Solution to dml #6

Advanced methods and approaches for solving Sudoku puzzles

Solution to dml #6

Postby gurth » Mon Dec 11, 2006 9:10 am

Solution to dml #6

Code: Select all
dml #6 - ER 10.7 - gsfr 99955
 *-----------*
 |9..|..4|...|
 |.8.|.2.|.3.|
 |..5|7..|...|
 |---+---+---|
 |..1|...|..4|
 |.6.|.8.|.7.|
 |3..|...|5..|
 |---+---+---|
 |...|..5|..1|
 |.7.|.3.|.9.|
 |...|6..|2..|
 *-----------*


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) ...

(1) ?1f6... (?5h1...??)-5h1...?? -1f6.

(2) ?1f4... (?5h1...??)-5h1...?? -1f4.

(3) ?3e6... (?5h1...??)-5h1...?? -3e6.

(4) ?1a5... (?6b1...??)-6b1, (?6b3...??)-6b3...?? -1a5.
(The idea behind 1a5: to force the 5-chain the OTHER way, the RIGHT way. See comments below.)

(5) ?6c5... (?4g2...??)-4g2...?? -6c5.

(6) ?8h1...?? -8h1.

(7) ?2h1... (?3c2...??)-3c2...?? -2h1.

(8) ?4h1... (?4g4...??)-4g4... (?1c8...??)-1c8...?? -4h1.

(9) ?6h1... (?7a3...??)-7a3...?? -6h1.

(10) ?8k8...?? -8k8.

(11) ?2d2...?? -2d2.

(12) ?2e4...?? -2e4.

(13) ?3e4...?? -3e4.

(14) ?4e4...?? -4e4.

(15) ?9e4...?? -9e4.

(16) ?6b9...?? -6b9.

(17) ?7b9...?? -7b9.

(18) ?9g2... (?9h6...??)-9h6...?? -9g2.

(19) ?9k2...?? -9k2.

(20) ?7g7... (?5k2...??)-5k2... (?8f9...??)-8f9...?? -7g7...

(21) ?7f3...?? -7f3...

(22) ?3a4...?? -3a4...

(23) ?9f9...?? -9f9...

(24) ?9f5...?? -9f5.

(25) ?8c7...?? -8c7.

(26) ?8c8...?? -8c8 and 50 singles to End.

Comments:

The most striking feature, after preliminary moves, was the candidate 5s. All in one chain, so eliminating any 5 would place them all. It soon seemed that this would not be easy, so I had a new idea. And that was to leave the solving of the 5s to the end!

This tactic could be exploited as follows: Each "wrong" 5 in each box was in a cell with several other candidates. so by assuming each of those candidates in turn, I would in any case be placing all the 5s correctly as the net proceeded. So I could test each of those candidates (except the true one) and eliminate them by placing all the 5s and other resultant placements.

So this led me to a setup where all the wrong 5s were united in bivalue cells to the true candidate for that cell, whereas the true 5s still had all their original companion candidates.

It followed that none of this work could help me to test the fives, because by assuming any 5, I would turn all those bivalues into 5s, so that the candidates I had eliminated would serve no purpose! So what was my idea?

Simply to avoid testing the 5s ever, except in subnets, where I could always give them their TRUE set of values. If ever one of the false 5s DID get eliminated outside a net, then I would cash in on the whole series of eliminated candidates, because all the bivalues they had formed would now instantly be singles.

So I expected the puzzle to collapse dramatically and suddenly. When this happened no candidate had been solved completely, but the remaining 50 cells all fell as singles.

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Postby leon1789 » Mon Dec 11, 2006 1:34 pm

Other solution :

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


C#z means -zC is proved, because C=z is a move that will be disproved by contradiction using elementary methods. Here, elementary methods are singles and locked sets.

1) if c6=8 then a2#2, k9#7, h9#5, and contradiction using elementary methods,
so -8c6.

2) now e4#3

3) now, if e7=3 then e4#1, k2#5, b7#4, and contradiction using elementary methods,
so -3e7.

4) now, if k6=8 then d5#5, k1#4, c5#6, k3#3, f9#9, and contradiction using elementary methods,
so -8k6.

5) now, h1#5.

6) now, b3#7, and finish with elementary methods.

Remarks:
* It's impossible to solve this puzzle with this method (studies on bivalue cases and bilocation numbers in contradiction nets and subnets) using singles only !
** Same property for Ocean #14/vert. symm.: suexrat 1630 (RMS < 8).
Last edited by leon1789 on Mon Dec 11, 2006 11:42 am, edited 1 time in total.
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Re: Solution to dml #6

Postby ronk » Mon Dec 11, 2006 1:48 pm

gurth, don't solutions on a thread per puzzle basis belong in the General/puzzle forum?
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Postby ravel » Mon Dec 11, 2006 3:55 pm

Nice solutions again.

leon1789 wrote:It's impossible to solve this puzzle with this method (studies on bivalue cases and bilocation numbers in contradiction nets and subnets) using singles only !

Same property for Ocean #14/vert. symm.: suexrat 1630 (RMS < 8).

Thats very interesting (i thought so, when i looked at dml6 yesterday). But it again shows the difficulty to rate puzzles.

How should i rate a puzzle that on the one hand can be solved with max. 7 contradiction chains using locked candidates, tuples, x-wing and UR1, but on the other hand cannot be solved with singles subnets (this is possible, because e.g. a triple cannot be resolved with a singles subnet, thats the reason, why suexrat overrates some puzzles extremely), which seems to be very rare also among the hardest?
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Postby leon1789 » Mon Dec 11, 2006 6:04 pm

ravel wrote:How should i rate a puzzle that on the one hand can be solved with max. 7 contradiction chains using locked candidates, tuples, x-wing and UR1, but on the other hand cannot be solved with singles subnets (this is possible, because e.g. a triple cannot be resolved with a singles subnet, thats the reason, why suexrat overrates some puzzles extremely), which seems to be very rare also among the hardest?


Yes, it seems relatively rare... until proof of the opposite:) puzzle's mysteries:D

How should you rate it ? ...with multiple scores (as you already do it)
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Postby StrmCkr » Wed Dec 13, 2006 2:30 am

removed
Last edited by StrmCkr on Sat Dec 13, 2014 6:40 am, edited 4 times in total.
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Re: Solution to dml #6

Postby gurth » Thu Dec 14, 2006 10:53 am

ronk wrote:gurth, don't solutions on a thread per puzzle basis belong in the General/puzzle forum?


ronk, after hearing from my main correspondents on these threads, whom I mainly aim to please, I don't think so.

Your friendly suggestions are always welcome, even when I don't agree. I think your intervention over the notation proliferation was very timely and useful: well done. I also thank Leon for his cooperative response to that. I do appreciate it very much.

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Re: Solution to dml #6

Postby ronk » Thu Dec 14, 2006 12:06 pm

gurth wrote:
ronk wrote:gurth, don't solutions on a thread per puzzle basis belong in the General/puzzle forum?

ronk, after hearing from my main correspondents on these threads, whom I mainly aim to please, I don't think so.

Take a look at the number of replies to your "Solutions to .... " threads. A goodly number of them -- maybe even a majority -- have zero replies. That's hardly correspondence IMO. You and your correspondents could just as easily do all that correspondence in separate threads on the General/puzzle forum ... or on a single Gurth's Solutions thread in either forum.

Mine was a polite question to which I thought common sense would prevail. Obviously -- but not unexpectedly -- I thought wrong.

gurth wrote:I think your intervention over the notation proliferation was very timely and useful: well done.

Not surprising that you would think so, since leon agreed to use your notation.

Speaking of notation: I suspect at least 95% of the people in this forum are accustomed to the r1c1 - r9c9 style of row/column notation. Combine your foreign, i.e., different a1 - k9 notation with the extreme difficulty of the puzzles, and precious few will even attempt to follow your solutions, let alone correspond.

When a subject is difficult, the language should not impede understanding. -- Confucious (Well, maybe he said it:) )
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