The New Sudoku Players' Forum

[urhegyi]

Code: Select all

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


Play this puzzle online at the Daily Sudoku site

[Leren]

GSP Symmetry => r5c5 = 3. Then solves with basics. Leren

[Yogi]

I don't know that move. Can someone explain it, please?
Neither I nor Andoku could solve the puzzle without 3r5c5.

[Cenoman]

Hi Yogi,
The word symmetrical here has to be read as a synonym of automorphic.
The puzzle pattern is symmetric about its center (r5c5) (or equivalently, in a 180° rotation)
If you run such a transformation, you get:

Code: Select all

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

And now, if you relabel this puzzle with (1,5) (2,4) (3,3) (6,9) (7,8), you get urhegyi's original puzzle, with demonstrate the automorphism (i.e. a transformation to itself, different from identity). In this symmetry, r5c5 is invariant in the pattern move, must contain the invariant digit in the relabelling.

For a complete study of sudoku automorphisms, read the following eleven's thread.


PM's without any basics (not even singles)

Code: Select all

 +----------------------------+----------------------+----------------------------+
 |  1       2478     3        |  48     58    6      |  24578    245789   2789    |
 |  4789    478      4789     |  1348   2     3459   |  145678   345789   36789   |
 |  489     5        6        |  7      138   349    |  1248     23489    2389    |
 +----------------------------+----------------------+----------------------------+
 |  2       3478     4-78     |  5      6     347    |  78*      3789     1       |
 |  3478    9        1478     |  2348   78+3  2347   |  2578     6        2378    |
 |  5       3678     78*      |  238    9     1      |  2-78     2378     4       |
 +----------------------------+----------------------+----------------------------+
 |  3467    23467    2457     |  236    357   8      |  9        1        267     |
 |  36789   123678   125789   |  1236   4     2357   |  2678     278      2678    |
 |  4678    124678   12478    |  9      17    27     |  3        2478     5       |
 +----------------------------+----------------------+----------------------------+

The givens have a central symmetry, with digit relabelling (1,5) (2,4) (3,3) (6,9) (7,8)
=> +3 r5c5
Look at symmetrical cells r4c7, r6c3: if one is 7, the other is 8 => they form a remote pair => -78 r4c3, r6c7; ste