by **Guest** » Wed Apr 13, 2005 11:00 pm

Starting from the puzzle

1 3 4 9

7 4 9

3 9 8 7 2

9 7 2 1 5 3

3 5 9 7

5 1 7 9 3 2

9 3 5 2

3 9 6

6 9 7 5

If you run Milo's rules with n=1 you do only get to

1 2568 258 256 3 4 5678 678 9

7 4 258 1256 16 9 3568 368 18

3 56 9 156 8 7 2 46 14

48 9 68 7 2 68 1 5 3

28 3 268 1468 16 5 9 468 7

5 1 7 468 9 3 468 2 48

9 78 3 68 5 168 478 1478 2

28 2578 1258 3 4 128 78 9 6

6 28 1248 9 7 128 38 138 5

From this stage you can open the rules up for n>1 and get the following steps:

Rule 2: in row 4 possible 86 exists in exactly 2 columns {4,3}=68 {4,6}=68 so eliminate 8 from cell {4,1} old=48 new=4

Rule 2: in box 7 possible 82 exists in exactly 2 cells {8,1}=28 {9,2}=28 so eliminate 8 from cell {7,2} old=78 new=7

Rule 2: in box 7 possible 82 exists in exactly 2 cells {8,1}=28 {9,2}=28 so eliminate 8 from cell {8,2} old=2578 new=257

Rule 2: in box 7 possible 82 exists in exactly 2 cells {8,1}=28 {9,2}=28 so eliminate 2 from cell {8,2} old=257 new=57

Rule 2: in box 7 possible 82 exists in exactly 2 cells {8,1}=28 {9,2}=28 so eliminate 8 from cell {8,3} old=1258 new=125

Rule 2: in box 7 possible 82 exists in exactly 2 cells {8,1}=28 {9,2}=28 so eliminate 2 from cell {8,3} old=125 new=15

Rule 2: in box 7 possible 82 exists in exactly 2 cells {8,1}=28 {9,2}=28 so eliminate 8 from cell {9,3} old=1248 new=124

Rule 2: in box 7 possible 82 exists in exactly 2 cells {8,1}=28 {9,2}=28 so eliminate 2 from cell {9,3} old=124 new=14

Rule 2: in column 2 possible 567 exists in exactly 3 rows {3,2}=56 {7,2}=7 {8,2}=57 so eliminate 5 from cell {1,2} old=2568 new=268

Rule 2: in column 2 possible 567 exists in exactly 3 rows {3,2}=56 {7,2}=7 {8,2}=57 so eliminate 6 from cell {1,2} old=268 new=28

Rule 2: in box 1 possible 285 exists in exactly 3 cells {1,2}=28 {1,3}=258 {2,3}=258 so eliminate 5 from cell {3,2} old=56 new=6

Rule 2: in box 7 possible 287 exists in exactly 3 cells {7,2}=7 {8,1}=28 {9,2}=28 so eliminate 7 from cell {8,2} old=57 new=5

Rule 2: in box 7 possible 571 exists in exactly 3 cells {7,2}=7 {8,2}=5 {8,3}=15 so eliminate 1 from cell {9,3} old=14 new=4

Rule 2: in box 7 possible 574 exists in exactly 3 cells {7,2}=7 {8,2}=5 {9,3}=4 so eliminate 5 from cell {8,3} old=15 new=1

Rule 3: in row 3 possible 15 exists in exactly 2 columns{3,4}=156 {3,9}=14 so reduce cell {3,4} old=156 new=15

Rule 3: in row 3 possible 15 exists in exactly 2 columns{3,4}=156 {3,9}=14 so reduce cell {3,9} old=14 new=1

Rule 3: in row 3 possible 54 exists in exactly 2 columns{3,4}=15 {3,8}=46 so reduce cell {3,4} old=15 new=5

Rule 3: in row 3 possible 54 exists in exactly 2 columns{3,4}=15 {3,8}=46 so reduce cell {3,8} old=46 new=4

Rule 3: in column 9 possible 84 exists in exactly 2 rows {2,9}=18 {6,9}=48 so reduce cell {2,9} old=18 new=8

Rule 3: in row 8 possible 287 exists in exactly 3 columns{8,1}=28 {8,6}=128 {8,7}=78 so reduce cell {8,6} old=128 new=28

Rule 3: in box 2 possible 261 exists in exactly 3 cells {1,4}=256 {2,4}=1256 {2,5}=16 so reduce cell {1,4} old=256 new=26

Rule 3: in box 2 possible 261 exists in exactly 3 cells {1,4}=256 {2,4}=1256 {2,5}=16 so reduce cell {2,4} old=1256 new=126

Rule 3: in row 7 possible 6814 exists in exactly 4 columns{7,4}=68 {7,6}=168 {7,7}=478 {7,8}=1478 so reduce cell {7,7} old=478 new=48

Rule 3: in row 7 possible 6814 exists in exactly 4 columns{7,4}=68 {7,6}=168 {7,7}=478 {7,8}=1478 so reduce cell {7,8} old=1478 new=148

Rule 3: in box 3 possible 5673 exists in exactly 4 cells {1,7}=5678 {1,8}=678 {2,7}=3568 {2,8}=368 so reduce cell {1,7} old=5678 new=567

Rule 3: in box 3 possible 5673 exists in exactly 4 cells {1,7}=5678 {1,8}=678 {2,7}=3568 {2,8}=368 so reduce cell {1,8} old=678 new=67

Rule 3: in box 3 possible 5673 exists in exactly 4 cells {1,7}=5678 {1,8}=678 {2,7}=3568 {2,8}=368 so reduce cell {2,7} old=3568 new=356

Rule 3: in box 3 possible 5673 exists in exactly 4 cells {1,7}=5678 {1,8}=678 {2,7}=3568 {2,8}=368 so reduce cell {2,8} old=368 new=36

Rule 3: in row 2 possible 25163 exists in exactly 5 columns{2,3}=258 {2,4}=126 {2,5}=16 {2,7}=356 {2,8}=36 so reduce cell {2,3} old=258 new=25

Rule 3: in column 8 possible 67381 exists in exactly 5 rows {1,8}=67 {2,8}=36 {5,8}=468 {7,8}=148 {9,8}=138 so reduce cell {5,8} old=468 new=68

Rule 3: in column 8 possible 67381 exists in exactly 5 rows {1,8}=67 {2,8}=36 {5,8}=468 {7,8}=148 {9,8}=138 so reduce cell {7,8} old=148 new=18

Rule 1: in row 5 possible 4 exists only in box 5 so eliminate it from cell {6,4} old=468 new=68

Rule 1: in column 9 possible 4 exists only in box 6 so eliminate it from cell {6,7} old=468 new=68

Rule 1: in column 8 possible 7 exists only in box 3 so eliminate it from cell {1,7} old=567 new=56

Rule 1: in box 3 possible 8 exists only in column 9 so eliminate it from cell {6,9} old=48 new=4

Rule 2: in row 8 possible 28 exists in exactly 2 columns {8,1}=28 {8,6}=28 so eliminate 8 from cell {8,7} old=78 new=7

Rule 2: in column 4 possible 68 exists in exactly 2 rows {6,4}=68 {7,4}=68 so eliminate 6 from cell {1,4} old=26 new=2

Rule 2: in column 4 possible 68 exists in exactly 2 rows {6,4}=68 {7,4}=68 so eliminate 6 from cell {2,4} old=126 new=12

Rule 2: in column 4 possible 68 exists in exactly 2 rows {6,4}=68 {7,4}=68 so eliminate 6 from cell {5,4} old=1468 new=148

Rule 2: in column 4 possible 68 exists in exactly 2 rows {6,4}=68 {7,4}=68 so eliminate 8 from cell {5,4} old=148 new=14

Rule 2: in box 2 possible 12 exists in exactly 2 cells {1,4}=2 {2,4}=12 so eliminate 1 from cell {2,5} old=16 new=6

Rule 2: in box 2 possible 26 exists in exactly 2 cells {1,4}=2 {2,5}=6 so eliminate 2 from cell {2,4} old=12 new=1

Rule 2: in box 5 possible 68 exists in exactly 2 cells {4,6}=68 {6,4}=68 so eliminate 6 from cell {5,5} old=16 new=1

Rule 2: in row 1 possible 285 exists in exactly 3 columns {1,2}=28 {1,3}=258 {1,4}=2 so eliminate 5 from cell {1,7} old=56 new=6

Rule 2: in row 1 possible 286 exists in exactly 3 columns {1,2}=28 {1,4}=2 {1,7}=6 so eliminate 2 from cell {1,3} old=258 new=58

Rule 2: in row 1 possible 286 exists in exactly 3 columns {1,2}=28 {1,4}=2 {1,7}=6 so eliminate 8 from cell {1,3} old=58 new=5

Rule 2: in row 1 possible 286 exists in exactly 3 columns {1,2}=28 {1,4}=2 {1,7}=6 so eliminate 6 from cell {1,8} old=67 new=7

Rule 2: in row 1 possible 256 exists in exactly 3 columns {1,3}=5 {1,4}=2 {1,7}=6 so eliminate 2 from cell {1,2} old=28 new=8

Rule 2: in row 2 possible 536 exists in exactly 3 columns {2,5}=6 {2,7}=356 {2,8}=36 so eliminate 5 from cell {2,3} old=25 new=2

Rule 2: in row 7 possible 681 exists in exactly 3 columns {7,4}=68 {7,6}=168 {7,8}=18 so eliminate 8 from cell {7,7} old=48 new=4

Rule 2: in column 4 possible 168 exists in exactly 3 rows {2,4}=1 {6,4}=68 {7,4}=68 so eliminate 1 from cell {5,4} old=14 new=4

Rule 2: in column 7 possible 368 exists in exactly 3 rows {1,7}=6 {6,7}=68 {9,7}=38 so eliminate 3 from cell {2,7} old=356 new=56

Rule 2: in column 7 possible 368 exists in exactly 3 rows {1,7}=6 {6,7}=68 {9,7}=38 so eliminate 6 from cell {2,7} old=56 new=5

Rule 2: in column 7 possible 568 exists in exactly 3 rows {1,7}=6 {2,7}=5 {6,7}=68 so eliminate 8 from cell {9,7} old=38 new=3

Rule 3: in column 3 possible 68 exists in exactly 2 rows {4,3}=68 {5,3}=268 so reduce cell {5,3} old=268 new=68

Rule 3: in box 9 possible 18 exists in exactly 2 cells {7,8}=18 {9,8}=138 so reduce cell {9,8} old=138 new=18

Rule 1: in column 2 possible 2 exists only in box 7 so eliminate it from cell {8,1} old=28 new=8

Rule 1: in box 7 possible 2 exists only in row 9 so eliminate it from cell {9,6} old=128 new=18

Rule 1: in row 1 possible 6 exists only in box 3 so eliminate it from cell {2,8} old=36 new=3

Rule 1: in column 8 possible 6 exists only in box 6 so eliminate it from cell {6,7} old=68 new=8

Rule 1: in box 6 possible 6 exists only in row 5 so eliminate it from cell {5,3} old=68 new=8

Rule 1: in column 3 possible 8 exists only in box 4 so eliminate it from cell {5,1} old=28 new=2

Rule 1: in column 7 possible 8 exists only in box 6 so eliminate it from cell {5,8} old=68 new=6

Rule 1: in box 1 possible 8 exists only in column 2 so eliminate it from cell {9,2} old=28 new=2

Rule 1: in box 6 possible 8 exists only in row 6 so eliminate it from cell {6,4} old=68 new=6

Rule 1: in box 7 possible 8 exists only in row 8 so eliminate it from cell {8,6} old=28 new=2

Rule 2: in column 3 possible 8 exists in exactly 1 rows {5,3}=8 so eliminate 8 from cell {4,3} old=68 new=6

Rule 2: in column 4 possible 6 exists in exactly 1 rows {6,4}=6 so eliminate 6 from cell {7,4} old=68 new=8

Rule 2: in box 5 possible 6 exists in exactly 1 cells {6,4}=6 so eliminate 6 from cell {4,6} old=68 new=8

Rule 2: in box 8 possible 8 exists in exactly 1 cells {7,4}=8 so eliminate 8 from cell {7,6} old=168 new=16

Rule 2: in box 8 possible 8 exists in exactly 1 cells {7,4}=8 so eliminate 8 from cell {9,6} old=18 new=1

Rule 2: in row 7 possible 18 exists in exactly 2 columns {7,4}=8 {7,8}=18 so eliminate 1 from cell {7,6} old=16 new=6

Rule 2: in row 7 possible 68 exists in exactly 2 columns {7,4}=8 {7,6}=6 so eliminate 8 from cell {7,8} old=18 new=1

Rule 1: in row 7 possible 1 exists only in box 9 so eliminate it from cell {9,8} old=18 new=8

The final result is

1 8 5 2 3 4 6 7 9

7 4 2 1 6 9 5 3 8

3 6 9 5 8 7 2 4 1

4 9 6 7 2 8 1 5 3

2 3 8 4 1 5 9 6 7

5 1 7 6 9 3 8 2 4

9 7 3 8 5 6 4 1 2

8 5 1 3 4 2 7 9 6

6 2 4 9 7 1 3 8 5

[/quote]