The New Sudoku Players' Forum

[Yogi]

....62..3.....8.6.1........7..5..1.....49...........2....1..3...62.......9.......

Code: Select all

.---------.---------.---------.
| .  .  . | .  6  2 | .  .  3 |
| .  .  . | .  .  8 | .  6  . |
| 1  .  . | .  .  . | .  .  . |
:---------+---------+---------:
| 7  .  . | 5  .  . | 1  .  . |
| .  .  . | 4  9  . | .  .  . |
| .  .  . | .  .  . | .  2  . |
:---------+---------+---------:
| .  .  . | 1  .  . | 3  .  . |
| .  6  2 | .  .  . | .  .  . |
| .  9  . | .  .  . | .  .  . |
'---------'---------'---------'


I've had trouble logging in again.

[rjamil]

An attempt to solve with POM moves:

Code: Select all

 +-------------------+--------------+-------------------+
 | 9     458    458  | 7   6     2  | 458   1     3     |
 | 2     3457   3457 | 39  1     8  | 4579  6     4579  |
 | 1     34578  6    | 39  345   45 | 2     4578  45789 |
 +-------------------+--------------+-------------------+
 | 7     48     9    | 5   2     3  | 1     48    6     |
 | 6     2      58   | 4   9     1  | 578   3     578   |
 | 345   1      345  | 6   8     7  | 459   2     459   |
 +-------------------+--------------+-------------------+
 | 458   4578   4578 | 1   457   6  | 3     9     2     |
 | 345   6      2    | 8   3457  9  | 457   457   1     |
 | 3458  9      1    | 2   3457  45 | 6     4578  4578  |
 +-------------------+--------------+-------------------+

#VT: (1 1 4 23 33 1 12 3 3)
Single-digit POM: 3 @ r1c9 r2c234 r3c245 r4c6 r5c8 r6c13 r7c7 r8c15 r9c15
Digit 3 not in 4 Templates => -3 @ r2c3 r3c5 r6c1
Digit 3 in all 4 Templates => 3 @ r6c3

Single-digit POM: 4 @ r1c237 r2c2379 r3c25689 r4c28 r5c4 r6c179 r7c1235 r8c1578 r9c15689
Digit 4 not in 23 Templates => -4 @ r3c2 r3c8 r3c9

Single-digit POM: 5 @ r1c237 r2c2379 r3c25689 r4c4 r5c379 r6c179 r7c1235 r8c1578 r9c15689
Digit 5 not in 33 Templates => -5 @ r3c2 r3c8 r3c9 r8c7 r9c9

Single-digit POM: 7 @ r1c4 r2c2379 r3c289 r4c1 r5c79 r6c6 r7c235 r8c578 r9c589
Digit 7 not in 12 Templates => -7 @ r7c5

Single-digit POM: 8 @ r1c237 r2c6 r3c289 r4c28 r5c379 r6c5 r7c123 r8c4 r9c189
Digit 8 not in 3 Templates => -8 @ r1c2 r5c9 r7c2 r7c3 r9c1
Digit 8 in all 3 Templates => 8 @ r7c1

Code: Select all

 +----------------+--------------+------------------+
 | 9    45    458 | 7   6     2  | 458   1     3    |
 | 2    3457  457 | 39  1     8  | 4579  6     4579 |
 | 1    378   6   | 39  45    45 | 2     78    789  |
 +----------------+--------------+------------------+
 | 7    48    9   | 5   2     3  | 1     48    6    |
 | 6    2     58  | 4   9     1  | 578   3     57   |
 | 45   1     3   | 6   8     7  | 459   2     459  |
 +----------------+--------------+------------------+
 | 8    457   457 | 1   45    6  | 3     9     2    |
 | 345  6     2   | 8   3457  9  | 47    457   1    |
 | 345  9     1   | 2   3457  45 | 6     4578  478  |
 +----------------+--------------+------------------+

Double-digit POM: 4 @ r1c237 r2c2379 r3c56 r4c28 r5c4 r6c179 r7c235 r8c1578 r9c15689
and POM: 5 @ r1c237 r2c2379 r3c56 r4c4 r5c379 r6c179 r7c235 r8c158 r9c1568
Digit 4 not in 5 Templates => -4 @ r2c2 r8c5 r8c8 r9c1 r9c5 r9c9

Double-digit POM: 4 @ r1c237 r2c379 r3c56 r4c28 r5c4 r6c179 r7c235 r8c17 r9c68
and POM: 8 @ r1c37 r2c6 r3c289 r4c28 r5c37 r6c5 r7c1 r8c4 r9c89
Digit 4 not in 3 Templates => -4 @ r1c7 r2c3 r7c2

Double-digit POM: 5 @ r1c237 r2c2379 r3c56 r4c4 r5c379 r6c179 r7c235 r8c158 r9c1568
and POM: 4 @ r1c23 r2c79 r3c56 r4c28 r5c4 r6c179 r7c35 r8c17 r9c68
Digit 5 not in 6 Templates => -5 @ r1c3 r6c7 r8c5 r9c5

Double-digit POM: 7 @ r1c4 r2c2379 r3c289 r4c1 r5c79 r6c6 r7c23 r8c578 r9c589
and POM: 8 @ r1c37 r2c6 r3c289 r4c28 r5c37 r6c5 r7c1 r8c4 r9c89
Digit 7 not in 8 Templates => -7 @ r2c9 r9c9

Code: Select all

 +---------------+------------+----------------+
 | 9    45   48  | 7   6   2  | 58    1    3   |
 | 2    357  57  | 39  1   8  | 4579  6    459 |
 | 1    378  6   | 39  45  45 | 2     78   79  |
 +---------------+------------+----------------+
 | 7    48   9   | 5   2   3  | 1     48   6   |
 | 6    2    58  | 4   9   1  | 578   3    57  |
 | 45   1    3   | 6   8   7  | 49    2    459 |
 +---------------+------------+----------------+
 | 8    57   457 | 1   45  6  | 3     9    2   |
 | 345  6    2   | 8   37  9  | 47    57   1   |
 | 35   9    1   | 2   37  45 | 6     457  8   |
 +---------------+------------+----------------+

Triple-digit POM: 3 @ r1c9 r2c24 r3c24 r4c6 r5c8 r6c3 r7c7 r8c15 r9c15
and POM: 7 @ r1c4 r2c237 r3c289 r4c1 r5c79 r6c6 r7c23 r8c578 r9c58
and POM: 8 @ r1c37 r2c6 r3c28 r4c28 r5c37 r6c5 r7c1 r8c4 r9c9
Digit 3 not in 2 Templates => -3 @ r2c4 r3c2
Digit 3 in all 2 Templates => 3 @ r2c2 r3c4

Triple-digit POM: 4 @ r1c23 r2c79 r3c56 r4c28 r5c4 r6c179 r7c35 r8c17 r9c68
and POM: 1 @ r1c8 r2c5 r3c1 r4c7 r5c6 r6c2 r7c4 r8c9 r9c3
and POM: 5 @ r1c27 r2c379 r3c56 r4c4 r5c379 r6c19 r7c235 r8c18 r9c168
Digit 4 not in 2 Templates => -4 @ r1c2 r3c5 r4c8 r6c1 r7c3 r8c7 r9c6
Digit 4 in all 2 Templates => 4 @ r1c3 r3c6 r4c2 r7c5 r8c1 r9c8

Triple-digit POM: 4 @ r1c3 r2c79 r3c6 r4c2 r5c4 r6c79 r7c5 r8c1 r9c8
and POM: 1 @ r1c8 r2c5 r3c1 r4c7 r5c6 r6c2 r7c4 r8c9 r9c3
and POM: 9 @ r1c1 r2c479 r3c9 r4c3 r5c5 r6c79 r7c8 r8c6 r9c2
Digit 4 not in 1 Template => -4 @ r2c9 r6c7
Digit 4 in all 1 Template => 4 @ r2c7 r6c9

Triple-digit POM: 5 @ r1c27 r2c39 r3c5 r4c4 r5c379 r6c1 r7c23 r8c8 r9c16
and POM: 1 @ r1c8 r2c5 r3c1 r4c7 r5c6 r6c2 r7c4 r8c9 r9c3
and POM: 2 @ r1c6 r2c1 r3c7 r4c5 r5c2 r6c8 r7c9 r8c3 r9c4
Digit 5 not in 2 Templates => -5 @ r5c3 r9c1
Digit 5 in all 2 Templates => 5 @ r8c8

Triple-digit POM: 5 @ r1c27 r2c39 r3c5 r4c4 r5c79 r6c1 r7c23 r8c8 r9c6
and POM: 1 @ r1c8 r2c5 r3c1 r4c7 r5c6 r6c2 r7c4 r8c9 r9c3
and POM: 7 @ r1c4 r2c3 r3c289 r4c1 r5c79 r6c6 r7c23 r8c57 r9c5
Digit 5 not in 1 Template => -5 @ r1c7 r2c3 r5c9 r7c2
Digit 5 in all 1 Template => 5 @ r2c9 r5c7 r7c3

Triple-digit POM: 7 @ r1c4 r2c3 r3c289 r4c1 r5c9 r6c6 r7c2 r8c57 r9c5
and POM: 1 @ r1c8 r2c5 r3c1 r4c7 r5c6 r6c2 r7c4 r8c9 r9c3
and POM: 2 @ r1c6 r2c1 r3c7 r4c5 r5c2 r6c8 r7c9 r8c3 r9c4
Digit 7 not in 1 Template => -7 @ r3c2 r3c9 r8c5
Digit 7 in all 1 Template => 7 @ r3c8 r9c5; stte

Note: Not sure about if not all Double-digit and Triple-digit POM moves are required to crack the puzzle.

R. Jamil

[P.O.]

basics:

Hidden Text: Show

Code: Select all

( n1r9c3   n1r2c5   n1r1c8   n2r4c5   n2r9c4   n6r6c4   n6r3c3   n8r6c5   n8r8c4
  n3r4c6   n1r8c9   n2r7c9   n3r5c8   n6r7c6   n6r4c9   n6r5c1   n9r8c6   n9r7c8
  n2r5c2   n2r2c1   n6r9c7   n9r4c3   n1r5c6   n1r6c2   n2r3c7   n7r6c6   n9r1c1
  n7r1c4 )

intersections:
((((8 0) (9 8 9) (4 5 7 8)) ((8 0) (9 9 9) (4 5 7 8)))
 (((8 0) (7 1 7) (4 5 8)) ((8 0) (9 1 7) (3 4 5)))
 (((7 0) (7 2 7) (4 5 7)) ((7 0) (7 3 7) (4 5 7)))
 (((5 0) (3 5 2) (3 4 5)) ((5 0) (3 6 2) (4 5)))
 (((4 0) (3 5 2) (3 4 5)) ((4 0) (3 6 2) (4 5)))
 (((3 0) (8 5 8) (3 4 5 7)) ((3 0) (9 5 8) (3 4 5 7)))
 (((3 0) (8 1 7) (3 4 5)) ((3 0) (9 1 7) (3 4 5)))
 (((3 0) (2 2 1) (3 4 5 7)) ((3 0) (3 2 1) (3 7 8))) ( n8r7c1   n3r6c3 )
 (((5 0) (8 8 9) (4 5 7)) ((5 0) (9 8 9) (4 5 7 8))))

PAIR COL: ((3 5 2) (4 5)) ((7 5 8) (4 5)) 
(((8 5 8) (3 4 5 7)) ((9 5 8) (3 4 5 7)))


Code: Select all

9     458   458   7     6     2     458   1     3             
2     3457  457   39    1     8     4579  6     4579           
1     378   6     39    45    45    2     78    789           
7     48    9     5     2     3     1     48    6             
6     2     58    4     9     1     578   3     578           
45    1     3     6     8     7     459   2     459           
8     457   457   1     45    6     3     9     2             
345   6     2     8     37    9     47    457   1             
345   9     1     2     37    45    6     4578  478           

8r5c7 => r2c3 <> 4,5,7
 r5c7=8 - r4c8{n8 n4} - b4n4{r4c2 r6c1} - r8n4{c1 c7} - c9n4{r9 r2}
 r5c7=8 - r5c3{n8 n5}
 r5c7=8 - r4c8{n8 n4} - b4n4{r4c2 r6c1} - r8n4{c1 c7} - c7n7{r8 r2}
 
=> r5c7 <> 8
ste.


Hi R. Jamil, i have a POM solution with the combination (4 7 8):

Hidden Text: Show

Code: Select all

....62..3.....8.6.1........7..5..1.....49...........2....1..3...62.......9.......
#VT: (1 1 4 30 48 1 12 3 3)
Cells: NIL NIL (48) NIL NIL NIL NIL (55) NIL
SetVC: ( n3r6c3   n8r7c1 )

#VT: (1 1 4 14 24 1 12 3 3)
Cells: NIL NIL NIL NIL NIL NIL NIL NIL NIL
Candidates: NIL NIL (23) (20 26 27) (20 26 27 70 81) NIL (59) (2 45) NIL

9     45    458   7     6     2     458   1     3             
2     3457  457   39    1     8     4579  6     4579           
1     378   6     39    45    45    2     78    789           
7     48    9     5     2     3     1     48    6             
6     2     58    4     9     1     578   3     57             
45    1     3     6     8     7     459   2     459           
8     457   457   1     45    6     3     9     2             
345   6     2     8     3457  9     47    457   1             
345   9     1     2     3457  45    6     4578  478           
94 candidates. 47 values.

(4 7 8) 20 instances

..87..4....4..87...7...4..878.....4....4..8.74...87...847.........84..7.....7..84
..87..4...74..8........4.7878.....4....4..8.74...87...847.........84.7......7..84
..87..4...47..8........4.7878.....4....4..8.74...87...874.........84.7......7..84
..47..8....7..8..4.8...4..774.....8...84..7......874..87..4.......87..4.4......78
..47..8....7..8..4.8...4.7.74.....8...84....7....874..87..4.......8..74.4...7...8
..47..8...7...8..4.8...4..774.....8...84..7......874..8.7.4.......87..4.4......78
..47..8...7...8..4.8...4.7.74.....8...84....7....874..8.7.4.......8..74.4...7...8
..47..8....7..8..4.8...4..774.....8...84..7......874..87..4....4..8...7.....7..48
..47..8....7..8..4.8...4.7.74.....8...84....7....874..87..4....4..8..7......7..48
..47..8...7...8..4.8...4..774.....8...84..7......874..8.7.4....4..8...7.....7..48
..47..8...7...8..4.8...4.7.74.....8...84....7....874..8.7.4....4..8..7......7..48
..47..8....7..84...8...4..774.....8...84..7......87..487..4.......87..4.4......78
..47..8....7..84...8...4.7.74.....8...84....7....87..487..4.......8..74.4...7...8
..47..8...7...84...8...4..774.....8...84..7......87..48.7.4.......87..4.4......78
..47..8...7...84...8...4.7.74.....8...84....7....87..48.7.4.......8..74.4...7...8
..47..8....7..84...8...4..774.....8...84..7......87..487..4....4..8...7.....7..48
..47..8....7..84...8...4.7.74.....8...84....7....87..487..4....4..8..7......7..48
..47..8...7...84...8...4..774.....8...84..7......87..48.7.4....4..8...7.....7..48
..47..8...7...84...8...4.7.74.....8...84....7....87..48.7.4....4..8..7......7..48
.487.......7..84.......4.7878.....4....4..8.74...87...874.........84.7......7..84

......4....4...........4..........4....4.....4.........4...........4............4
......4...4............4..........4....4.....4..........4..........4............4
..4..............4.....4....4..........4...........4......4...........4.4........
..4..............4.....4....4..........4...........4......4....4...............4.
..4............4.......4....4..........4.............4....4...........4.4........
..4............4.......4....4..........4.............4....4....4...............4.
.4.............4.......4..........4....4.....4..........4..........4............4

...7...........7...7.......7................7.....7.....7.............7.....7....
...7.......7..............77..............7.......7....7..............7.....7....
...7.......7..............77..............7.......7....7...........7...........7.
...7.......7.............7.7................7.....7....7.............7......7....
...7......7...............77..............7.......7.....7.............7.....7....
...7......7...............77..............7.......7.....7..........7...........7.
...7......7..............7.7................7.....7.....7............7......7....

......8.......8....8..............8...8..........8....8...........8.............8
..8...........8...........8.8.............8......8....8...........8............8.

#VT: (1 1 4 7 24 1 7 2 3)
Cells: NIL NIL NIL (24) NIL NIL NIL NIL NIL
SetVC: ( n4r3c6   n5r9c6   n5r3c5   n4r7c5   n5r8c8   n5r6c1   n8r5c3   n4r4c2   n8r4c8   n5r1c2
         n4r1c3   n8r1c7   n7r2c3   n7r3c8   n9r3c9   n4r6c9   n7r7c2   n5r7c3   n4r9c8   n3r2c2
         n9r2c4   n5r2c9   n8r3c2   n3r3c4   n7r5c9   n9r6c7   n7r8c7   n3r9c1   n7r9c5   n8r9c9
         n4r2c7   n5r5c7   n4r8c1   n3r8c5 )
9 5 4   7 6 2   8 1 3
2 3 7   9 1 8   4 6 5
1 8 6   3 5 4   2 7 9
7 4 9   5 2 3   1 8 6
6 2 8   4 9 1   5 3 7
5 1 3   6 8 7   9 2 4
8 7 5   1 4 6   3 9 2
4 6 2   8 3 9   7 5 1
3 9 1   2 7 5   6 4 8


[rjamil]

Hi P.O.,

It seems that you applied Triple-digit POM move (4 7 8) only one, where as, I applied several at a same time. Thats why, our POM moves differed but the end results were same.

R. Jamil

[P.O.]

Note: Not sure about if not all Double-digit and Triple-digit POM moves are required to crack the puzzle.

you do not update and check the grid after making placements or eliminations
for this puzzle, you could have stopped after this:

Code: Select all

Triple-digit POM: 3 @ r1c9 r2c24 r3c24 r4c6 r5c8 r6c3 r7c7 r8c15 r9c15
and POM: 7 @ r1c4 r2c237 r3c289 r4c1 r5c79 r6c6 r7c23 r8c578 r9c58
and POM: 8 @ r1c37 r2c6 r3c28 r4c28 r5c37 r6c5 r7c1 r8c4 r9c9
Digit 3 not in 2 Templates => -3 @ r2c4 r3c2
Digit 3 in all 2 Templates => 3 @ r2c2 r3c4

Triple-digit POM: 4 @ r1c23 r2c79 r3c56 r4c28 r5c4 r6c179 r7c35 r8c17 r9c68
and POM: 1 @ r1c8 r2c5 r3c1 r4c7 r5c6 r6c2 r7c4 r8c9 r9c3
and POM: 5 @ r1c27 r2c379 r3c56 r4c4 r5c379 r6c19 r7c235 r8c18 r9c168
Digit 4 not in 2 Templates => -4 @ r1c2 r3c5 r4c8 r6c1 r7c3 r8c7 r9c6
Digit 4 in all 2 Templates => 4 @ r1c3 r3c6 r4c2 r7c5 r8c1 r9c8


[rjamil]

Hi P.O.,

you do not update and check the grid after making placements or eliminations

True. This is because, my approach is to solve the bulk puzzles in speed and not to find the shortest solution path.

I developed a BFS search routine first time for POM move in efficient way. That's why, I applied all instances of only POM placement and elimination moves as and when detected.

R. Jamil

[P.O.]

the first POM procedure i wrote did just that: apply all size 2 combinations before updating and checking the grid, then all size 3 combinations, etc.
and then i developed other procedures to find the smallest number of combinations needed to solve the puzzle.

[rjamil]

Hi P.O.,

Great jobs.

But I am still in an initial stage of developing the solver. I see lot of solvers, here and there, solving for speed. Few last one was developed by Zhou, tdillon, etc.

R. Jamil