The New Sudoku Players' Forum

[Tordenskjold]

Hi Forum.
I have recently moved from the Hard to Expert level puzzles in my Sudoku app.
For the life of me, I cannot crack this one.
https://imgur.com/Rch7I3K

I have exhausted the basic solving techniques (including X-Wing and Swordfish).
What am I missing?

Best regards.

[SpAce]

Hello. First, you haven't actually exhausted all basics. There's a naked pair (48) / hidden pair (69) on row 2, as well as a hidden pair (69) / naked quad (2458) on column 4. They don't really make a difference, though.

This puzzle requires at least one relatively advanced technique (AIC or Sue de Coq, for example) to solve. There are a couple of simpler Unique Rectangles and a W-Wing available, but they're not enough to solve the puzzle. The simplest single move that leaves just singles is probably this short AIC (or one of its variants):

Code: Select all

.-----------------.------------------.--------------.
| 6    3      9   | 458   2     458  | 7     1   48 |
| 5    7      1   | 4689  4689  48   | 3     2   48 |
| 8    2      4   | 7     3     1    | 9     6   5  |
:-----------------+------------------+--------------:
| 1   d(8)-4  6   | 2458  4578  9    |a2(4)  57  3  |
| 47   9     c278 | 3     4578  6    |b24    57  1  |
| 347  5      237 | 24    1     247  | 6     8   9  |
:-----------------+------------------+--------------:
| 347  468    378 | 1     678   378  | 5     9   2  |
| 2    68     358 | 5689  5689  358  | 1     4   7  |
| 9    1      57  | 245   457   2457 | 8     3   6  |
'-----------------'------------------'--------------'

(4=2)r4c7 - r5c7 = (2-8)r5c3 = (8)r4c2 => -4 r4c2; stte

The chain proves that either r4c7=4 or r4c2=8; in both cases r4c2<>4. Once you eliminate that, the rest is easy.

PS. If I'm not wrong, some people call that chain pattern an H2-Wing. But I may very well be wrong, so I'd appreciate if someone either confirmed or corrected that. (Not that it really matters what it's called as long as it works.)

[Tordenskjold]

Thank you so much.
That was very educational.

I guess that is the wondrous world of Sudoku. Always nuances to learn.
Will read up on AIC.

Thanks again.