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5/13/07 Nightmare

 
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Sudtyro
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PostPosted: Sun May 20, 2007 9:42 pm    Post subject: 5/13/07 Nightmare Reply with quote

After running through the basics:
Code:

----------------------------------------------------
47    269   147  | 3    17   8    | 269   5    26     
239   23689 1368 | 12   69   5    | 4     2369 7     
23579 23569 367  | 27   4    69   | 8     1    236   
-----------------+----------------+-----------------
1     356   36   | 57   2    4    | 367   8    9     
459   569   2    | 8    357  37   | 1     467  46     
8     7     34   | 6    19   19   | 23    234  5     
-----------------+----------------+-----------------
237   4     9    | 57-1 8    1367 | 23567 2367 1236   
6     238   5    | 9    137  137  | 237   2347 12348 
37    1     378  | 4    3567 2    | 35679 3679 368   
----------------------------------------------------


To advance beyond this point, there are numerous grouped AICs and ALSs available. However, one very productive ALS-XZ rule (from Andrew Stuart’s solver) is:

(1=2378)r8c2567 - (8=23691)r2c12458 => r7c4 <> 1

This particular ALS application was hard to spot manually, so I’m curious to know if there are more obvious alternative solution strategies that provide the same elimination?
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Jean-Christophe
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PostPosted: Mon May 21, 2007 6:19 am    Post subject: Reply with quote

Here is an (non grouped) AIC which yields the same elimination:

(1)R2C4=(1)R2C3-(8)R2C3=(8)R2C2-(8)R8C2=(8)R8C9-(1)R8C9=(1)R7C9 -> R7C4<>1

Not sure it's easier to spot, thought
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Sudtyro
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PostPosted: Mon May 21, 2007 10:58 am    Post subject: And another question... Reply with quote

Thanks, J-C...very nice chain and maybe easier to find, at least for me!

This brings up another general question:
For every grouped AIC, including ALS-rule applications, does there always exist an equivalent non-grouped AIC for the same elimination?
This particular case seems to say yes, but what about, say, a simple XYZ-Wing? Are there always other cells available that allow for a non-grouped AIC?
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Jean-Christophe
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PostPosted: Mon May 21, 2007 2:14 pm    Post subject: Re: And another question... Reply with quote

Sudtyro wrote:
For every grouped AIC, including ALS-rule applications, does there always exist an equivalent non-grouped AIC for the same elimination?
This particular case seems to say yes, but what about, say, a simple XYZ-Wing? Are there always other cells available that allow for a non-grouped AIC?


No, sometimes one may find other ways or techniques to eliminate the same candidate, but not always.
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Ron Moore
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PostPosted: Mon May 28, 2007 3:25 pm    Post subject: Uniqueness Argument Reply with quote

Sudtyro,

You may not consider this easy to see, but I've found that uniqueness based arguments are often productive, so I tend to give priority to looking for and using such arguments.

Code:
----------------------------------------------------
47    269   147  | 3    17   8    | 269   5    26     
239   23689 1368 | 12   69   5    | 4     2369 7     
23579 23569 367  |*2-7  4    69   | 8     1    236   
-----------------+----------------+-----------------
1     356   36   |#57   2    4    | 367   8    9     
459   569   2    | 8   ^357 ^37   | 1     467  46     
8     7     34   | 6    19   19   | 23    234  5     
-----------------+----------------+-----------------
237   4     9    |#157  8    1367 | 23567 2367 1236   
6     238   5    | 9   ^137 ^137  | 237   2347 12348 
37    1     378  | 4    3567 2    | 35679 3679 368   
----------------------------------------------------


There is a potential deadly pattern in r58c56 (marked with "^"in the diagram), based on the digits 3,7. To avoid the deadly pattern, we must have a 5 in r5c5 or a 1 in one of r8c56. We can use this fact in an AIC, as follows:
    (7=5)r4c4 - (5=37)r5c56 - UR - (37=1)r8c56 - (1=57)r47c4 => r3c4 <> 7
Of course, this quickly leads to (or follows from) the elimination you give.
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Sudtyro
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PostPosted: Fri Jun 01, 2007 11:10 am    Post subject: Re: Uniqueness Argument Reply with quote

Thanks, RM...that’s a clever and interesting AIC with its use of the potential UR.

[Edit for late addendum]: Perhaps one could even get the original elimination directly from
(5)r7c4 = (5)r4c4 - (5=37)r5c56 - UR - (37=1)r8c56 => r7c4 <> 1


Last edited by Sudtyro on Thu Jun 14, 2007 6:08 pm; edited 1 time in total
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Sudtyro
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PostPosted: Sun Jun 10, 2007 8:57 pm    Post subject: 5/13/07 Nightmare - revisited Reply with quote

To continue a bit on this thread...
After follow-up and one Turbot Fish, (7): r5c8 = r4c6 - r4c4 = r7c4 => r7c8 <> 7, the unresolved 7’s grid becomes:

Code:
. . . | . . . | . . .
. . . | . . . | . . .
7 . 7 | . . . | . . .
------+-------+------
. . . | 7 . . | 7 . .
. . . | . . 7 | . 7 .
. . . | . . . | . . .
------+-------+------
7 . . | 7 . 7 | 7 . .
. . . | . . 7 | 7 7 .
7 . 7 | . . . | . 7 .

I’m no fish expert, but based on Ron Moore’s recent Nightmare posting (1 June 2007 – “Almost” Swordfish), the above grid appears to host an “almost” X-wing with two possible “spoilers.”

r39c13 would be a column (or row) X-Wing except for the spoiler in r7c1 (or r9c8). Following Ron’s lead, an AIC for the column X-wing plus spoiler is
[X-wing r39c13] = r7c1 – r7c4 = r4c4 - r4c7 = r5c8 => r9c8 <> 7.
But, note that this elimination now makes the “almost” column X-wing a true row X-wing that then forces r7c1 <> 7.

The double elimination suggests that other techniques/patterns are available. E.g., the grouped AIC,
r9c13 = r7c1 - r7c4 = r4c4 - r4c7 = r5c8 => r9c8 <> 7,
yields the same elimination without specifically using r3c13. Still, it seems much easier to initially spot that “almost” X-wing than to pick out the grouped AIC (or a more complex single-digit pattern).
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Para
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PostPosted: Sun Jun 10, 2007 9:07 pm    Post subject: Reply with quote

Hi

Thought you might be interested to know that there is a Finned X-wing
There is a Finned X-wing on R58 with R8C7 being the fin in the grid before the turbot fish that eliminates 7 from both R79C8.

Code:
. . . | . . . | . . .
. . . | . . . | . . .
7 . 7 | . . . | . . .
------+-------+------
. . . | 7 . . | 7 . .
. . . | . . 7*| . 7*.
. . . | . . . | . . .
------+-------+------
7 . . | 7 . 7 | 7 7-.
. . . | . . 7*| 7#7*.
7 . 7 | . . . | . 7-.


greetings

Para
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Sudtyro
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PostPosted: Sun Jun 10, 2007 9:22 pm    Post subject: Reply with quote

Thanks, Para...you are "da Master!"
Memo to self: Submit all future posts before happy hour!
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Myth Jellies
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PostPosted: Thu Jun 14, 2007 2:20 am    Post subject: Reply with quote

Having additional ways to see easily overlooked reductions is no bad thing. Smile
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Sudtyro
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PostPosted: Tue Jul 03, 2007 4:53 pm    Post subject: Reply with quote

MJ,

Regarding your comment, I just recently ran across arcilla’s “a new(?) view of fish (naked or hidden)” 11/3/2006 thread in the other forum. It appears that his technique would very neatly find both the finned and the “almost” X-Wings in the 7’s grid.
Arcilla’s lists for Para's grid would appear as:

Row numbers, per col: (379)(-)(39)(47)(-)(578)(478)(5789)(-)
Col numbers, per row: (-)(-)(13)(47)(68)(-)(14678)(678)(138)

The row numbers reveal c1’s (379) and c3’s (39), for one of the “almost” X-Wings, r7c1 being the spoiler.
The col numbers reveal r3’s (13) and r9’s (138), for the other “almost” X-Wing, r9c8 being the spoiler.
The col numbers also reveal r5’s (68) and r8’s (678), for the finned X-Wing, r8c7 being the fin.
[Edit]: Just noticed that the row numbers also reveal c4's (47) and c7's (478), for yet another finned X-Wing, r8c7 again being the fin.

That seems pretty amazing!


Last edited by Sudtyro on Wed Jul 04, 2007 10:41 am; edited 1 time in total
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Myth Jellies
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PostPosted: Wed Jul 04, 2007 7:19 am    Post subject: Reply with quote

Yes, Arcilla's trick converts fish into either hidden or naked sets. In Arcilla's representation, Almost Locked Sets and Almost Hidden Sets will correspond to finned fish, although the fin may not occupy the same box as any of the fish vertices (which is hard to see in Arcilla's representation) and so might not be immediately useful. Also note that some finned fish can have 2 to 4 candidates in the "fin" and still be immediately useful. These will translate into something more complicated than an ALS, etc.
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Novajlija
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PostPosted: Mon Oct 13, 2008 8:11 pm    Post subject: Reply with quote

Number 4 is LOCKED in R1C1 and R1C3. If there is naked pair 4-7 then we have R1C5=1, R3C4=7, R4C7=7 and R6C3=4. So we ken eliminate number 7 from R1C1 or R1C1=4.

There is few more this kind of elimination...
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