The New Sudoku Players' Forum

[Jackie]

Hello,

I am totally stuck on which technique to use to solve this puzzle without trying, can you please provide a little hint?

Code: Select all

 *-----------*
 |1..|.2.|463|
 |3.6|.4.|752|
 |254|736|891|
 |---+---+---|
 |5..|6.2|..4|
 |4.9|357|..6|
 |6..|8.4|..5|
 |---+---+---|
 |932|.7.|648|
 |841|269|537|
 |765|483|219|
 *-----------*

Thanks alot

[champagne]

as often when so many cells are filled, the puzzle has more than one solution

[Leren]

That may be a partial solution where you have made a mistake at some stage. If so, provide the original puzzle and we may be able to help. Leren

[m_b_metcalf]

That may be a partial solution where you have made a mistake at some stage. If so, provide the original puzzle and we may be able to help. Leren

Is it actually possible to add a wrong value to a valid puzzle so as create one with multiple, rather than zero, solutions? Perhaps more likely that the original puzzle was ill formed or it was incorrectly copied (a missed clue).

Regards,

Mike Metcalf

[Jackie]

Sorry, I made a mistake. I forgot one "1", now the puzzle should be solvable. I am interested in a logical way to solve this, not by trying which is rather easy

Code: Select all

 *-----------*
 |1..|.2.|463|
 |3.6|.4.|752|
 |254|736|891|
 |---+---+---|
 |5..|6.2|..4|
 |4.9|357|1.6|
 |6..|8.4|..5|
 |---+---+---|
 |932|.7.|648|
 |841|269|537|
 |765|483|219|
 *-----------*

[m_b_metcalf]

There are still four solutions.

M

[Leren]

Here are the 4 solutions to your amended "puzzle" in line format.

187925463396148752254736891518692374429357186673814925932571648841269537765483219
197528463386941752254736891518692374429357186673814925932175648841269537765483219
178925463396148752254736891517692384489357126623814975932571648841269537765483219
178925463396148752254736891583612974429357186617894325932571648841269537765483219

As I said before, if this is your partial solution to an original puzzle, it's best to give us that. If not, you still haven't got enough clues fora single solution. Leren

[JC Van Hay]

Code: Select all

+-------------+------------+-----------+
| 1  789  78  | 59  2   58 | 4   6   3 |
| 3  89   6   | 19  4   18 | 7   5   2 |
| 2  5    4   | 7   3   6  | 8   9   1 |
+-------------+------------+-----------+
| 5  178  378 | 6   19  2  | 39  78  4 |
| 4  28   9   | 3   5   7  | 1   28  6 |
| 6  127  37  | 8   19  4  | 39  27  5 |
+-------------+------------+-----------+
| 9  3    2   | 15  7   15 | 6   4   8 |
| 8  4    1   | 2   6   9  | 5   3   7 |
| 7  6    5   | 4   8   3  | 2   1   9 |
+-------------+------------+-----------+

From the 2 solutions of C46 :

Code: Select all

+---------------+-----------------+-------------+
| 1  789a  7a8  | 5a9A  2    5A8a | 4    6    3 |
| 3  8a9A  6    | 1A9a  4    1a8A | 7    5    2 |
| 2  5     4    | 7     3    6    | 8    9    1 |
+---------------+-----------------+-------------+
| 5  1a78  378a | 6     19a  2    | 3a9  7a8  4 |
| 4  2a8   9    | 3     5    7    | 1    28a  6 |
| 6  127a  3a7  | 8     1a9  4    | 39a  2a7  5 |
+---------------+-----------------+-------------+
| 9  3     2    | 1a5A  7    1A5a | 6    4    8 |
| 8  4     1    | 2     6    9    | 5    3    7 |
| 7  6     5    | 4     8    3    | 2    1    9 |
+---------------+-----------------+-------------+

5r1c4(a) -> 1 solution

9r1c4(A) -> 7 singles
From the 2 solutions of C8 :

Code: Select all

+------------------+------------+--------------+
| 1  7a8      78a  | 9   2    5 | 4    6     3 |
| 3  9        6    | 1   4    8 | 7    5     2 |
| 2  5        4    | 7   3    6 | 8    9     1 |
+------------------+------------+--------------+
| 5  1a(-7)8  37a8 | 6   19a  2 | 3a9  7A8a  4 |
| 4  2A8a     9    | 3   5    7 | 1    2a8A  6 |
| 6  12a7     3a7  | 8   1a9  4 | 39   2A7a  5 |
+------------------+------------+--------------+
| 9  3        2    | 5   7    1 | 6    4     8 |
| 8  4        1    | 2   6    9 | 5    3     7 |
| 7  6        5    | 4   8    3 | 2    1     9 |
+------------------+------------+--------------+

8r4c8(a) -> 1 solution

On the other hand, 7r2c1(a)==7r4c8(A) => -7r4c2
Proof of -7r4c2 : for example, XYZ-Wing(378)r46c3,r4c8

7r4c8(A) -> 4 singles and a puzzle having 2 solutions

Code: Select all

+-----------+----------+----------+
| 1  78  78 | 9  2   5 | 4   6  3 |
| 3  9   6  | 1  4   8 | 7   5  2 |
| 2  5   4  | 7  3   6 | 8   9  1 |
+-----------+----------+----------+
| 5  18  38 | 6  19  2 | 39  7  4 |
| 4  2   9  | 3  5   7 | 1   8  6 |
| 6  17  37 | 8  19  4 | 39  2  5 |
+-----------+----------+----------+
| 9  3   2  | 5  7   1 | 6   4  8 |
| 8  4   1  | 2  6   9 | 5   3  7 |
| 7  6   5  | 4  8   3 | 2   1  9 |
+-----------+----------+----------+

Note : the 4 solutions of the puzzle only exclude 7r4c2 via an XYZ-Wing.

[Jackie]

I made a photo from the newspaper I found it in, can't believe they priont such a thing, or am I mising something? You can easily see the original figures given, or did I do a typo?

[JC Van Hay]

Here is the corrected possibility matrix :

Code: Select all

+-------------+------------+-------------+
| 1  789  78  | 59  2   58 | 4   6    3  |
| 3  89   6   | 19  4   18 | 7   25   25 |
| 2  5    4   | 7   3   6  | 8   9    1  |
+-------------+------------+-------------+
| 5  178  378 | 6   19  2  | 39  78   4  |
| 4  28   9   | 3   5   7  | 1   28   6  |
| 6  127  37  | 8   19  4  | 39  257  25 |
+-------------+------------+-------------+
| 9  3    2   | 15  7   15 | 6   4    8  |
| 8  4    1   | 2   6   9  | 5   3    7  |
| 7  6    5   | 4   8   3  | 2   1    9  |
+-------------+------------+-------------+

From the "pseudo-UR"(25)r2c89=7r6c8 :
2r6c8 -> "pseudo-BUG+1" ["pseudo-BUG"=8r1c2] -> 3 solutions where r1c2=7 or 8 or 9
5r6c8 -> "pseudo-BUG+1" ["pseudo-BUG"=8r1c2] -> 3 solutions where r1c2=7 or 8 or 9
7r6c8 -> 1 solution
Conclusion : the puzzle has 7 solutions, only removing 7r4c2 via the XYZ-Wing(378)r46c3.r4c8

[Leren]

Confirmed the original "puzzle" has 7 solutions. Here they all are in line format.

187925463396148725254736891518692374429357186673814952932571648841269537765483219
187925463396148752254736891518692374429357186673814925932571648841269537765483219
197528463386941725254736891518692374429357186673814952932175648841269537765483219
197528463386941752254736891518692374429357186673814925932175648841269537765483219
178925463396148725254736891583612974429357186617894352932571648841269537765483219
178925463396148752254736891517692384489357126623814975932571648841269537765483219
178925463396148752254736891583612974429357186617894325932571648841269537765483219

Leren

<edit> You can reduce the puzzle to a single solution by adding a clue. You can do this in a few places, but in each case the puzzle solves in singles.

Here's one example. I've added a clue 2 in r6c2. The resulting solution is the sixth one in my list:

Code: Select all

1...2...3
..6...7..
.54.3.89.
...6.2...
4.9...1.6
.2.8.4...
.32.7.64
..1...5..
7...8...9

Leren

[StrmCkr]

made a photo from the newspaper I found it in, can't believe they priont such a thing, or am I mising something? You can easily see the original figures given, or did I do a typo?

unfortunately a list of puzzle book printing places do not check for 1 solution on any of the grids they publish, and rely solely on the honesty of the puzzle maker to verify the grid is in fact solvable with unique solution.

there is a Sudoku of shame on these forums that feature and lists known publicized work that all fail in that regards.

edit: or perhaps as pat mentioned a mistake on the publisher whom changed aesthetics and manged the puzzle converting it.

[Pat]

from the newspaper

Code: Select all

 1 . . | . 2 . | . . 3
 . . 6 | . . . | 7 . .
 . 5 4 | . 3 . | 8 9 .
-------+-------+------
 . . . | 6 . 2 | . . .
 4 . 9 | . . . | 1 . 6
 . . . | 8 . 4 | . . .
-------+-------+------
 . 3 2 | . 7 . | 6 4 .
 . . 1 | . . . | 5 . .
 7 . . | . 8 . | . . 9



the original "puzzle" has 7 solutions

You can reduce the puzzle to a single solution by adding a clue.
You can do this in a few places

suppose we keep the pattern
and try changing one of the givens?

[StrmCkr]

from the newspaper

Code: Select all

 1 . . | . 2 . | . . 3
 . . 6 | . . . | 7 . .
 . 5 4 | . 3 . | 8 9 .
-------+-------+------
 . . . | 6 . 2 | . . .
 4 . 9 | . . . | 1 . 6
 . . . | 8 . 4 | . . .
-------+-------+------
 . 3 2 | . 7 . | 6 4 .
 . . 1 | . . . | 5 . .
 7 . . | . 8 . | . . 9



the original "puzzle" has 7 solutions

You can reduce the puzzle to a single solution by adding a clue.
You can do this in a few places

suppose we keep the pattern
and try changing one of the givens?

like this ?

Code: Select all

 1 . . | . 2 . | . . 3
 . . 6 | . . . | 7 . .
 . 5 4 | . 3 . | 8 9 .
-------+-------+------
 . . . | 6 . 2 | . . .
 4 . 9 | . . . | 1 . 6
 . . . | 8 . 4 | . . .
-------+-------+------
 . 3 2 | . 7 . | 6 8 .
 . . 1 | . . . | 5 . .
 7 . . | . 8 . | . . 9

[Pat]

thanks

GridChecker --similar --relabel 1 --unique
1...2...3..6...7...54.3.89....6.2...4.9...1.6...8.4....32.7.64...1...5..7...8...9
finds "4"

1...2...3..6...7...54.3.89....6.2...4.9...1.2...8.4....32.7.64...1...5..7...8...9
1...2...3..6...7...54.3.89....6.2...4.9...1.6...8.4....32.7.68...1...5..7...8...9
1...2...3..6...7...54.3.89....6.2...4.9...1.6...8.4....82.7.64...1...5..7...8...9
1...2...3..6...7...54.3.89....6.2...8.9...1.6...8.4....32.7.64...1...5..7...8...9

but dobrichev, one of them has 0 answers!
(note this ran without --minimals)

the other 3 are OK
(and only need "hidden singles")