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5/13/07 Nightmare
Posted: Sun May 20, 2007 9:42 pm
by Sudtyro
After running through the basics:
Code: Select all
----------------------------------------------------
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?
Posted: Mon May 21, 2007 6:19 am
by Jean-Christophe
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
And another question...
Posted: Mon May 21, 2007 10:58 am
by Sudtyro
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?
Re: And another question...
Posted: Mon May 21, 2007 2:14 pm
by Jean-Christophe
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.
Uniqueness Argument
Posted: Mon May 28, 2007 3:25 pm
by Ron Moore
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: Select all
----------------------------------------------------
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.
Re: Uniqueness Argument
Posted: Fri Jun 01, 2007 11:10 am
by Sudtyro
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
5/13/07 Nightmare - revisited
Posted: Sun Jun 10, 2007 8:57 pm
by Sudtyro
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: Select all
. . . | . . . | . . .
. . . | . . . | . . .
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).
Posted: Sun Jun 10, 2007 9:07 pm
by Para
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: Select all
. . . | . . . | . . .
. . . | . . . | . . .
7 . 7 | . . . | . . .
------+-------+------
. . . | 7 . . | 7 . .
. . . | . . 7*| . 7*.
. . . | . . . | . . .
------+-------+------
7 . . | 7 . 7 | 7 7-.
. . . | . . 7*| 7#7*.
7 . 7 | . . . | . 7-.
greetings
Para
Posted: Sun Jun 10, 2007 9:22 pm
by Sudtyro
Thanks, Para...you are "da Master!"
Memo to self: Submit all future posts before happy hour!
Posted: Thu Jun 14, 2007 2:20 am
by Myth Jellies
Having additional ways to see easily overlooked reductions is no bad thing.
Posted: Tue Jul 03, 2007 4:53 pm
by Sudtyro
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!
Posted: Wed Jul 04, 2007 7:19 am
by Myth Jellies
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.
Posted: Mon Oct 13, 2008 8:11 pm
by Novajlija
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...