tarek wrote:a SDC puzzle

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`. . .|8 . 2|. . .`

. . 4|. . .|3 . .

. 6 .|. . .|. 8 .

-----+-----+-----

9 . .|4 . 8|. . 5

. . .|. . .|. . .

8 . .|2 . 5|. . 4

-----+-----+-----

. 1 .|. . .|. 2 .

. . 6|. . .|1 . .

. . .|3 . 7|. . .

tarek

Okay...so I just promised Don that I wouldn't start posting again...and I'm not going to, but just this once as I had so much fun solving ronk's puzzle and now tarek's puzzle.

First, (after SSTS, of course) I found a couple Sue De Coq's. Unfortunately, all of the one's I found still left an xy-wing to solve the puzzle (at least they do individually). Then I noticed the potential deadly pattern in r46c257[37/36/67]. This gives the easy elimination r6c8<>9. However, this again leaves a couple of xy-wings. On the hand, a larger chain using the same potential deadly pattern, implies r7c9<>9 and this does crack the puzzle in one step.

But then I remembered that not everyone like uniqueness steps and so I tried to see another way to kill that 9. It took all of a click of the pairs button in simple sudoku followed by clicking on the 9 button to see that a transported xyz-wing will do the job. More precisely, the xyz-wing in r2c8/r9c89[569] implies a strong inference (9)r2c8=r9c89. From this, a simple chain is born:

(9)r6c7 = r56c8 - r2c8 = r9c89, => r9c7<>9.

There are more things in there, though. An hxy-loop (forgive me, denis) that jumps out at you if you look in rn-space. Almost certainly, there will be some xyt-chains that will crack it (or almost xy-chains, if you're into that sort of thing).

Awesome puzzle, tarek.