The New Sudoku Players' Forum

[yzfwsf]

Code: Select all

*-----------*
 |.3.|...|67.|
 |.1.|3..|..2|
 |7.9|...|..3|
 |---+---+---|
 |...|.5.|...|
 |.56|2..|...|
 |...|1..|9.5|
 |---+---+---|
 |89.|.3.|.46|
 |.41|..8|.5.|
 |5..|..4|2.8|
 *-----------*
.3....67..1.3....27.9.....3....5.....562........1..9.589..3..46.41..8.5.5....42.8

[Leren]

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*-------------------------------------------------------*
| 24  3   2458  | 4589    12489   1259  | 6     7   149 |
| 46  1   458   |*3      *7-4689 *57-69 | 458   89  2   |
| 7   268 9     | 4568    12468   1256  | 1458  18  3   |
|---------------+-----------------------+---------------|
| 19  278 23478 |*7-4689 *5      *37-69 | 13478 26  147 |
| 19  5   6     | 2       4789    379   | 13478 138 147 |
| 234 278 23478 | 1       4678    367   | 9     26  5   |
|---------------+-----------------------+---------------|
| 8   9   27    |*57     *3      *57-12 | 17    4   6   |
| 236 4   1     | 679     2679    8     | 37    5   79  |
| 5   67  37    | 679     1679    4     | 2     139 8   |
*-------------------------------------------------------*

Row Sticks Symmetry : [12] [48] [69] [3] [5] [7] . Elimination Rows 247 Columns 4-6 => - 4689 r2c5, r4c4, - 69 r24c6, , - 12 r7c6; stte

Leren

[Cenoman]

Code: Select all

 |.3.|...|67.|
 |.1.|3..|..2|
 |7.9|...|..3|
 |---+---+---|
 |...|.5.|...|
 |.56|2..|...|
 |...|1..|9.5|
 |---+---+---|
 |89.|.3.|.46|
 |.41|..8|.5.|
 |5..|..4|2.8|

I have been teached Sticks symmetry already twice: here and here
Now, yzfwsf has added it to his solver, and Leren had solved the puzzle within minutes. A manual solution is of little interest.
Nevertheless, here is my way to a manual solution.
In any symmetry, the candidates are symmetric, and so is the pattern.
First look at the pattern:
The number of givens in boxes maps as follows:

Code: Select all

 | 4 | 1 | 4 |
 | 2 | 3 | 2 |
 | 5 | 3 | 5 |

The similarity between stacks 1, 3 is a clue for a row sticks symmetry, with sticks located in stack 2.
Let's try to find similar patterns in pair of boxes [13] and [79]. A permutation of columns is need in stack 3.
Swapping circularly columns 7,8,9 to [7->9, 8->7, 9->8].

Code: Select all

 |.3.|...|7.6|    
 |.1.|3..|.2.|
 |7.9|...|.3.|
 |---+---+---|
 |...|.5.|...|
 |.56|2..|...|
 |...|1..|.59|
 |---+---+---|
 |89.|.3.|46.|
 |.41|..8|5..|
 |5..|..4|.82|

At that point, it is easy to find the sticks: in b2, r2c456; in b5, r4c456, in b8, r7c456 (the rows that have a pattern different from the other two's). From there, the automorphism is obvious:
swap stacks [13], then swap rows [13] [56] [89] (the sticks don't move)
Edit: corrected the diagram below, as well as the followings, consistently with the above (thanks to Leren for spotting the mistake)
Correction: swapped rows [56] [78]

Code: Select all

 |.3.|...|7.9|
 |.2.|3..|.1.|
 |7.6|...|.3.|
 |---+---+---|
 |...|.5.|...|
 |.59|1..|...|
 |...|2..|.56|
 |---+---+---|
 |46.|.3.|89.|
 |.82|..4|5..|
 |5..|..8|.41|

then carry out digit permutation [12] [48] [69] [3] [5] [7]. The above puzzle is recovered:

Code: Select all

 |.3.|...|7.6|
 |.1.|3..|.2.|
 |7.9|...|.3.|
 |---+---+---|
 |...|.5.|...|
 |.56|2..|...|
 |...|1..|.59|
 |---+---+---|
 |89.|.3.|46.|
 |.41|..8|5..|
 |5..|..4|.82|

Back to the start puzzle by the inverse of the initial isomorphism: swapping circularly columns 7,8,9 to [7->8, 8->9, 9->7].

Code: Select all

 |.3.|...|67.|
 |.1.|3..|..2|
 |7.9|...|..3|
 |---+---+---|
 |...|.5.|...|
 |.56|2..|...|
 |...|1..|9.5|
 |---+---+---|
 |89.|.3.|.46|
 |.41|..8|.5.|
 |5..|..4|2.8|

Note that the puzzle is rated SE 9.2
The way to use the symmetry has been given by Leren.

[jco]

Hello, Cenoman

(...)
A manual solution is of little interest. (...)

Thank you for the explanation! IMO manual solutions are great. When presented in some detail (like here), they are precious learning tools to newcomers (like me).

Happy New Year!!
jco

[Cenoman]

Hello, Cenoman
Thank you for the explanation! IMO manual solutions are great. When presented in some detail (like here), they are precious learning tools to newcomers (like me).
Happy New Year!!
jco

Thank you for the feedback. I'm glad you found it helpful. When I was a newcomer, I was helped by players happy to share their knowledge (on this topic, notably eleven and Leren). It's my turn to do the same, as far as I can.

Happy New Year to you and to all !

Cenoman