The New Sudoku Players' Forum

[P.O.]

note that blue's puzzle is solved with only one size 3 combination (2 6 7) and note further that there are only two instances of this combination:

Hidden Text: Show

Code: Select all

.2..5....4.......7...6..1....17..........5.2.8.......6....4..5...7...9...6...2...

#VT: (50 2 5898 60 14 13 6 684 674)
Cells: nil nil nil nil nil nil nil nil nil
Candidates:nil (14 50 55 63) nil nil nil nil nil nil nil

13679   2       3689    13489   5       134789  3468    34689   3489             
4       13589   35689   12389   1389    1389    23568   3689    7               
3579    35789   3589    6       23789   34789   1       3489    234589           
23569   3459    1       7       23689   34689   3458    3489    34589           
3679    3479    3469    13489   13689   5       3478    2       13489           
8       34579   23459   12349   139     1349    3457    13479   6               
139     1389    2389    1389    4       136789  23678   5       138             
1235    13458   7       1358    1368    1368    9       13468   12348           
1359    6       34589   13589   13789   2       3478    13478   1348             
284 candidates.


1: (2 6 7): 2 instances

.2...76....6...2.77..62....2..76....67.....2....2...76..2..67....7....62.6..72...
72....6....6...2.7...627...2..76....67.....2....2...76..2..67....7....62.6..72...

.2.............2......2....2...............2....2.......2..............2.....2...

......6....6.........6.........6....6................6.....6..........6..6.......

.....7...........77...........7......7..............7.......7....7..........7....
7................7.....7......7......7..............7.......7....7..........7....

#VT: (50 1 5898 60 14 1 2 684 674)
Cells: nil (16 23 28 49 57 72) nil nil nil (7 12 32 37 60 71) (38 53 61 77) nil nil
SetVC: ( n6r1c7   n6r2c3   n2r2c7   n2r3c5   n2r4c1   n6r4c5
         n6r5c1   n7r5c2   n2r6c4   n7r6c8   n2r7c3   n6r7c6
         n7r7c7   n6r8c8   n2r8c9   n7r9c5   n1r9c8   n1r5c9
         n4r8c2   n5r3c9   n5r2c2   n1r7c2   n1r1c1   n5r6c3
         n5r4c7   n7r3c1   n7r1c6   n8r9c3   n8r3c2   n4r5c3
         n8r7c9   n8r5c7   n4r1c4   n8r4c6   n8r1c8   n4r6c6
         n4r3c8   n3r6c7   n4r9c7   n3r9c9   n9r1c9   n3r2c8
         n9r4c8   n4r4c9   n9r6c2   n1r6c5   n3r1c3   n9r3c3
         n3r3c6   n3r4c2   n1r8c6   n9r2c6   n8r2c5   n3r8c5
         n1r2c4   n9r5c5   n9r7c4   n5r8c1   n8r8c4   n9r9c1
         n5r9c4   n3r5c4   n3r7c1 )
1 2 3   4 5 7   6 8 9
4 5 6   1 8 9   2 3 7
7 8 9   6 2 3   1 4 5
2 3 1   7 6 8   5 9 4
6 7 4   3 9 5   8 2 1
8 9 5   2 1 4   3 7 6
3 1 2   9 4 6   7 5 8
5 4 7   8 3 1   9 6 2
9 6 8   5 7 2   4 1 3


[denis_berthier]

.
irrelevant. What counts in the complexity of the solution is how many templates MUST be checked.
.

[blue]

Thanks to P.O., for pointing out that I posted the solution for the wrong puzzle.
This is the right one.
Better numbers, but still a lot of templates ...

Hidden Text: Show

Code: Select all

puzzle: .......719......6..2.........4.7.....3....4.....91....7..6....8...3..2..1........
singles: 2r2c9, 3r4c6, 4r6c6
after singles
+---------------------+----------------------+--------------------+
| 34568  4568    3568 |  2458 2345689  25689 |  3589     7      1 |
|     9 14578   13578 | 14578    3458   1578 |   358     6      2 |
| 34568     2  135678 | 14578  345689 156789 |  3589 34589   3459 |
+---------------------+----------------------+--------------------+
|  2568 15689       4 |   258       7      3 | 15689 12589    569 |
|  2568     3 1256789 |   258    2568   2568 |     4 12589   5679 |
|  2568  5678   25678 |     9       1      4 | 35678  2358   3567 |
+---------------------+----------------------+--------------------+
|     7   459    2359 |     6    2459   1259 |  1359 13459      8 |
|  4568 45689    5689 |     3    4589  15789 |     2  1459  45679 |
|     1 45689  235689 | 24578   24589  25789 | 35679  3459 345679 |
+---------------------+----------------------+--------------------+
{ 5 28 19 21 3862 92 7 742 132 }
*** Entering level 1 ***
no template for digit 1 includes r2c6 -> elimination: 1r2c6
no template for digit 1 includes r3c6 -> elimination: 1r3c6
{ 5 28 19 21 3862 92 7 742 132 }
wasted {?} (5)
no template for digit 2 includes r5c3 -> elimination: 2r5c3
no template for digit 2 includes r6c3 -> elimination: 2r6c3
{ 5 28 19 21 3862 92 7 742 132 }
wasted {?} (33)
no template for digit 3 includes r1c3 -> elimination: 3r1c3
no template for digit 3 includes r2c3 -> elimination: 3r2c3
no template for digit 3 includes r3c3 -> elimination: 3r3c3
{ 5 28 19 21 3862 92 7 742 132 }
wasted {?} (52)
no template for digit 4 includes r3c1 -> elimination: 4r3c1
no template for digit 4 includes r3c4 -> elimination: 4r3c4
no template for digit 4 includes r3c5 -> elimination: 4r3c5
{ 5 28 19 21 3862 92 7 742 132 }
wasted {?} (3935)
no template for digit 6 includes r5c1 -> elimination: 6r5c1
no template for digit 6 includes r5c3 -> elimination: 6r5c3
no template for digit 6 includes r5c9 -> elimination: 6r5c9
{ 5 28 19 21 3862 92 7 742 132 }
wasted {?} (4027)
no template for digit 7 includes r2c6 -> elimination: 7r2c6
{ 5 28 19 21 3862 92 7 742 132 }
wasted {?} (4908)
+--------------------+---------------------+--------------------+
| 34568  4568    568 |  2458 2345689 25689 |  3589     7      1 |
|     9 14578   1578 | 14578    3458    58 |   358     6      2 |
|  3568     2  15678 |  1578   35689 56789 |  3589 34589   3459 |
+--------------------+---------------------+--------------------+
|  2568 15689      4 |   258       7     3 | 15689 12589    569 |
|   258     3  15789 |   258    2568  2568 |     4 12589    579 |
|  2568  5678   5678 |     9       1     4 | 35678  2358   3567 |
+--------------------+---------------------+--------------------+
|     7   459   2359 |     6    2459  1259 |  1359 13459      8 |
|  4568 45689   5689 |     3    4589 15789 |     2  1459  45679 |
|     1 45689 235689 | 24578   24589 25789 | 35679  3459 345679 |
+--------------------+---------------------+--------------------+
*** Entering level 2 ***
wasted {?,?} (1079)
pruning tlist for d=5, after {1,5} [9649]
{ 5 28 19 21 3585 92 7 742 132 }
wasted {?} (4631)
wasted {?,?} (48718)
pruning tlist for d=5, after {3,5} [26463]
{ 5 28 19 21 3555 92 7 742 132 }
wasted {?} (4601)
wasted {?,?} (74865)
pruning tlist for d=5, after {4,5} [28324]
{ 5 28 19 21 3532 92 7 742 132 }
wasted {?} (4578)
wasted {?,?} (224523)
pruning tlist for d=1, after {1,7} [4]
pruning tlist for d=7, after {1,7} [4]
{ 3 28 19 21 3532 92 3 742 132 }
no template for digit 1 includes r4c8 -> elimination: 1r4c8
no template for digit 1 includes r7c8 -> elimination: 1r7c8
{ 3 28 19 21 3532 92 3 742 132 }
wasted {?} (3695)
no template for digit 7 includes r2c3 -> elimination: 7r2c3
no template for digit 7 includes r6c3 -> elimination: 7r6c3
no template for digit 7 includes r6c9 -> elimination: 7r6c9
no template for digit 7 includes r9c9 -> elimination: 7r9c9
{ 3 28 19 21 3532 92 3 742 132 }
wasted {?} (4572)
pruning tlist for d=2, after {1,2} [70]
{ 3 27 19 21 3532 92 3 742 132 }
wasted {?} (4571)
wasted {?,?} (943)
pruning tlist for d=5, after {1,5} [5717]
{ 3 27 19 21 3385 92 3 742 132 }
wasted {?} (4424)
wasted {?,?} (211082)
pruning tlist for d=4, after {4,7} [33]
{ 3 27 19 19 3385 92 3 742 132 }
wasted {?} (4422)
wasted {?,?} (208378)
pruning tlist for d=5, after {5,7} [5336]
{ 3 27 19 19 3063 92 3 742 132 }
wasted {?} (4100)
wasted {?,?} (195999)
pruning tlist for d=6, after {6,7} [128]
{ 3 27 19 19 3063 80 3 742 132 }
wasted {?} (4088)
wasted {?,?} (181300)
pruning tlist for d=8, after {1,8} [1203]
{ 3 27 19 19 3063 80 3 684 132 }
wasted {?} (4030)
wasted {?,?} (831117)
pruning tlist for d=8, after {7,8} [1130]
{ 3 27 19 19 3063 80 3 662 132 }
wasted {?} (4008)
wasted {?,?} (808089)
pruning tlist for d=9, after {1,9} [154]
{ 3 27 19 19 3063 80 3 662 97 }
wasted {?} (3973)
wasted {?,?} (936491)
pruning tlist for d=9, after {7,9} [122]
{ 3 27 19 19 3063 80 3 662 91 }
wasted {?} (3967)
wasted {?,?} (956971)
+--------------------+---------------------+-------------------+
| 34568  4568    568 |  2458 2345689 25689 |  3589     7     1 |
|     9 14578    158 | 14578    3458    58 |   358     6     2 |
|  3568     2  15678 |  1578   35689 56789 |  3589 34589  3459 |
+--------------------+---------------------+-------------------+
|  2568 15689      4 |   258       7     3 | 15689  2589   569 |
|   258     3  15789 |   258    2568  2568 |     4 12589   579 |
|  2568  5678    568 |     9       1     4 | 35678  2358   356 |
+--------------------+---------------------+-------------------+
|     7   459   2359 |     6    2459  1259 |  1359  3459     8 |
|  4568 45689   5689 |     3    4589 15789 |     2  1459 45679 |
|     1 45689 235689 | 24578   24589 25789 | 35679  3459 34569 |
+--------------------+---------------------+-------------------+
*** Entering level 3 ***
wasted {?,?,?} (84142)
pruning tlist for d=5, after {2,3,5} [77459]
{ 3 27 19 19 2376 80 3 662 91 }
wasted {?} (68)
no template for digit 5 includes r7c3 -> elimination: 5r7c3
no template for digit 5 includes r9c3 -> elimination: 5r9c3
{ 3 27 19 19 2376 80 3 662 91 }
wasted {?} (3280)
wasted {?,?} (755033)
wasted {?,?,?} (150267)
pruning tlist for d=5, after {1,4,5} [18796]
{ 3 27 19 19 2355 80 3 662 91 }
wasted {?} (3259)
wasted {?,?} (749094)
wasted {?,?,?} (350954)
pruning tlist for d=6, after {2,3,6} [4243]
{ 3 27 19 19 2355 72 3 662 91 }
wasted {?} (2423)
no template for digit 6 includes r9c3 -> elimination: 6r9c3
{ 3 27 19 19 2355 72 3 662 91 }
wasted {?} (3251)
wasted {?,?} (737475)
wasted {?,?,?} (1251186)
pruning tlist for d=4, after {1,4,7} [17]
{ 3 27 19 15 2355 72 3 662 91 }
wasted {?} (49)
no template for digit 4 includes r1c4 -> elimination: 4r1c4
no template for digit 4 includes r1c5 -> elimination: 4r1c5
no template for digit 4 includes r2c2 -> elimination: 4r2c2
{ 3 27 19 15 2355 72 3 662 91 }
wasted {?} (3247)
wasted {?,?} (51785)
pruning tlist for d=5, after {4,5} [12984]
{ 3 27 19 15 2331 72 3 662 91 }
wasted {?} (3223)
wasted {?,?} (724708)
wasted {?,?,?} (147544)
pruning tlist for d=5, after {1,4,5} [14351]
{ 3 27 19 15 2303 72 3 662 91 }
wasted {?} (3195)
wasted {?,?} (716256)
wasted {?,?,?} (275577)
pruning tlist for d=5, after {3,4,5} [25181]
{ 3 27 19 15 2295 72 3 662 91 }
wasted {?} (3187)
wasted {?,?} (714103)
wasted {?,?,?} (1127946)
pruning tlist for d=3, after {3,4,7} [153]
{ 3 27 16 15 2295 72 3 662 91 }
wasted {?} (30)
no template for digit 3 includes r6c7 -> elimination: 3r6c7
{ 3 27 16 15 2295 72 3 662 91 }
wasted {?} (3184)
wasted {?,?} (709321)
wasted {?,?,?} (1062091)
pruning tlist for d=5, after {1,5,7} [2617]
{ 3 27 16 15 1582 72 3 662 91 }
wasted {?} (61)
no template for digit 5 includes r2c2 -> elimination: 5r2c2
no template for digit 5 includes r5c3 -> elimination: 5r5c3
no template for digit 5 includes r8c6 -> elimination: 5r8c6
{ 3 27 16 15 1582 72 3 662 91 }
wasted {?} (2471)
wasted {?,?} (505143)
wasted {?,?,?} (789407)
pruning tlist for d=5, after {4,5,7} [10961]
{ 3 27 16 15 1474 72 3 662 91 }
wasted {?} (2363)
wasted {?,?} (474669)
wasted {?,?,?} (756607)
pruning tlist for d=6, after {1,6,7} [102]
{ 3 27 16 15 1474 58 3 662 91 }
wasted {?} (2349)
wasted {?,?} (462009)
wasted {?,?,?} (395458)
pruning tlist for d=5, after {3,5,6} [100350]
{ 3 27 16 15 1471 58 3 662 91 }
wasted {?} (2346)
wasted {?,?} (461112)
wasted {?,?,?} (495124)
pruning tlist for d=5, after {4,5,6} [94026]
{ 3 27 16 15 1461 58 3 662 91 }
wasted {?} (2336)
wasted {?,?} (458420)
wasted {?,?,?} (652272)
pruning tlist for d=5, after {5,6,7} [29896]
{ 3 27 16 15 1445 58 3 662 91 }
wasted {?} (2320)
wasted {?,?} (453579)
wasted {?,?,?} (693382)
pruning tlist for d=8, after {2,3,8} [17322]
{ 3 27 16 15 1445 58 3 581 91 }
wasted {?} (1567)
no template for digit 8 includes r9c3 -> elimination: 8r9c3
{ 3 27 16 15 1445 58 3 581 91 }
wasted {?} (2239)
wasted {?,?} (406796)
wasted {?,?,?} (709291)
pruning tlist for d=8, after {1,4,8} [5522]
{ 3 27 16 15 1445 58 3 577 91 }
wasted {?} (2235)
wasted {?,?} (404763)
wasted {?,?,?} (4455413)
pruning tlist for d=8, after {1,7,8} [612]
{ 3 27 16 15 1445 58 3 391 91 }
wasted {?} (1567)
no template for digit 8 includes r2c2 -> elimination: 8r2c2
no template for digit 8 includes r5c3 -> elimination: 8r5c3
no template for digit 8 includes r8c6 -> elimination: 8r8c6
{ 3 27 16 15 1445 58 3 391 91 }
wasted {?} (2049)
wasted {?,?} (309194)
wasted {?,?,?} (3076864)
pruning tlist for d=8, after {4,7,8} [3279]
{ 3 27 16 15 1445 58 3 354 91 }
wasted {?} (2012)
wasted {?,?} (289672)
wasted {?,?,?} (2992952)
pruning tlist for d=9, after {2,3,9} [3869]
{ 3 27 16 15 1445 58 3 354 65 }
wasted {?} (1921)
no template for digit 9 includes r7c3 -> elimination: 9r7c3
no template for digit 9 includes r8c6 -> elimination: 9r8c6
no template for digit 9 includes r9c3 -> elimination: 9r9c3
{ 3 27 16 15 1445 58 3 354 65 }
wasted {?} (1986)
wasted {?,?} (263513)
wasted {?,?,?} (3004570)
pruning tlist for d=5, after {1,5,9} [35918]
{ 3 27 16 15 1329 58 3 354 65 }
wasted {?} (61)
no template for digit 5 includes r4c2 -> elimination: 5r4c2
{ 3 27 16 15 1329 58 3 354 65 }
wasted {?} (1870)
wasted {?,?} (245029)
wasted {?,?,?} (3251728)
pruning tlist for d=6, after {1,6,9} [2325]
{ 3 27 16 15 1329 52 3 354 65 }
wasted {?} (1390)
no template for digit 6 includes r4c2 -> elimination: 6r4c2
{ 3 27 16 15 1329 52 3 354 65 }
wasted {?} (1864)
wasted {?,?} (240315)
wasted {?,?,?} (3322247)
pruning tlist for d=1, after {1,7,9} [4]
pruning tlist for d=7, after {1,7,9} [4]
pruning tlist for d=9, after {1,7,9} [4]
{ 1 27 16 15 1329 52 1 354 4 }
every template for digit 1 includes r2c2 -> placement: 1r2c2
every template for digit 1 includes r3c4 -> placement: 1r3c4
every template for digit 1 includes r4c7 -> placement: 1r4c7
every template for digit 1 includes r5c3 -> placement: 1r5c3
every template for digit 1 includes r7c6 -> placement: 1r7c6
every template for digit 1 includes r8c8 -> placement: 1r8c8
singles: 6r1c3, 7r2c4, 4r2c5, 3r2c7, 7r3c3, 6r4c1, 9r4c2, 5r4c9, 9r5c8, 7r5c9, 7r6c2, 6r6c7, 3r6c9, 9r8c3, 7r8c6, 4r9c4, 7r9c7
18 templates removed from d=2 list
12 templates removed from d=3 list
12 templates removed from d=4 list
1295 templates removed from d=5 list
48 templates removed from d=6 list
334 templates removed from d=8 list
{ 1 9 4 3 34 4 1 20 4 }
wasted {?} (17)
no template for digit 5 includes r5c1 -> elimination: 5r5c1
{ 1 9 4 3 34 4 1 20 4 }
wasted {?} (56)
no template for digit 8 includes r3c8 -> elimination: 8r3c8
{ 1 9 4 3 34 4 1 20 4 }
wasted {?} (76)
no template for digit 9 includes r3c5 -> elimination: 9r3c5
{ 1 9 4 3 34 4 1 20 4 }
wasted {?} (80)
wasted {?,?} (59)
pruning tlist for d=3, after {3,4} [5]
{ 1 9 3 3 34 4 1 20 4 }
wasted {?} (79)
wasted {?,?} (12)
pruning tlist for d=2, after {2,3} [10]
{ 1 7 3 3 34 4 1 20 4 }
wasted {?} (1)
no template for digit 2 includes r1c5 -> elimination: 2r1c5
{ 1 7 3 3 34 4 1 20 4 }
wasted {?} (77)
wasted {?,?} (83)
pruning tlist for d=2, after {2,5} [74]
pruning tlist for d=5, after {2,5} [74]
{ 1 5 3 3 28 4 1 20 4 }
wasted {?} (1)
no template for digit 2 includes r5c4 -> elimination: 2r5c4
{ 1 5 3 3 28 4 1 20 4 }
wasted {?} (12)
no template for digit 5 includes r1c6 -> elimination: 5r1c6
{ 1 5 3 3 28 4 1 20 4 }
wasted {?} (69)
wasted {?,?} (140)
pruning tlist for d=5, after {3,5} [42]
{ 1 5 3 3 26 4 1 20 4 }
wasted {?} (67)
wasted {?,?} (172)
pruning tlist for d=5, after {4,5} [30]
{ 1 5 3 3 24 4 1 20 4 }
wasted {?} (65)
wasted {?,?} (331)
pruning tlist for d=8, after {2,8} [33]
{ 1 5 3 3 24 4 1 18 4 }
wasted {?} (63)
wasted {?,?} (443)
pruning tlist for d=5, after {5,8} [42]
pruning tlist for d=8, after {5,8} [42]
{ 1 5 3 3 17 4 1 14 4 }
wasted {?} (12)
no template for digit 5 includes r1c5 -> elimination: 5r1c5
no template for digit 5 includes r3c5 -> elimination: 5r3c5
no template for digit 5 includes r3c6 -> elimination: 5r3c6
{ 1 5 3 3 17 4 1 14 4 }
wasted {?} (52)
wasted {?,?} (558)
wasted {?,?,?} (236)
pruning tlist for d=5, after {3,4,5} [16]
{ 1 5 3 3 12 4 1 14 4 }
wasted {?} (12)
no template for digit 5 includes r1c7 -> elimination: 5r1c7
no template for digit 5 includes r3c1 -> elimination: 5r3c1
no template for digit 5 includes r7c2 -> elimination: 5r7c2
stte
solved: max level = 3
+-------+-------+-------+
| 4 5 6 | 2 3 9 | 8 7 1 |
| 9 1 8 | 7 4 5 | 3 6 2 |
| 3 2 7 | 1 6 8 | 5 4 9 |
+-------+-------+-------+
| 6 9 4 | 8 7 3 | 1 2 5 |
| 8 3 1 | 5 2 6 | 4 9 7 |
| 2 7 5 | 9 1 4 | 6 8 3 |
+-------+-------+-------+
| 7 4 2 | 6 5 1 | 9 3 8 |
| 5 6 9 | 3 8 7 | 2 1 4 |
| 1 8 3 | 4 9 2 | 7 5 6 |
+-------+-------+-------+
CPU time : 0.89s


[P.O.]

irrelevant. What counts in the complexity of the solution is how many templates MUST be checked.

what matters in the complexity of a solution is the complexity of the solution and this one is extremely simple

[denis_berthier]

.
With such total absence of conceptual thinking, I have a still simpler one: the solution grid!
.

[P.O.]

once again off the mark Denis

[denis_berthier]

.
Why am I not surprised that you wouldn't understand my answer?
.

[P.O.]

are you even incapable of understanding yourself?