The New Sudoku Players' Forum

[Leren]

Code: Select all

*-----------*
|7..|...|...|
|...|...|3.5|
|.12|...|.6.|
|---+---+---|
|176|8..|.3.|
|..9|.2.|..8|
|...|.3.|..7|
|---+---+---|
|...|5..|7..|
|267|.9.|.5.|
|.8.|1..|9..|
*-----------*
7..............3.5.12....6.1768...3...9.2...8....3...7...5..7..267.9..5..8.1..9..

[denis_berthier]

.
SER = 9.1
I have a solution in W10 or gW9, but I guess the mystery allows a simpler one.

[yzfwsf]

Gurth's symmetry placement

[Cenoman]

Explicitation of yzfwsf's terse message:

Code: Select all

 +------------------------+-------------------------+------------------------+
 |  7       3459   3458   |  3469   4568   46-3589  |  1248   4-1289  1249   |
 |  6       49     48     |  2      1      4-89     |  3      7       5      |
 |  4-3589  1      2      |  3479   4578   47-3589  |  48     6       49     |
 +------------------------+-------------------------+------------------------+
 |  1       7      6      |  8      45     459      |  245    3       249    |
 |  345     345    9      |  467    2      14567    |  1456   14      8      |
 |  458     2      458    |  469    3      14569    |  1456   149     7      |
 +------------------------+-------------------------+------------------------+
 |  349     349    1      |  5      468    23468    |  7      248     2346   |
 |  2       6      7      |  34     9      348      |  148    5       134    |
 |  345     8      345    |  1      467    23467    |  9      24      2346   |
 +------------------------+-------------------------+------------------------+

Map of givens and map of givens + singles, in boxes:

Code: Select all

3|0|3    4|2|4
4|3|3    5|3|3
4|3|3    5|3|3

Clue for a column stick symmetry, with sticks in band 1

Map of givens+singles in columns

Code: Select all

4 5 5 | 4 4 0 | 3 3 3

Clue for sticks in columns 1 & 6, to be decided later in box 3
A better similarity of patterns in bands 2 & 3 is helped by the isopmorphism: swap circularly rows in band 2 (4->5, 5->6, 6->4) to the following puzzle:

Code: Select all

*-----------*
|7..|...|...|
|...|...|3.5|
|.12|...|.6.|
|---+---+---|
|...|.3.|..7|
|176|8..|.3.|
|..9|.2.|..8|
|---+---+---|
|...|5..|7..|
|267|.9.|.5.|
|.8.|1..|9..|
*-----------*

Then, swap bands [23] , swap columns [23] [45] [79], carry out digit permutation [12][35][89][4][6][7] proves the above puzzle to be automorphic. It has a column stick symmetry with sticks invariant at r123c1, r123c6, r123c8. Same for the starting puzzle, through the inverse isomorphism in band 2 (swap circularly rows 5->4, 6->5, 4->6), hence the eliminations: -3589 r1c6, r3c16, -1289 r1c8; ste

[jco]

Hello Cenoman,

Explicitation of yzfwsf's terse message (...)

Very nice! Thank you for taking the time to explain that solution in detail.

Regards,
jco