## Solution to ArtoI's "Etana"

Advanced methods and approaches for solving Sudoku puzzles

### Solution to ArtoI's "Etana"

Solution to ArtoI's "Etana".

Code: Select all
` *-----------* |1..|..7|.9.| |.3.|.2.|..8| |..9|6..|5..| |---+---+---| |..5|3..|9..| |.1.|.8.|..2| |6..|..4|...| |---+---+---| |3..|...|.1.| |.4.|...|..7| |..7|...|3..| *-----------*`

NOTE: "..." denotes steps using Simple Sudoku program.
Sub-nets are enclosed thus: (?xay...??) and sub-sub-nets thus: ((?xay...??)).

Solution:

(1) 1h3.

(2) ?3e8..., -8g6(MC)... (?3h5...??)-3h5... (?-1b7...??)1b7...
(?-1c5... -2g2(MC)...((?-7e1f7(GMET)...??))(7e1 OR 7f7), -7f2e7, 6e7...??)1c5... (?-7e1f5...??)(7e1 OR 7f7), -7f2e7, 6e7...?? -3e8...

(3) ?3c5... (?-5a5f9...??)-5f5, (?-1c6f9..., -2g6(MC), -2hk4(X-Wing 2fg34)...??)(1c6 OR 1f9), -1c9, 4c9... (?1f9..., -5a5(MC)...??)-1f9, 5f9, -9f4g6k146(swordfish 9beh146), -8k8(MC), -9e6(XY-Wing 579b16e1), -5b4(XY-Wing 579b1e14)...?? -3c3.

(4) ?3f9..., -1f5(MC), -1k4(X-Wing 1bf47), -8h7(X-Wing 8fg37)..., -2k1(MC)...?? -3f9...

(5) ?3h6... (?-1c5f9...??)(1c5 OR 1f9), -1f5, (?7f2...??)-7f2, (?1d5...??)-1d5..., (?-1c5d6...??)(1c5 OR 1d6), -1c6, 8c6..., -8h7(X-Wing 8fg37)..., -2d7f3g6(colours).

(6) ?1d9..., -2k8(X-Wing 2ch18), -5a5b1g2k58(colours)...?? -1d9...

(7) ?1f9...?? -1f9, 5f9..., -8f2(XY-Wing 278d2f3)...

(8) ?-9b6e4...?? (9b6 OR 9e4), -9b4, 1b4...

(9) ?6b3...?? -6b3, 4b3..., -6d6g6k68(swordfish 6beh678).

(10) ?4k8...?? -4k8, 5k8... End.

Notes:
Only one sub-sub-net used, in step (2).
No nets were tried and then rejected.
I might find shorter paths, but then I am adding to my total work. My aim is to solve the puzzle as quickly as possible, not to find the shortest solution, which would take much more work and searching.
gurth

Posts: 358
Joined: 11 February 2006
Location: Cape Town, South Africa

Other solution :

Code: Select all
`   abc def ghi  *-----------*1 |1..|..7|.9.|2 |.3.|.2.|..8|3 |..9|6..|5..|  |---+---+---|4 |..5|3..|9..|5 |.1.|.8.|..2|6 |6..|..4|...|  |---+---+---|7 |3..|...|.1.|8 |.4.|...|..7|9 |..7|...|3..|  *-----------* `

1) if 3c6 then f3#3, a5#7, i7#9, and contradiction with singles,
so -3c6

2) after that, if 5b1 then d1#4, a2#4, i3#1, b6#7, f3#3, g6#8, i4#1, e1#4, and contradiction with singles,
so -5b1

3) after that, if 5d1 then d2#9, f5#6, c1#8, c1#2, e1#4, i1#4, a4#8, and contradiction with singles,
so -5d1

4) after that, g6#8, g2#1, b6#8, c1#4, and if 4d1 then i4#4, and contradiction with singles,
so -4d1

5) after that, b1#2, b3#7, a4#2 and finish with singles.
leon1789

Posts: 37
Joined: 15 November 2006

Would you please get together to decide on one common row/column labeling

Code: Select all
`   123 456 789                  abc def ghi   *-----------*                *-----------* a |1..|..7|.9.|              1 |1..|..7|.9.| b |.3.|.2.|..8|              2 |.3.|.2.|..8| c |..9|6..|5..|              3 |..9|6..|5..|   |---+---+---|                |---+---+---| d |..5|3..|9..|              4 |..5|3..|9..| e |.1.|.8.|..2|              5 |.1.|.8.|..2| f |6..|..4|...|              6 |6..|..4|...|   |---+---+---|                |---+---+---| g |3..|...|.1.|              7 |3..|...|.1.| h |.4.|...|..7|              8 |.4.|...|..7| k |..7|...|3..|              9 |..7|...|3..|   *-----------*                *-----------*                       gurth's row/columns          leon's row/columns                    `
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

ronk wrote:Would you please get together to decide on one common row/column labeling

Code: Select all
`   123 456 789                  abc def ghi   *-----------*                *-----------* a |1..|..7|.9.|              1 |1..|..7|.9.| b |.3.|.2.|..8|              2 |.3.|.2.|..8| c |..9|6..|5..|              3 |..9|6..|5..|   |---+---+---|                |---+---+---| d |..5|3..|9..|              4 |..5|3..|9..| e |.1.|.8.|..2|              5 |.1.|.8.|..2| f |6..|..4|...|              6 |6..|..4|...|   |---+---+---|                |---+---+---| g |3..|...|.1.|              7 |3..|...|.1.| h |.4.|...|..7|              8 |.4.|...|..7| k |..7|...|3..|              9 |..7|...|3..|   *-----------*                *-----------*                       gurth's row/columns          leon's row/columns                    `

gurth is the first, so I will choose his labelling for next puzzles
leon1789

Posts: 37
Joined: 15 November 2006