The New Sudoku Players' Forum

by **Draco** » Sat May 10, 2008 9:04 pm

Seems like a slow Saturday, so here's a 23-spot puzzle to mull:

Code: Select all: 7 . . | . . 2 | . . . . . . | . . . | . . 4 . 9 . | . 7 . | 6 . 1 ------+-------+------ 3 . 4 | . . . | 5 2 . . . . | . 1 . | . . . . 5 8 | . . . | 4 . 7 ------+-------+------ 1 . 7 | . 3 . | . 9 . 8 . . | . . . | . . . . . . | 6 . . | . . 3

After SSTS you'll find:

Code: Select all: 7 368 1356 | 13458 456 2 | 39 358 589 56 38 135 | 13589 59 13689 | 2 7 4 4 9 2 | 358 7 38 | 6 358 1 ------------+------------------+----------- 3 1 4 | 78 69 78 | 5 2 69 2 7 69 | 45 1 45 | 39 368 689 69 5 8 | 39 2 369 | 4 1 7 ------------+------------------+----------- 1 46 7 | 245 3 45 | 8 9 256 8 346 36 | 124579 459 179 | 17 56 256 59 2 59 | 6 8 17 | 17 4 3

I've found a single, short forcing chain that cracks it to SSTS to solve using the coloring on 4's for my bi-value:

r1c4=4 r1c3=1 + r1c5=4 r2c6=6 r2c1=5 ==> r1c3<>5.

Looking for interesting alternatives.

Cheers...

- drac

[edit: oops on acronyms corrected]
[edit: pasted correct PM's into msg - thanks RW!]

by RW » Sat May 10, 2008 10:52 pm

Draco wrote:After SSTS you'll find:
Code: Select all
7 368 1356 | 134589 4569 2 | 39 358 589 56 368 1356 | 13589 569 135689 | 2 7 4 4 9 2 | 358 7 358 | 6 358 1 ------------+--------------------+----------- 3 1 4 | 789 69 6789 | 5 2 689 2 7 69 | 34589 1 345689 | 39 368 689 69 5 8 | 39 2 369 | 4 1 7 ------------+--------------------+----------- 1 46 7 | 245 3 45 | 8 9 256 8 346 3569 | 124579 459 14579 | 17 56 256 59 2 59 | 6 8 1579 | 17 4 3

After SSTS I find:

Code: Select all: *-----------------------------------------------------------------------------* | 7 368 1356 | 13458 456 2 | 39 358 589 | | 56 38 135 | 13589 59 13689 | 2 7 4 | | 4 9 2 | 358 7 38 | 6 358 1 | |-------------------------+-------------------------+-------------------------| | 3 1 4 | 78 69 78 | 5 2 69 | | 2 7 69 | 45 1 45 | 39 368 689 | | 69 5 8 | 39 2 369 | 4 1 7 | |-------------------------+-------------------------+-------------------------| | 1 46 7 | 245 3 45 | 8 9 256 | | 8 346 36 | 124579 459 179 | 17 56 256 | | 59 2 59 | 6 8 17 | 17 4 3 | *-----------------------------------------------------------------------------*

One of the two type 1 URs will crack it (together with SSTS).

RW

by **Draco** » Sat May 10, 2008 11:25 pm

Oops... pasted the wrong PM's the first time; thanks RW. I've corrected the original post.

I'm not seeing the UR's (and am also bad at spotting them); would you mind calling them out more specifically? Thx!

- drac

by **Glyn** » Sat May 10, 2008 11:50 pm

Draco here's two UR's

1)r57c46 => r7c4=2 to avoid {45}
2)r89c67 => r8c6=9 to avoid {17}

by **Draco** » Sun May 11, 2008 1:27 am

Sigh -- thanks Glyn.

by **Jean-Christophe** » Sun May 11, 2008 9:22 am

If you don't want using uniqueness techniques, here is an alternative:

Sashimi Swordfish on 5 in r357 and c468 with fin in r7c9 -> r8c8 <> 5 = 6
or
Grouped 2 String Kite (5): r3c8=r3c4-r12c5=r8c5 -> r8c8 <> 5 = 6

by **Carcul** » Sun May 11, 2008 11:37 am

Code: Select all: *--------------------------------------------------------------------* | 7 3468 1356 | 13458 456 2 | 39 358 589 | | 56 368 1356 | 13589 569 13689 | 2 7 4 | | 245 9 235 | 3458 7 38 | 6 358 1 | |----------------------+-----------------------+---------------------| | 3 1 4 | 78 69 78 | 5 2 69 | | 269 7 269 | 45 1 45 | 39 368 689 | | 69 5 8 | 239 269 369 | 4 1 7 | |----------------------+-----------------------+---------------------| | 1 46 7 | 245 3 45 | 8 9 256 | | 8 346 356 | 124579 2459 179 | 17 456 256 | | 459 2 59 | 6 8 17 | 17 45 3 | *--------------------------------------------------------------------*

[r7c2]=6=[r7c9]-6-[r89c8]-5-[r3c68]-3,8-[r35c4]-4-[r18c4]=4=[r8c2]-4-[r7c2], => r7c2<>4 and the puzzle is solved.

by **ronk** » Sun May 11, 2008 2:44 pm

Carcul wrote:
Code: Select all
*----------------------------------------------------------* | 7 3468 1356 | 13458 456 2 | 39 358 589 | | 56 368 1356 | 13589 569 13689 | 2 7 4 | | 245 9 235 | 3458 7 38 | 6 358 1 | |------------------+---------------------+-----------------| | 3 1 4 | 78 69 78 | 5 2 69 | | 269 7 269 | 45 1 45 | 39 368 689 | | 69 5 8 | 239 269 369 | 4 1 7 | |------------------+---------------------+-----------------| | 1 46 7 | 245 3 45 | 8 9 256 | | 8 346 356 | 124579 2459 179 | 17 456 256 | | 459 2 59 | 6 8 17 | 17 45 3 | *----------------------------------------------------------*

[r7c2]=6=[r7c9]-6-[r89c8]-5-[r3c68]-3,8-[r35c4]-4-[r18c4]=4=[r8c2]-4-[r7c2], => r7c2<>4 and the puzzle is solved.

All I see one of Mike Barker's kraken x-wings, but the notation sure doesn't say that. However, if that is the technique you're using, it's one of the few cases where I prefer AIC notation over NL notation.

Code: Select all: (4)x-wing:r18\c25 || (4)fin:r8c8 - (4)r9c8 = (4)r9c1 || (4)fin:r18c4 - (4=38)r35c4 - (38=5)r3c68 - (5=46)r89c8 - (6)r7c9 =(6)r7c2 ==> r7c2<>4

by **Carcul** » Mon May 12, 2008 10:12 pm

No, that's not the technique I used. Where are your doubts (if any)?

by **Draco** » Mon May 12, 2008 10:53 pm

Jean-Christophe wrote:If you don't want using uniqueness techniques, here is an alternative:

Sashimi Swordfish on 5 in r357 and c468 with fin in r7c9 -> r8c8 <> 5 = 6
or
Grouped 2 String Kite (5): r3c8=r3c4-r12c5=r8c5 -> r8c8 <> 5 = 6

Thanks Jean... it's not that I don't like UR's. It's that I cannot believe how blind I am when it comes to spotting them!

by **Draco** » Mon May 12, 2008 11:04 pm

Carcul wrote:[r7c2]=6=[r7c9]-6-[r89c8]-5-[r3c68]-3,8-[r35c4]-4-[r18c4]=4=[r8c2]-4-[r7c2], => r7c2<>4 and the puzzle is solved.

That is one heckuva' chain! Compared to using ALS's in a chain, I find UR's easy

.

I am able to follow it (I think) up to ... "[r18c4]=4=[r8c2]". Why is r8c2 set to 4? Isn't r8c8=4 also valid from the posted PMs and your chain up to that point? What am I missing?

Cheers...

- drac

by **ronk** » Tue May 13, 2008 12:27 am

Carcul wrote:No, that's not the technique I used. Where are your doubts (if any)?

Instead of playing Mr. Cutesy, why don't you explain your derived strong inference?

[edit: Don't explain on my account though, as I've lost interest.]

by **daj95376** » Tue May 13, 2008 8:14 am

If you perform Colors on 4 after [r18c4]=4=, then you get [r8c5] and [r8c8] as the same color. This forces =4=[r8c2].

Thus, Carcul's [r18c4]=4=[r8c2].

by **Draco** » Wed May 14, 2008 3:29 am

daj95376 wrote:If you perform Colors on 4 after [r18c4]=4=, then you get [r8c5] and [r8c8] as the same color. This forces =4=[r8c2].

Thus, Carcul's [r18c4]=4=[r8c2].

Ah, ok. I was trying with a static grid. Thx...

- drac

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