## Solution to dml #3

Advanced methods and approaches for solving Sudoku puzzles

### Solution to dml #3

Solution to dml #3

Code: Select all
`dml #3 - ER 10.6 - gsfr 99972 *-----------* |8..|..3|...| |.7.|.6.|.9.| |..4|5..|...| |---+---+---| |..5|...|..7| |.2.|..9|.3.| |1..|...|8..| |---+---+---| |...|..7|..1| |.3.|.2.|.6.| |...|4..|5..| *-----------*`

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) ?7e5...?? -7e5. Off to a flying start, but prepare for a rough ride.

(3) ?8e5...?? -8e5. Minor turbulence approaching.

(4) ?4e5... (?8h3...??)-8h3... (?8h9...??)-8h9... (?1c5...??)-1c5... (?3f3...??)-3f3...?? -4e5. Now you can relax for a while.

(5) ?5f9...?? -5f9.

(6) ?4f8...?? -4f8. Now fasten your seat belts!

(7) ?5a9... (?3b9... ((?6e7...??))-6e7... ((?4e7...??))-4e7... ((?9f9...??))-9f9...??)-3b9, (?3c9... ((?7e4...??))-7e4... ((?4e7...??))-4e7...??)-3c9... (?7e4...??)-7e4... (?6e4...??)-6e4, (?6e3...??)-6e3, (?7e3...??)-7e3... (?4g7...??)-4g7...?? -5a9.

The worst of the storm is over. No more sub-sub-nets. But that 5a9 had to be removed!

(8) ?4g2... (?2b6...??)-2b6, (?1b6...??)-1b6... (?6e4...??)-6e4, (?6e7...??)-6e7, (?6e3...??)-6e3, (?1e4...??)-1e4... (?1k6...??)-1k6... (?9f3...??)-9f3, (?3b3...??)-3b3...?? -4g2...

(9) ?7f3... (?8g2...??)-8g2...?? -7f3...

(10) ?6f3... (?9h9...??)-9h9... (?2g8...??)-2g8, (?2f9...??)-2f9...?? -6f3.

(11) ?-45b9...?? -238b9... A neat example of GMET to get rid of 3 candidates together. Prepare to land.

(12) ?5b9... (?6f9...??)-6f9, (?6e4...??)-6e4, (?6e3...??)-6e3, (?8e4...??)-8e4...?? -5b9 and 59 singles to End.

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P.S. ravel, where would you prefer me to post these solutions? Seems like my addiction to them is not on the wane, as I keep getting new ideas from my experience, which I can't wait to try out.
gurth

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

### Re: Solution to dml #3

gurth wrote:P.S. ravel, where would you prefer me to post these solutions?
Oh, i dont mind and i am no moderator here (but i think your technique is advanced ). I also like the one thread per puzzle, so it is easy to compare solutions.
ravel

Posts: 998
Joined: 21 February 2006

ravel wrote:I also like the one thread per puzzle, so it is easy to compare solutions.

I agree with you

An other method : studies on bivalue cells and bilocation numbers in contradiction nets and subnets, using elementary methods. Here, elementary methods are singles only.

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

Notation : C#z means -zC is proved, because C=z is a move that will be disproved by contradiction using elementary methods. Moreover, "bold" results are definitively true.

1) g5#5

2) now, if 8d2 then e5#8, f5#5, g2#4, f4#2, f9#9, a2#5, f5#7, and contradiction using elementary methods,
so -8d2

3) now, if 8h4 then f3#3, a2#5, c9#3, k8#7, g4#9, f4#3, and contradiction using elementary methods,
so -8h4

4) a8#7
5) g2#8
6) g4#6
7) g1#5
8) h1#7
9) e7#1, and finish with elementary methods.
leon1789

Posts: 37
Joined: 15 November 2006

### Re: Solution to dml #3

ravel wrote:
gurth wrote:P.S. ravel, where would you prefer me to post these solutions?
Oh, i dont mind and i am no moderator here (but i think your technique is advanced ). I also like the one thread per puzzle, so it is easy to compare solutions.

All I recall seeing is ... "here is my solution." Where did I miss an attempt to teach the technique?
ronk
2012 Supporter

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

Ronk wrote:All I recall seeing is ... "here is my solution." Where did I miss an attempt to teach the technique?

I agree on that. However, not only I don't see a "technique", but also I don't see a "solution".

Carcul
Carcul

Posts: 724
Joined: 04 November 2005

Carcul wrote:I agree on that. However, not only I don't see a "technique", but also I don't see a "solution".
Carcul

Please, explain your technique(s) and solution for this puzzle. ...with ALS for instance ? I didn't see anything after 5h6 (with a 5-cycle). Perhaps with AALS ?
leon1789

Posts: 37
Joined: 15 November 2006