The New Sudoku Players' Forum

[urhegyi]

I detected the Gurth's symmetrical placement with mappings:
1<-->3
2<-->4
5<-->5
6<-->8
7<-->9
How can you use this theorem to solve this puzzle in the most easy way?
Because of the 180 degrees rotational symmetry when you use a method to eliminate one candidate from a cell, you can also eliminate the mapped candidate from the opposite symmetrical cell.
I have a multi steps solution, but like to know if anyone sees a shorter way.
Any ideas?

Code: Select all

.2..48.5754.7...3..792....4...1.24.9....5....7.24.3...2....479..1...9.2595.62..4.

[marek stefanik]

Hi urhegyi,
There is a surprisingly simple solution.

Have a look at the ALS 368r4c12.
If we were to put 6 or 8 in r4c8, it would force the other one into r6c2, breaking the ALS. So 7r4c8, stte.
I don't know how to notate that though.

Marek

[jco]

Hi urhegyi,
There is a surprisingly simple solution.

Have a look at the ALS 368r4c12.
If we were to put 6 or 8 in r4c8, it would force the other one into r6c2, breaking the ALS. So 7r4c8, stte.
I don't know how to notate that though.

Marek

Nice solution!
Regarding the notation issue, it can be written in two steps (two discontinuous nice loops):

Code: Select all

.---------------------------------------------------.
| 136   2    136   | 39  4    8  | 169    5    7    |
| 5     4    168   | 7   169  16 | 12689  3    1268 |
| 1368  7    9     | 2   136  5  | 168    168  4    |
|------------------+-------------+------------------|
|*368  *368  5     | 1   678  2  | 4     #678  9    |
| 14    689  14    | 89  5    67 | 23     678  23   |
| 7    #689  2     | 4   689  3  | 5      168  168  |
|------------------+-------------+------------------|
| 2     368  368   | 5   138  4  | 7      9    1368 |
| 3468  1    34678 | 38  378  9  | 368    2    5    |
| 9     5    378   | 6   2    17 | 138    4    138  |
'---------------------------------------------------'

(6)r4c8 - (6=38)r4c12 - (8)r6c2 == ((7|8) - 6)r4c8 => -6 r4c8, -8 r6c2
(8)r4c8 - (8=36)r4c12 - (6)r6c2 == (7 - 8)r4c8 => -8 r4c8, -6 r6c2
----------------
=> +7 r4c8, +9 r6c2

Edit: improved writing of eliminations.