 Templates => 1 @ r9c2

Triple-digit POM: 22.2.2....2.2.2.........2......2....22...............2.......2...2.........2.2...
and POM: 55.5.5...........55....5.........5.....5.5.....5..........5.....5.....5.5......5.
and POM: 66...........6............6.....6...66.....6..6....6....6.........6..66....6...6.
Digit 2 not in 2 Templates => -2 @ r1c1 r1c2 r2c4 r2c6 r5c2
Digit 2 in all 2 Templates => 2 @ r2c2 r5c1

Triple-digit POM: ..444......44............4.44.............4.......4...........4.4.4.....4.444....
and POM: ..1....1...1....1....1.............1....1....1..............1.......1....1.......
and POM: ...2.2....2.............2......2....2................2.......2...2.........2.2...
Digit 4 not in 4 Templates => -4 @ r9c3

Triple-digit POM: ..444......44............4.44.............4.......4...........4.4.4.....4..44....
and POM: ..1....1...1....1....1.............1....1....1..............1.......1....1.......
and POM: ....9999......9.9..9.........9..............9...9.....9..............99.....99...
Digit 4 not in 3 Templates => -4 @ r1c4

Triple-digit POM: 55.5.5...........55....5.........5.....5.5.....5..........5.....5.....5.5......5.
and POM: ..1....1...1....1....1.............1....1....1..............1.......1....1.......
and POM: 66...........6............6.....6....6.....6..6....6....6.........6..66....6...6.
Digit 5 not in 3 Templates => -5 @ r1c1

Triple-digit POM: .5.5.5...........55....5.........5.....5.5.....5..........5.....5.....5.5......5.
and POM: ...2.2....2.............2......2....2................2.......2...2.........2.2...
and POM: 66...........6............6.....6....6.....6..6....6....6.........6..66....6...6.
Digit 5 not in 2 Templates => -5 @ r1c4 r5c6
Digit 5 in all 2 Templates => 5 @ r5c4

Triple-digit POM: .5...5...........55....5.........5.....5.......5..........5.....5.....5.5......5.
and POM: 66...........6............6.....6....6.....6..6....6....6.........6..66....6...6.
and POM: 8.8..8.........8..8....8...8..8.......8.............8..8...........8............8
Digit 5 not in 1 Template => -5 @ r1c6 r3c1 r8c2 r9c8
Digit 5 in all 1 Template => 5 @ r1c2 r3c6 r8c8 r9c1

Triple-digit POM: 6............6............6.....6....6.....6..6....6....6.........6..6.....6...6.
and POM: ..1....1...1....1....1.............1....1....1..............1.......1....1.......
and POM: ...2.2....2.............2......2....2................2.......2...2.........2.2...
Digit 6 in all 2 Templates => 6 @ r1c1

Triple-digit POM: 6............6............6.....6....6.....6..6....6....6.........6..6.....6...6.
and POM: ..1....1...1....1....1.............1....1....1..............1.......1....1.......
and POM: ....9999......9.9..9.........9..............9...9.....9..............9......99...
Digit 6 not in 1 Template => -6 @ r5c8 r6c2 r8c7 r9c4
Digit 6 in all 1 Template => 6 @ r5c2 r6c7 r8c4

Triple-digit POM: ......77.7............7.....7.7...7...7..7.7..7..........7.7...........7..7......
and POM: ..1....1...1....1....1.............1....1....1..............1.......1....1.......
and POM: ...2.2....2.............2......2....2................2.......2...2.........2.2...
Digit 7 not in 2 Templates => -7 @ r1c8 r4c2 r5c3
Digit 7 in all 2 Templates => 7 @ r1c7

Triple-digit POM: ......7..7............7.......7...7......7.7..7..........7.7...........7..7......
and POM: ..1....1...1....1....1.............1....1....1..............1.......1....1.......
and POM: ........3...3.3.....3.......3.....3........3.....3.......3.3...3..............3..
Digit 7 not in 1 Template => -7 @ r4c4 r5c8 r7c6
Digit 7 in all 1 Template => 7 @ r4c8 r7c4

Triple-digit POM: ..8..8.........8..8........8..8.......8.............8..8...........8............8
and POM: ..1....1...1....1....1.............1....1....1..............1.......1....1.......
and POM: ...2.2....2.............2......2....2................2.......2...2.........2.2...
Digit 8 not in 1 Template => -8 @ r1c3 r4c1
Digit 8 in all 1 Template => 8 @ r1c6

Triple-digit POM: ....9..9......9.9..9.........9..............9...9.....9..............9......99...
and POM: ..1....1...1....1....1.............1....1....1..............1.......1....1.......
and POM: ...2......2.............2......2....2................2.......2...2.........2.2...
Digit 9 not in 1 Template => -9 @ r1c5 r2c8 r9c6
Digit 9 in all 1 Template => 9 @ r1c8 r2c6 r9c5; stte

R. Jamil

[Cenoman]

Thank you for your solutions.
In the same kind of ideas as Steve's, I had this solution

Code: Select all

 +---------------------+---------------------+-------------------+
 |  26   12456   148   |  2458  z49   2589   |  7-9   179   3    |
 |  7    124     14    |  234    6   e239    |  8    e19    5    |
 |  58   9       3     |  158    7    158    |  2     4     6    |
 +---------------------+---------------------+-------------------+
 | b48   347     9     | c78     2    6      |  5     37    1    |
 |  26   236     78    |  578    1    578    |  4     36    9    |
 |  1    67      5     |  9      3    4      |  67    8     2    |
 +---------------------+---------------------+-------------------+
 |  9    8       6     | c37     5   d37     |  1     2     4    |
 |  3    145     2     |  146    8    19     | B69    569   7    |
 | b45   1457    147   |  1246  y49   129    |  3  xAa569   8    |
 +---------------------+---------------------+-------------------+

Kraken cell (569)r9c8
||(5)r9c8 - (5=48)r49c1 - (8=73)r57c4 - r7c6 = (39)r2c68
||(6)r9c8 - (6=9)r8c7
||(9)r9c8 - r9c5 = (9)r1c5
=> -9 r1c7; ste

There also this kraken row (9)r8c678 (almost kite):
(9-5)r8c8 = r8c2 - (5=48)r49c1 - (8=73)r57c4 - r7c6 = (39)r2c68
||
kite (9)[r8c7 = r8c6 - r9c5 = r1c5]
=> -9 r1c7; ste

With uniqueness, as jco's:

Code: Select all

 +---------------------+---------------------+-------------------+
 |  26   12456   148   |  2458   49   2589   | O7-9* a179*  3    |
 |  7    124     14    |  234    6   n239    |  8   ob19    5    |
 |  58   9       3     |  158    7    158    |  2     4     6    |
 +---------------------+---------------------+-------------------+
 |  48   347*    9     |  78     2    6      |  5     37*   1    |
 | M26   236*   x78    |  578    1    578    |  4     36*   9    |
 |  1   N67*     5     |  9      3    4      | O67*   8     2    |
 +---------------------+---------------------+-------------------+
 |  9    8       6     |  37     5    37     |  1     2     4    |
 |  3    145     2     | A146    8   m19     | B69*   569*  7    |
 |  45   1457    147   |  1246   49   129    |  3     569   8    |
 +---------------------+---------------------+-------------------+

DP(3679)r18c78,r45c28,r6c27 (*), using mixed internal-externals:
(1)r1c8 - (1=9)r2c8
(6)r8c4 - (6=9)r8c7
(9)r8c6 - r2c6 = (9)r2c8
(6)r5c1 - r6c2 = (67)r16c7
(7)r5c3 - (73)r57c6 = (39)r2c68
=> -9 r1c7; ste

Sorry for rjamil, I have no skills at POM.

[rjamil]

Hi Cenoman,

Sorry for rjamil, I have no skills at POM.

I see POM in depth. Now I understand how patterns are tedious and error prone when working manually,

However, if one search all digits' POM templates via some kind of computer aided, the remaining part of the play simplifies greatly.

I played 46656 templates in MS-Excel sheets and see how patterns are symmetrical. Each chunk of 5184 repeats nine times. This concept was already burried when I first attempted to program by swapping the rows, columns, bands and stacks first, then apply only 5184 templates for all possible combinations of each digits. Now, I have hard coded the swappings and apply the 5184 templates again. The results are found as expected.

Those who feel that the POM is boring, is due to the reason none other than that it is tedious and error prone to search manually. But, with the help of proper computer program, its fun, and now I crack it to work lighting fast with tiny data. (Credit goes to Myth Jellies)

R. Jamil