dailysudoku.com

[immpy]

Hello all, enjoy the puzzle...

[ZeroAssoluto]

Hi everyone,

[TomC]

Hi Gianni,

My solution, not as elegant though!

Eliminate the 7 in r4c1 to avoid UR of 38 in r46c24

Then eliminate the 8 in r8c3 to avoid UR of 23 in r37c23

Tom

[immpy]

Nicely done Gianni! I lacked confidence in using the WXYZ pattern here. Too many overlapping candidates it seemed. I was somehow uncomfortable with it. But I did use two forms of Rectangle, one Hidden, one Empty.

[immpy]

First step was a Hidden Rectangle (23) r37c23 with r7c2<>3.

That takes us here...

[immpy]

The second step was the Empty Rectangle on (3) r58c7 with boxes 4 and 7.
r5c3<>3.

cheers...immp

[immpy]

Yes TomC, yours works nicely as well.

[immpy]

I am thinking that there are interesting boxes here as well for the candidate (3). They would be boxes 4, 6, 7, and 9. These form a rectangle, as keith had suggested in a previous post, applied to a previous puzzle. After identifying any strong links on 3, it appears that, in the second grid, the cells of r7c3 and r5c7 would act as pincers on (3), thus making the same elimination as the Empty Rectangle; r5c3<>3. I am hoping my logic is correct and sound. Please let me know if I am wrong in my application of this. Thank you all.


cheers...immp

[keith]

immpy,

Thank you for making my New Year!

First, let me say you are correct. Given the Hidden Rectangle elimination, you have pointed out the links that make the elimination of 3 in r5c3.

I had to stare at the Hidden Rectangle for a while, but then I recognized it as a UR overlaid on a X-wing. That is something I can claim to have discovered just about 15 years ago! The original discussion is here:

http://forum.enjoysudoku.com/uniqueness-type-6-ur-meets-x-wing-t3709.html

I'll post a more detailed discussion of this puzzle in a while. First, I need to think about my assertion about "interesting" boxes and how it applies to Empty Rectangles.

Keith

[immpy]

Thanks Keith. I have identified countless UR types in puzzles, but always had trouble with the specifics. Which type (of 6) was it? The Hidden Rectangle always afforded me the opportunity to make the correct elimination (if any) in the proper cell. I rely on it a lot. It is indeed a UR overlaid on an X-Wing. Most harder puzzles don't feature a simple Type 1 or Type 2 UR. They are complicated by extra candidates in various component cells of the UR. Rarely do they solve in one step, but many times, as in this case, they make a key elimination of a candidate.

The presence of interesting boxes is truly beautiful. I was able to identify one in the most recent VH daily. They seem to be present quite a bit. That is a very good thing! Looking at puzzles in a whole new light now.

cheers...immp

[immpy]

And also Keith, thanks for discovering the Hidden Rectangle 15 years ago. A must have in my toolbox!

immp