Ocean's New Years Present

Advanced methods and approaches for solving Sudoku puzzles

Ocean's New Years Present

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Last edited by StrmCkr on Sat Dec 13, 2014 6:29 am, edited 5 times in total.
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StrmCkr

Posts: 900
Joined: 05 September 2006

Ocean's New Year's present for RW

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` *-----------* |...|..1|.2.| |3..|.4.|5..| |...|6..|..7| |---+---+---| |..2|...|..1| |.8.|.9.|.3.| |4..|...|8..| |---+---+---| |5..|..2|...| |.9.|.3.|4..| |..6|7..|...| *-----------*   SE 11.2`

Ocean, what a stupendous puzzle! And what a joy to solve it, using the ever more fascinating Contradiction Nets.

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:

(1) ...

(2) ?4g4... (?2e4... ((?1h8...??))-1h8, ((?1k8...))-1k8... ((??1k5...??))-1k5...??)-2e4... (?4d6... ((?3c7...??))-3c7... ((?5h8...??))-5h8, ((?3g2...??))-3g2... ((?3k9...??))-3k9...??)-4d6... (?3f4...??)-3f4, (?3f6...??)-3f6... (?9c1...??)-9c1... (?9f3...??)-9f3... (?8a1...??)-8a1, (?6a7...??)-6a7... (?8b6...??)-8b6... (?1c1...??)-1c1...?? -4g4...

(3) ?4a2...?? -4a2.

(4) ?4c3... (?2f4... ((?3d2...??))-3d2...??)-2f4... (?3f2... ((?8c6...??))-8c6, ((?8b6...??))-8b6, ((?8a5...??))-8a5, ((?8a4...??))-8a4...??)-3f2, (?3g3... ((?8c6...??))-8c6... ((?8b6...??))-8b6... ((?8a5...??))-8a5...??)-3g3... (?8a5...??)-8a5...?? -4c3.

A very aggressive strategy has been pursued, aiming to remove difficult but key candidates instead of settling for easier targets. All those sub-nets and sub-sub-nets, just to establish a few key points, but already the puzzle has been fatally wounded, its resistance compromised, and no more sub-sub-nets will be needed. The next step will really decimate candidates.

(5) ?4a3... (?8c6...??)-8c6, (?8b6...??)-8b6, (?8a4...??)-8a4, (?8a5...??)-8a5, (?2f4...??)-2f4, (it's very softened up by the removal of those 8s ... now I can sculpt anything!)... (?2k1...??)-2k1, (?2c2 ...with purpose-conscious certainty! ...??)-2c2... (?2c1...??)-2c1...?? -4a3... ... these that are now going are going for good! This must be the turning point...

(6) ?2b4 ...(many bivalues)... (?7e3...??)-7e3... (?7d2...??)-7d2... (?8h3...??)-8h3...?? -2b4... ... ...

(7) ?6g8...?? -6g8...End.
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gurth

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