## Solution to dml1

Advanced methods and approaches for solving Sudoku puzzles

### Solution to dml1

Solution to dml1

Congratulations on producing this world-beater, dml!
Code: Select all
` *-----------* |4..|..9|...| |.3.|.1.|.2.| |..6|7..|...| |---+---+---| |..1|...|..4| |.5.|2..|.7.| |8..|...|6..| |---+---+---| |...|..4|..8| |.7.|.3.|.1.| |...|5..|9..| *-----------*`

Note: This solution is designed to be followed using the Simple Sudoku program.
"..." means proceed as far as SS allows, following the hints given by SS in the order given.
This will facilitate rapid checking of this solution.

"?" introduces a move that will be disproved by contradiction. (These moves are only introduced when SS grinds to a halt, saying "no hint available".) In order to "play" this move, you will have to turn off the "block invalid moves" feature of the program. Then insert the move and follow all hints given until you see a contradiction. Once you find the contradiction, you must retrace (withdraw in reverse order) all moves made since the disproved move, by clicking the "undo" arrow repeatedly. Then "correct" the disproved move. EG if this move was "?3f6", then REMOVE the 3 at f6, because you have proved the 3 at f6 false.

Solution:

(0) No hint available from SS. A wonderful start! Turquoise-Pearl of size 6.7, as it turns out.

(1) ?4c5...?? -4c5, 4b4.

(2) ?4f5... (?3e1... ((?3f4...??))-3f4...??)-3e1... (?1g2...??)-1g2... (?9d2... ((?7k5...??))-7k5... ((?7k6...??))-7k6...??)-9d2... (?6k9...??)-6k9, (?3k9...??)-3k9, (?3g7...??)-3g7... (?6h9...??)-6h9... (?9f2...??)-9f2...... (?2k9...??)-2k9...?? -4f5, 4e5.

(3) ?9d1...?? -9d1.

(4) ?3d1...?? -3d1.

(5) ?9f2...?? -9f2.

(6) ?9f3...?? -9f3.

(7) ?3f3... (?1c1...??)-1c1...?? -3f3...

(8) ?9e1... (?5c1...??)-5c1... (?1g1...??)-1g1...?? -9e1.

(9) ?4f3...?? -4f3, 4f2.

(10) ?1e6...?? -1e6...

(11) ?8e7... (?1k6...??)-1k6...?? -8e7......

(12) ?5b1...?? -5b1...

(13) ?1k6...?? -1k6... End.

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gurth

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

Other solution :

Code: Select all
`   123 456 789  *-----------*a |4..|..9|...|b |.3.|.1.|.2.|c |..6|7..|...|  |---+---+---|d |..1|...|..4|e |.5.|2..|.7.|f |8..|...|6..|  |---+---+---|g |...|..4|..8|h |.7.|.3.|.1.|k |...|5..|9..|  *-----------* `

1) f4#4

2) now, if f5=4 then f9#2, f3#2, d8#9, f6#5, d8#3, e5#8, b3#8, b9#9, b1#9, e5#6, b6#6, and contradiction using singles,
so -4f5.

3) now, if e7=8, then e6#1, b6#6, b1#7, c8#8, b6#5, g7#7, g1#1, and contradiction using singles,
so -8e7.

4) and now f3#4, f3#2, i5#8, e3#9, a3#5, c2#1, and finish with singles.
leon1789

Posts: 37
Joined: 15 November 2006