The New Sudoku Players' Forum

[shye]

Code: Select all

+-------+-------+-------+
| 6 . 8 | . 3 . | . . 9 |
| . 5 . | 9 . . | 8 . . |
| . . . | . . 5 | . 4 . |
+-------+-------+-------+
| 1 . 5 | 7 . . | 9 . . |
| 2 . . | . 9 . | . . 1 |
| . . 9 | . . 8 | 6 . 2 |
+-------+-------+-------+
| . 3 . | 6 . . | . . . |
| . . 7 | . . 9 | . 6 . |
| 9 . . | . 4 . | 7 . 5 |
+-------+-------+-------+
6.8.3...9.5.9..8.......5.4.1.57..9..2...9...1..9..86.2.3.6.......7..9.6.9...4.7.5

estimated rating: 7.3

[eleven]

Rotational symmetry (12)(34)(56)(78)(9)

Code: Select all

+---------------------+----------------------+----------------------+
| 6      1247   8     | 124    3      1247   | 125    125    9      |
| 347    5      1234  | 9      1267   12467  | 8     c123    67     |
| 37     9      123   | 128    12678  5      | 123    4      67     |
+---------------------+----------------------+----------------------+
| 1      468    5     | 7      26     2346   | 9     d38     34-8   |
| 2      78     346   | 345    9      346    | 345    78     1      |
| 347    47     9     | 1345   15     8      | 6      357    2      |
+---------------------+----------------------+----------------------+
| 58     3     b124   | 6      12578  127    | 124    9     a48     |
| 58    c124    7     | 12358  1258   9      | 1234   6      348    |
| 9      126    126   | 1238   4      123    | 7      123-8  5      |
+---------------------+----------------------+----------------------+

(8=4)r7c9 - r7c3 = 4r8c3 & 3r2c8 - (3=8)r4c8 => -8r9c8,r4c9

Code: Select all

+--------------------+---------------------+-------------------+
|  6     124   8     |  124    3     7     | 125   125   9     |
| a34    5     1234  |  9      126   46-12 | 8     123   7     |
|  7     9     123   | #12     8     5     | 123   4     6     |
+--------------------+---------------------+-------------------+
|  1     468   5     |  7      26    2346  | 9     38    34    |
|  2     78    346   |  345    9     346   | 345   78    1     |
| *34    47    9     | *1345   15    8     | 6    *357   2     |
+--------------------+---------------------+-------------------+
|  5     3     124   |  6      7    #12    | 124   9     8     |
|  8     124   7     |  5-123  125   9     | 1234  6    a34    |
|  9     126   126   |  8      4    c123   | 7    b123   5     |
+--------------------+---------------------+-------------------+

12r3c4,r7c6 => -12r2c6,r8c4

Kraken 3r6:
3r6c1 - r2c1 = 4r2c1 & 3r8c9
3r6c4
3r6c8 - r9c8 = r9c6
=> -3r8c4, 5r8c4, 6r2c6, stte

[rjamil]

Multiple POM solution:

Code: Select all

 +-----------------+---------------------+-----------------+
 | 6    1247  8    | 124    3      1247  | 125   1257  9   |
 | 347  5     1234 | 9      1267   12467 | 8     1237  367 |
 | 37   9     123  | 128    12678  5     | 123   4     367 |
 +-----------------+---------------------+-----------------+
 | 1    468   5    | 7      26     2346  | 9     38    348 |
 | 2    4678  346  | 345    9      346   | 345   3578  1   |
 | 347  47    9    | 1345   15     8     | 6     357   2   |
 +-----------------+---------------------+-----------------+
 | 458  3     124  | 6      12578  127   | 124   9     48  |
 | 458  1248  7    | 12358  1258   9     | 1234  6     348 |
 | 9    1268  126  | 1238   4      123   | 7     1238  5   |
 +-----------------+---------------------+-----------------+

1) #VT: (28 28 22 22 8 8 7 7 1)
Single-digit POM: .7...7.7.7...77.777...7...7...7......7.....7.77.....7.....77.....7............7..
Digit 7 not in 7 Templates => -7 @ r1c8 r2c8

Single-digit POM: ..8............8.....88.....8.....88.8.....8......8...8...8...888.88...8.8.8...8.
Digit 8 not in 7 Templates => -8 @ r8c2 r9c2

Code: Select all

 +-----------------+---------------------+-----------------+
 | 6    1247  8    | 124    3      1247  | 125   125   9   |
 | 347  5     1234 | 9      1267   12467 | 8     123   367 |
 | 37   9     123  | 128    12678  5     | 123   4     367 |
 +-----------------+---------------------+-----------------+
 | 1    468   5    | 7      26     2346  | 9     38    348 |
 | 2    4678  346  | 345    9      346   | 345   3578  1   |
 | 347  47    9    | 1345   15     8     | 6     357   2   |
 +-----------------+---------------------+-----------------+
 | 458  3     124  | 6      12578  127   | 124   9     48  |
 | 458  124   7    | 12358  1258   9     | 1234  6     348 |
 | 9    126   126  | 1238   4      123   | 7     1238  5   |
 +-----------------+---------------------+-----------------+

2) #VT: (28 28 22 22 8 8 7 7 1)
Triple-digit POM: .2.2.222...2.22.2...222.2......22...2................2..2.222...2.22.2...222.2.2.
and POM: .1.1.111...1.11.1...111.1..1................1...11......1.111...1.11.1...111.1.1.
and POM: .7...7...7...77..77...7...7...7......7.....7.77.....7.....77.....7............7..
Digit 2 not in 24 Templates => -2 @ r1c6

Triple-digit POM: ....3....3.3....333.3...3.3.....3.33..33.333.3..3...3..3..........3..3.3...3.3.3.
and POM: 6............66..6....6...6.6..66....66..6.........6.....6............6..66......
and POM: .7...7...7...77..77...7...7...7......7.....7.77.....7.....77.....7............7..
Digit 3 not in 10 Templates => -3 @ r2c9 r3c9

Triple-digit POM: ....3....3.3....3.3.3...3.......3.33..33.333.3..3...3..3..........3..3.3...3.3.3.
and POM: .7...7...7...77..77...7...7...7......7.....7.77.....7.....77.....7............7..
and POM: ..8............8.....88.....8.....88.8.....8......8...8...8...88..88...8...8...8.
Digit 3 not in 8 Templates => -3 @ r5c8

Triple-digit POM: .4.4.4...4.4..4..........4..4...4..4.444.44..44.4.....4.4...4.444....4.4....4....
and POM: .1.1.111...1.11.1...111.1..1................1...11......1.111...1.11.1...111.1.1.
and POM: .7...7...7...77..77...7...7...7......7.....7.77.....7.....77.....7............7..
Digit 4 not in 13 Templates => -4 @ r4c2

Triple-digit POM: .4.4.4...4.4..4..........4......4..4.444.44..44.4.....4.4...4.444....4.4....4....
and POM: .2.2..22...2.22.2...222.2......22...2................2..2.222...2.22.2...222.2.2.
and POM: .7...7...7...77..77...7...7...7......7.....7.77.....7.....77.....7............7..
Digit 4 not in 11 Templates => -4 @ r1c6 r5c2

Triple-digit POM: .4.4.....4.4..4..........4......4..4..44.44..44.4.....4.4...4.444....4.4....4....
and POM: ......55..5............5.....5.........5..55....55..5.5...5....5..55............5
and POM: ..8............8.....88.....8.....88.8.....8......8...8...8...88..88...8...8...8.
Digit 4 not in 5 Templates => -4 @ r5c3 r6c4 r7c1 r8c1

Triple-digit POM: ......55..5............5.....5.........5..55....55..5.5...5....5..55............5
and POM: .7...7...7...77..77...7...7...7......7.....7.77.....7.....77.....7............7..
and POM: ..8............8.....88.....8.....88.8.....8......8...8...8...88..88...8...8...8.
Digit 5 not in 5 Templates => -5 @ r5c8

Triple-digit POM: 6............66..6....6...6.6..66....66..6.........6.....6............6..66......
and POM: .7...7...7...77..77...7...7...7......7.....7.77.....7.....77.....7............7..
and POM: ..8............8.....88.....8.....88.8.....8......8...8...8...88..88...8...8...8.
Digit 6 not in 5 Templates => -6 @ r5c2

Triple-digit POM: .7...7...7...77..77...7...7...7......7.....7.77.....7.....77.....7............7..
and POM: .1.1.111...1.11.1...111.1..1................1...11......1.111...1.11.1...111.1.1.
and POM: .4.4.....4.4..4..........4......4..4...4.44..44.........4...4.4.4....4.4....4....
Digit 7 not in 4 Templates => -7 @ r1c2 r2c5 r2c6 r3c5 r6c1 r7c6
Digit 7 in all 4 Templates => 7 @ r1c6 r7c5

Triple-digit POM: ..8............8.....88.....8.....88.8.....8......8...8.......88..88...8...8...8.
and POM: .1.1..11...1.11.1...111.1..1................1...11......1..11...1.11.1...111.1.1.
and POM: ......55..5............5.....5.........5..5.....55..5.5........5..55............5
Digit 8 not in 2 Templates => -8 @ r3c4 r4c9 r7c1 r8c4 r8c5 r8c9 r9c8
Digit 8 in all 2 Templates => 8 @ r3c5 r7c9 r8c1 r9c4

Code: Select all

 +---------------+-----------------+---------------+
 | 6   124  8    | 124   3    7    | 125   125  9  |
 | 34  5    1234 | 9     126  1246 | 8     123  7  |
 | 7   9    123  | 12    8    5    | 123   4    6  |
 +---------------+-----------------+---------------+
 | 1   68   5    | 7     26   2346 | 9     38   34 |
 | 2   78   36   | 345   9    346  | 345   78   1  |
 | 34  47   9    | 135   15   8    | 6     357  2  |
 +---------------+-----------------+---------------+
 | 5   3    124  | 6     7    12   | 124   9    8  |
 | 8   124  7    | 1235  125  9    | 1234  6    34 |
 | 9   126  126  | 8     4    123  | 7     123  5  |
 +---------------+-----------------+---------------+

3) #VT: (15 15 4 4 3 3 2 2 1)
Single-digit POM: ....3....3.3....3...3...3.......3.33..33.33..3..3...3..3..........3..3.3.....3.3.
Digit 3 not in 4 Templates => -3 @ r4c6 r5c7 r6c8

Code: Select all

 +---------------+-----------------+---------------+
 | 6   124  8    | 124   3    7    | 125   125  9  |
 | 34  5    1234 | 9     126  1246 | 8     123  7  |
 | 7   9    123  | 12    8    5    | 123   4    6  |
 +---------------+-----------------+---------------+
 | 1   68   5    | 7     26   246  | 9     38   34 |
 | 2   78   36   | 345   9    346  | 45    78   1  |
 | 34  47   9    | 135   15   8    | 6     57   2  |
 +---------------+-----------------+---------------+
 | 5   3    124  | 6     7    12   | 124   9    8  |
 | 8   124  7    | 1235  125  9    | 1234  6    34 |
 | 9   126  126  | 8     4    123  | 7     123  5  |
 +---------------+-----------------+---------------+

4) #VT: (15 15 4 4 3 3 2 2 1)
Triple-digit POM: .1.1..11...1.11.1...11..1..1................1...11......1..11...1.11.1...11..1.1.
and POM: .2.2..22...2.22.2...22..2......22...2................2..2..22...2.22.2...22..2.2.
and POM: ....3....3.3....3...3...3.........33..33.3...3..3......3..........3..3.3.....3.3.
Digit 1 not in 8 Templates => -1 @ r1c4

Triple-digit POM: .1....11...1.11.1...11..1..1................1...11......1..11...1.11.1...11..1.1.
and POM: .2.2..22...2.22.2...22..2......22...2................2..2..22...2.22.2...22..2.2.
and POM: .4.4.....4.4..4..........4......4..4...4.44..44.........4...4...4....4.4....4....
Digit 1 not in 7 Templates => -1 @ r3c7 r7c3

Triple-digit POM: .1....11...1.11.1...11.....1................1...11.........11...1.11.1...11..1.1.
and POM: .2.2..22...2.22.2...22..2......22...2................2..2..22...2.22.2...22..2.2.
and POM: ......55..5............5.....5.........5..5.....55..5.5...........55............5
Digit 1 not in 7 Templates => -1 @ r8c5

Triple-digit POM: .1....11...1.11.1...11.....1................1...11.........11...1.1..1...11..1.1.
and POM: .2.2..22...2.22.2...22..2......22...2................2..2..22...2.22.2...22..2.2.
and POM: 6............66...........6.6..66.....6..6.........6.....6............6..66......
Digit 1 not in 5 Templates => -1 @ r1c2 r2c8 r9c3

Triple-digit POM: .2.2..22...2.22.2...22..2......22...2................2..2..22...2.22.2...22..2.2.
and POM: ......11...1.11.....11.....1................1...11.........11...1.1..1...1...1.1.
and POM: ....3....3.3....3...3...3.........33..33.3...3..3......3..........3..3.3.....3.3.
Digit 2 not in 6 Templates => -2 @ r3c7 r7c3 r9c6

Triple-digit POM: .2.2..22...2.22.2...22.........22...2................2.....22...2.22.2...22....2.
and POM: ......11...1.11.....11.....1................1...11.........11...1.1..1...1...1.1.
and POM: ......55..5............5.....5.........5..5.....55..5.5...........55............5
Digit 2 not in 3 Templates => -2 @ r1c7 r1c8 r2c3 r2c5 r2c6 r8c2 r8c4 r9c8
Digit 2 in all 3 Templates => 2 @ r2c8

Triple-digit POM: ....3....3.3........3...3.........33..33.3...3..3......3..........3..3.3.....3.3.
and POM: ......11...1.11.....11.....1................1...11.........11...1.1..1...1...1.1.
and POM: .2.2............2...22.........22...2................2.....22......2.2...22......
Digit 3 not in 3 Templates => -3 @ r3c3 r8c7

Triple-digit POM: ....3....3.3............3.........33..33.3...3..3......3..........3....3.....3.3.
and POM: 6............66...........6.6..66.....6..6.........6.....6............6..66......
and POM: ..8............8......8.....8.....8..8.....8......8...........88...........8.....
Digit 3 not in 2 Templates => -3 @ r2c1 r5c3 r6c4
Digit 3 in all 2 Templates => 3 @ r2c3 r6c1

Triple-digit POM: .4.4.....4....4..........4......4..4...4.44...4.........4...4...4....4.4....4....
and POM: ......11.....11.....11.....1................1...11.........11...1.1..1...1...1.1.
and POM: .2.2............2...22.........22...2................2.....22......2.2...22......
Digit 4 not in 2 Templates => -4 @ r1c2 r2c6 r5c4 r7c7 r8c2
Digit 4 in all 2 Templates => 4 @ r1c4 r6c2

Triple-digit POM: ...4.....4...............4......4..4.....44...4.........4............4.4....4....
and POM: .2..............2...22.........22...2................2.....22......2.2...22......
and POM: 6............66...........6.6..66.....6..6.........6.....6............6..66......
Digit 4 not in 1 Template => -4 @ r4c6 r5c7 r8c9
Digit 4 in all 1 Template => 4 @ r4c9 r5c6 r8c7

Triple-digit POM: ......55..5............5.....5.........5..5.....55..5.5...........55............5
and POM: ......11.....11.....11.....1................1...11.........11...1.1......1...1.1.
and POM: .2..............2...22.........22...2................2.....22......2.....22......
Digit 5 not in 1 Template => -5 @ r1c7 r5c4 r6c4 r6c8 r8c5
Digit 5 in all 1 Template => 5 @ r1c8 r6c5 r8c4

Triple-digit POM: 6............66...........6.6..66.....6............6.....6............6..66......
and POM: ......1......11.....11.....1................1...1..........11...1........1...1.1.
and POM: .2..............2...22.........22...2................2.....22......2.....22......
Digit 6 not in 1 Template => -6 @ r2c5 r4c2 r4c6 r9c3
Digit 6 in all 1 Template => 6 @ r2c6 r4c5 r9c2

Triple-digit POM: .....7...........77...........7......7.....7........7.....7......7............7..
and POM: ......1......1......11.....1................1...1..........11...1............1.1.
and POM: .2..............2...22..........2...2................2.....22......2......2......
Digit 7 not in 1 Template => -7 @ r5c8
Digit 7 in all 1 Template => 7 @ r5c2

Triple-digit POM: ..8............8......8.....8.....8........8......8...........88...........8.....
and POM: ......1......1......11.....1................1...1..........11...1............1.1.
and POM: .2..............2...22..........2...2................2.....22......2......2......
Digit 8 not in 1 Template => -8 @ r4c8; stte

R. Jamil

According to Google AI Overview:

The Pattern Overlay Method (POM) in Sudoku, also known as templating, is a non-idempotent process. While it is not a "trial and error" method (it does not require guessing), it is an iterative technique where applying the method multiple times to the same, unchanging state of the puzzle will continue to yield new information and eliminate possibilities, rather than producing the same output as the first iteration.

Why the Pattern Overlay Method is Non-Idempotent:

Iterative Reduction: POM works by identifying all possible valid "patterns" (or templates) for a single digit (9 instances of a digit) that conform to the current, known solved cells.

Sequential Elimination: Each time a pattern or set of patterns is eliminated (e.g., if a pattern never contains a certain cell), the total number of possible patterns for that digit decreases. This narrowing of possibilities makes it easier to eliminate more patterns in a subsequent pass.

The "Re-run" Effect: Because the initial step (identifying patterns) is based on the current set of "candidate spaces" for a digit, reducing the candidate space in step A allows step B to use that tighter constraint to eliminate even more patterns. Thus, POM(Puzzle) != POM(POM(Puzzle)).

Backtracking/BFS: Programmatic implementations often use a breadth-first search (BFS) that restarts at a two-pattern combination analysis every time a pattern is eliminated.

How the Method Works:

1. Isolate Candidates: Choose a digit and map all possible positions it could inhabit based on existing clues.
2. Generate Patterns: Identify all 46,656 possible standard patterns (or fewer, given the clues) that the digit can form.
3. Identify "Always On/Off": A cell that is part of all possible patterns for a digit is a "hidden single" (must be that digit). A cell that is part of no patterns for a digit can be eliminated.
4. Iterate: Once cells are solved using this method, the number of possible patterns for other digits shrinks, which is why the method is reapplied.

Contextual Application:
POM is considered a "last resort" technique that is inefficient in the early stages of a puzzle due to the high number of possible patterns, but highly effective in the endgame, often applied to break very difficult, non-consecutive, or otherwise constrained puzzles.

[eleven]

I never trust AI answers (though they are often right). This one is really bad, not to say completely wrong. Following it, i would never realize, that i would have to look at multidigits simultaneously for non-idempotency (i.e. not to get stuck).

[rjamil]

Hi all,

I also not believe in AI. After all, it seek information from human knowledge and manipulate it aggressively most of the time.

For above AI comments, especially last line, under "Contextual Application" heading, Sudoku experts are now applying POM at initial stage. Also the POM move is applying to solve the puzzle with singleton move only.

Similarly POM is no more considered as last resort and inefficient, when working with highly optimized and not full set of 46656 templates. Also, POM helps to find some advance and complex moves.

Also, today, AI failed to understand professional program coding and unable to detect and rectify the errors.

R. Jamil

[shye]

maybe best not to post AI content if you don't trust it

Code: Select all

+----------+----------+----------+
|  .  x  . |  x  .  x |  x  x  . |
|  .  .  x |  .  .  x |  .  x  . |
|  .  x  x |  x  .  . |  x  .  . |
+----------+----------+----------+
| #1  .  . |  . #2  . |  .  .  . |
| #2  .  . |  .  .  . |  .  . #1 |
|  .  .  . |  . #1  . |  .  . #2 |
+----------+----------+----------+
|  .  .  x |  .  .  x |  x  x  . |
|  .  x  . |  x  .  . |  x  .  . |
|  .  x  x |  x  .  x |  .  x  . |
+----------+----------+----------+

the symmetrical pair 2b5p2 & 1b5p8 gives a reverse BUG
the remaining 1s and 2s (marked with x) cannot be disambiguated
so by symmetry:
+2b5p3, +1b5p7, lcstte

[rjamil]

maybe best not to post AI content if you don't trust it

Don't take AI seriously. I added AI overview just for fun, laugh and entertainment!! After all, AI advises are based on data as garbage-in garbage-out basis. (Below signature are often considered as entertaining material.

As an example of AI comments on itself:

AI hilarity often stems from confidently incorrect, illogical, or bizarrely literal answers, caused by flawed training data or misinterpreting queries. Famous examples include suggesting glue to keep cheese on pizza, recommending eating mucus for health benefits, and proposing unsafe passwords.

Providing nonsensical answers because it works on probability rather than true understanding, struggle to differentiate between fiction and reality, leading to nonsensical but serious-sounding advice.

https://blog.richardvanhooijdonk.com/en/ai-bloopers-artificial-intelligences-most-memorable-mistakes/

Apologise and assure that this could be my last non-serious and out of context post.

R. Jamil

Sun Tzu: "Never interrupt your opponent while he is in the middle of making a mistake."

[shye]

for me personally, i both dont find it trustworthy or entertaining, but this is a topic for another non-sudoku conversation (not really fitting for here)

[eleven]

the symmetrical pair 2b5p2 & 1b5p8 gives a reverse BUG ...

Oh, thats very smart !