The New Sudoku Players' Forum

[Leren]

Code: Select all

*-----------*
|.2.|6..|..7|
|4..|.78|...|
|..9|...|...|
|---+---+---|
|8..|1..|.4.|
|.3.|...|.7.|
|.6.|..9|..2|
|---+---+---|
|...|...|1..|
|...|23.|..6|
|3..|..4|.8.|
*-----------*
.2.6....74...78.....9......8..1...4..3.....7..6...9..2......1.....23...63....4.8.

[Cenoman]

DDS

[Leren]

Congratulations Cenoman, well spotted ! Leren

[Mauriès Robert]

DDS

What's DDS?
You use a lot of acronyms on this forum, so it's not easy to understand!
Robert

[Leren]

Hi Robert, this puzzle possesses what is known as Double Diagonal Symmetry (of the clues) (DDS).

If the clues are arranged in a way that they are symmetrically positioned wrt to a diagonal, such that 3 digits are paired consistently with 3 different digits, and the remaining 3 digits only appear on the diagonal, then those 3 unpaired digits are the only ones that can appear on the diagonal.

Here is the PM for the Main Diagonal eliminations:

Code: Select all

*------------------------------------------------------------*
| 15    2      38    | 6    1459   135  | 34589 1359   7     |
| 4     15     36    | 359  7      8    | 2359  123569 1359  |
| 67    78     9     | 345  1245   1235 | 3458  1356   13458 |
|--------------------+------------------+--------------------|
| 8     579    257   | 1    26-5   37   | 3569  4      359   |
| 1259  3      1245  | 48-5 5-2468 26-5 | 5689  7      1589  |
| 157   6      1457  | 37   48-5   9    | 358   135    2     |
|--------------------+------------------+--------------------|
| 25679 4579   2567  | 5789 5689   567  | 1     23     34    |
| 1579  145789 1578  | 2    3      157  | 47    59     6     |
| 3     1579   12567 | 579  1569   4    | 27    8      59    |
*------------------------------------------------------------*

Main Diagonal (TLBR) Symmetry [24] [37] [68] + [1] [5] [9]. So only 1, 5 and 9 can appear on the diagonal.

For the Anti Diagonal you get Anti Diagonal (TRBL) Symmetry [19] [26] [48] + [3] [5] [7]. So only 357 can appear there, you get lots of eliminations and the puzzles solves with singles.

Leren

[Cenoman]

What's DDS?
You use a lot of acronyms on this forum, so it's not easy to understand!
Robert

Hi Robert,
DDS was just a sort of secrete code to Leren, to let him know that I had not forgotten his teaching eighteen months ago here
I'd have detailed the meaning and eliminations of the Double Diagonal Symmetry later, in order to let others be pleased to find it by themselves, hadn't Leren already done so.

EDIT: DDS is used more often as a sudoku acronym standing for Distributed Disjoint Subsets. See Obi-Wahn's thread

[eleven]

Robert,

so called digit symmetrical puzzles or puzzles with symmetrical givens are very rare, but interesting nevertheless.
There have been long threads about them, e.g. Symmetrical Givens and About Red Ed's Sudoku symmetry group.

[Mauriès Robert]

Thank you Eleven and Cenoman for this information, I had never used automorphisms to make eliminations, but it is true that puzzles with mathematical properties are not very common. In any case, I will observe better now.
Robert

[Ngisa]

I opt for three steps

Code: Select all

+-----------------------+---------------------+------------------------+
| 15      2       38    | 6      1459    135  | 34589   1359     7     |
| 4       15     a36    | 359    7       8    |e2359   d123569   1359  |
|b67      78      9     | 345    1245    1235 | 3458   c1356     13458 |
+-----------------------+---------------------+------------------------+
| 8       579     257   | 1      256     37   | 3569    4        359   |
| 1259    3       1245  | 458    24568   256  | 5689    7        158   |
| 157     6       1457  | 37     458     9    | 358     135      2     |
+-----------------------+---------------------+------------------------+
| 25679   4579    2567  | 5789   5689    567  | 1       23       34    |
| 1579    14578   1578  | 2      3       157  | 47      59       6     |
| 3       1579   g1257-6| 579    1569    4    |f27      8        59    |
+-----------------------+---------------------+------------------------+


Step 1:(6)r2c3 = r3c1 - r3c8 = (6-2)r2c8 = r2c7 - r9c7 = (2)r9c3 => - 6r9c3,

Code: Select all

+------------------------+--------------------+------------------------+
| 15       2       i38   | 6      1459   Ej35 | 34589    1359     7    |
| 4        15      h36   | 359    7        8  |d2359    e123569   1359 |
| g67      78       9    | 345    145      2  | 3458    f1356     13458|
+------------------------+--------------------+------------------------+
| 8        579      257  | 1      25      D37 | 6        4       C359  |
| 1259     3        1245 | 458    2458     6  | 589      7        1589 |
| 157      6        1457 | 37     458      9  | 358      135      2    |
+------------------------+--------------------+------------------------+
| a25679   4579    a2567 | 5789   589    Fk7-5| 1       b23      B34   |
| 579      4578     578  | 2      3        1  |B47       59       6    |
| 3        1579    A1257 | 579    6        4  |Bc27      8        59   |
+------------------------+--------------------+------------------------+


Step 2:Kraken Box (2)b7p139
(2)r7c13 - r7c8 = r9c7 - r2c7 = (2-6)r2c8 = r2c8 = r3c8 - r3c1 = (6-3)r2c3 = r1c3 - (3=5)r1c6 - r7c6
(2)r9c3 - (2=743)b9p743 - (3)r4c9 = r4c6 - (3=5)r1c6 - r7c6 => - 5r7c6,

Code: Select all

+---------------------+--------------------+------------------------+
| 1       2       38  | 6       49       5 | 3489     39        7   |
| 4       5       36  | 39      7        8 | 239      12369     13  |
| 67      78      9   | 34      1        2 | 3458     356       348 |
+---------------------+--------------------+------------------------+
| 8       79      27  | 1       25       3 | 6        4         59  |
| 29      3       124 | 458     2458     6 | 589      7         18  |
| 5       6       14  | 7       48       9 | 38       13        2   |
+---------------------+--------------------+------------------------+
| 269    c49      256 | 589     589      7 | 1        23        3-4 |
| b79     478     578 | 2       3        1 |a47       59        6   |
| 3       1       27  | 59      6        4 | 27       8         59  |
+---------------------+--------------------+------------------------+


Step 3 XY-Wing: (4=7)r8c7 - (7=9)r8c1 - (9=4)r7c2 => - 4r7c9; stte

Clement