the particularity of this puzzle is that although its resolution with chain techniques is relatively sophisticated with templates it is resolved at initialization where only patterns that involve a single value are found and since there are 21 eliminations of 9 this seemed to indicate a large fishy pattern that Shye's solution shows well
- Code: Select all
Initialization:
#VT: (3 5 6 6 12 12 32 38 16)
49 34579 359 3579 6 2 1 8 479
14689 123456789 23589 35789 379 5789 2679 49 24679
689 26789 289 789 4 1 5 3 2679
489 34589 3589 2 79 6789 689 59 1
7 589 6 89 1 3 4 2 589
2 89 1 4 5 689 689 7 3
3 189 4 1579 2 579 789 6 5789
5 269 7 69 8 4 3 1 29
1689 12689 289 135679 379 5679 2789 459 245789
Value: 2
Value Cells: (6 31 44 46 59)
Candidate Cells: (11 12 16 18 20 21 27 65 72 74 75 79 81)
Union csets: ( . 12 16 18 20 21 27 65 72 74 75 79 81)
Complementary Sets: 5
(12 27 65 79)
(16 20 72 75)
(16 21 65 81)
(16 21 72 74)
(18 21 65 79)
Candidate 2 to be eliminated in cells: (11)
Value: 6
Value Cells: (5 39 62)
Candidate Cells: (10 11 16 18 19 20 27 33 34 51 52 65 67 73 74 76 78)
Union csets: (10 11 . 18 19 20 27 33 34 51 52 65 67 73 74 76 .)
Complementary Sets: 12
(10 27 33 52 65 76)
(10 27 33 52 67 74)
(10 27 34 51 65 76)
(10 27 34 51 67 74)
(11 27 33 52 67 73)
(11 27 34 51 67 73)
(18 19 33 52 65 76)
(18 19 33 52 67 74)
(18 19 34 51 65 76)
(18 19 34 51 67 74)
(18 20 33 52 67 73)
(18 20 34 51 67 73)
Candidate 6 to be eliminated in cells: (16 78)
Value: 9
Value Cells: NIL
Candidate Cells: (1 2 3 4 9 10 11 12 13 14 15 16 17 18 19 20 21 22 27 28 29 30
32 33 34 35 38 40 45 47 51 52 56 58 60 61 63 65 67 72 73 74
75 76 77 78 79 80 81)
Union csets: (1 3 4 9 14 17 19 21 22 27 28 30 32 35 38 40 45 51 52 60 61 65
67 72 73 75 77 80)
Complementary Sets: 16
(1 14 27 30 40 52 60 65 80)
(1 14 27 35 38 51 61 67 75)
(1 17 22 30 45 51 61 65 77)
(1 17 22 32 38 52 60 72 75)
(3 14 27 28 40 52 60 65 80)
(3 14 27 35 38 51 61 67 73)
(3 17 22 28 45 51 61 65 77)
(3 17 22 32 38 52 60 72 73)
(4 17 19 30 45 51 61 65 77)
(4 17 19 32 38 52 60 72 75)
(9 14 19 30 40 52 60 65 80)
(9 14 19 35 38 51 61 67 75)
(4 17 21 28 45 51 61 65 77)
(4 17 21 32 38 52 60 72 73)
(9 14 21 28 40 52 60 65 80)
(9 14 21 35 38 51 61 67 73)
Candidate 9 to be eliminated in cells: (2 10 11 12 13 15 16 18 20 29 33 34 47
56 58 63 74 76 78 79 81)
ste.
regarding Cenoman's solution the contradiction with the x-wing is really fine
another way to get the same eliminations:
- Code: Select all
9r8c249 => r1234679c2 <> 9
r8c4=9 - b2n9{r123c4 r2c56} - b3n9{r2c789 r13c9} - r5n9{c9 c2}
r8c9=9 - b3n9{r123c9 r2c78} - b2n9{r2c456 r13c4} - r5n9{c4 c2}
bte:
- Code: Select all
( n8r6c2 n1r7c2 n1r9c4 n1r2c1 n3r9c5 n6r8c4 )
intersection:
((((8 0) (9 1 7) (6 8 9)) ((8 0) (9 3 7) (2 8 9))))
PAIR COL: ((1 1 1) (4 9)) ((4 1 4) (4 9))
(((3 1 1) (6 8 9)) ((9 1 7) (6 8 9)))
QUAD ROW: ((4 1 4) (4 9)) ((4 2 4) (3 4 5)) ((4 3 4) (3 5 9)) ((4 8 6) (5 9))
(((4 5 5) (7 9)) ((4 6 5) (6 7 8 9)) ((4 7 6) (6 8 9)))
( n7r4c5 n9r2c5 n4r2c8 n4r9c9 )
intersection:
((((9 0) (1 9 3) (7 9)) ((9 0) (3 9 3) (2 6 7 9)))
ste.
