The New Sudoku Players' Forum

[TopRank]

Can this be solved without BUG?

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+   -   -   -   +   -   -   -   +   -   -   -   +
|   3   4   9   |   1   6   2   |   7   5   8   |
|   8   5   1   |   39  34  7   |   2   6   49  |
|   2   7   6   |   8   5   49  |   13  34  149 |
+   -   -   -   +   -   -   -   +   -   -   -   +
|   7   1   8   |   5   34  6   |   9   34  2   |
|   5   6   2   |   39  7   49  |   13  8   14  |
|   9   3   4   |   2   8   1   |   5   7   6   |
+   -   -   -   +   -   -   -   +   -   -   -   +
|   6   9   7   |   4   2   3   |   8   1   5   |
|   4   2   5   |   7   1   8   |   6   9   3   |
|   1   8   3   |   6   9   5   |   4   2   7   |
+   -   -   -   +   -   -   -   +   -   -   -   +


I can follow the rule of a BUG+1, but I cannot explain it. If r3c9 is not 4 then for some reason the puzzle would not be solvable - I guess.

I cannot find an xy-wing, which, along with type 1 box uniqueness is the only technique I know more advanced than crossing out groups with pencil marks.

I also want to throw the idea out of a wikipedia article on Sudoku solving techniques. I plan on starting one. If one is started it would be great if the experts here add to it. Questions I am working on are what solving techniques should be added and how examples should be uploaded, meaning what is the best way to produce pictures that could be used in an article to illustrate solving techniques.

If anyone has a link to techniques that I can use I appreciate that . Of course I will do a search of this forum first anyway.

Also, I would really appreciate a list of advanced technques in order of the ones you experts find to be the most to least useful in solving new sudokus.

Wikipedia is a top-30 website and a lot of people would consider it an more logical place to look for solution techniques than even sudoku.com!

[Guest]

give me the original Q

[TopRank]

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+ -  -  -  + -  -  -  + -  -  -  +
|          |    6     |    5     |
| 8     1  |       7  | 2        |
| 2  7     | 8        |          |
+ -  -  -  + -  -  -  + -  -  -  +
|          | 5        |       2  |
|    6     |          |    8     |
| 9        |       1  |          |
+ -  -  -  + -  -  -  + -  -  -  +
|          |       3  |    1  5  |
|       5  | 7        | 6     3  |
|    8     |    9     |          |
+ -  -  -  + -  -  -  + -  -  -  +


[bennys]

Remote pairs,coloures,forcing chains

[Jeff]

I can follow the rule of a BUG+1, but I cannot explain it. If r3c9 is not 4 then for some reason the puzzle would not be solvable - I guess.

Hi TopRank, A reference to the proof has been added to the theorem in the BUG thread.

[tso]

Can this be solved without BUG?

Yes -- but nothing will be as quick and obvious as BUG.

ALL puzzles that have been reduced to the point where all undecided cells are bivalue except one that is trivalue have one or more xy-type forcing chains that will finish them off. This one is no exception. For example:

Code: Select all

 
  3    4    9    | 1    6    2    | 7    5    8   
  8    5    1    |[39]  34   7    | 2    6   [49] 
  2    7    6    | 8    5    49   | 13   34   149 
 ----------------+----------------+----------------
  7    1    8    | 5    34   6    | 9    34   2   
  5    6    2    |[39]  7   [49]  | 13   8   [14] 
  9    3    4    | 2    8    1    | 5    7    6   
 ----------------+----------------+----------------
  6    9    7    | 4    2    3    | 8    1    5   
  4    2    5    | 7    1    8    | 6    9    3   
  1    8    3    | 6    9    5    | 4    2    7   


Both values of r5c6 force r5c9=1.


The puzzle can also be solved by coloring 4's:

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  .    .    .    | .    .    .    | .    .    .   
  .    .    .    | .   +4    .    | .    .   -4   
  .    .    .    | .    .   -4    | .   -4    4 
 ----------------+----------------+----------------
  .    .    .    | .   -4    .    | .   +4    .   
  .    .    .    | .    .   +4    | .    .   -4   
  .    .    .    | .    .    .    | .    .    .   
 ----------------+----------------+----------------
  .    .    .    | .    .    .    | .    .    .   
  .    .    .    | .    .    .    | .    .    .   
  .    .    .    | .    .    .    | .    .    .   

Since there are two -4s within groups, they must be false. All the +4s are true.


Also, remote pairs:

Code: Select all

  3    4    9    | 1    6    2    | 7    5    8   
  8    5    1    | 39  +34   7    | 2    6    49   
  2    7    6    | 8    5    49   | 13  -34   149 
 ----------------+----------------+----------------
  7    1    8    | 5   -34   6    | 9   +34   2   
  5    6    2    | 39   7    49   | 13   8    14   
  9    3    4    | 2    8    1    | 5    7    6   
 ----------------+----------------+----------------
  6    9    7    | 4    2    3    | 8    1    5   
  4    2    5    | 7    1    8    | 6    9    3   
  1    8    3    | 6    9    5    | 4    2    7 

r2c5 and r4c5 form a naked pair
r4c5 and r4c8 form a naked pair
r4c8 and r3c8 form a naked pair

Each pair has opposite values. You can see that r2c5 must have the opposite value as r3c8 and any cell that can "see" both of these cells must not be 3 or 4 -- excluding 4 from r3c6 and r2c9. (Either of these cells can also complete another 5-cell xy-type forcing chain when combined with the four [34] cells.)

There is no xy-wing or simple uniqueness rectangle. BUG works for the same reason the a uniqueness rectangle works. If r3c9<>4, you've got one big network that can exist in two different states and nothing left to uncover that will distinguish one from the other.

I also want to throw the idea out of a wikipedia article on Sudoku solving techniques. I plan on starting one. If one is started it would be great if the experts here add to it. Questions I am working on are what solving techniques should be added and how examples should be uploaded, meaning what is the best way to produce pictures that could be used in an article to illustrate solving techniques.

If anyone has a link to techniques that I can use I appreciate that.

See:

-- Some popular tutorials -- Simple Sudoku, Sadman Sudoku, Susser.

-- Gaby Vanhegan's must-have dictionary of Sudoku Dictionary/Lexicon.

Of course I will do a search of this forum first anyway.

The search feature in this forum isn't that great. Try using Google's Advanced Search setting the domain to SUDOKU.COM.

Also, I would really appreciate a list of advanced technques in order of the ones you experts find to be the most to least useful in solving new sudokus.

This is subjective and contextual.