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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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 Posted: Sat Apr 26, 2008 12:20 am Post subject: old post from sudocue |
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| Code: | .2.|...|.7.
9..|5.8|..4
...|...|...
---+---+---
4..|.3.|..8
.7.|.9.|.2.
6..|.1.|..5
---+---+---
...|...|...
5..|6.4|..1
.3.|...|.9. |
http://www.sudocue.net/forum/viewtopic.php?t=52
this one wasn't commented on after it was posted on the sudocue site. it deserves examination because it doesn't give up singles from the start and there are some techniques that you may or may not need but are present.
Last edited by storm_norm on Sat Apr 26, 2008 3:50 am; edited 1 time in total |
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sheryl
Joined: 24 Sep 2007
Posts: 64
Location: New York
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| Posted: Sat Apr 26, 2008 2:52 am Post subject: |
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| i have a comment. Help! |
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Sat Apr 26, 2008 10:53 am Post subject: |
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xwing 2 and xwing 7. both in rows 2 and 8.
| Code: |
+--------------------------+--------------------------+--------------------------+
| 138 2 134568 | 139 46 139 | 13568 7 369 |
| 9 16 1367 | 5 267 8 | 1236 136 4 |
| 1378 1456 1345678 | 12379 2467 12379 | 123568 13568 2369 |
+--------------------------+--------------------------+--------------------------+
| 4 15 29 | 27 3 56 | 79 16 8 |
| 138 7 1358 | 48 9 56 | 1346 2 36 |
| 6 89 2389 | 48 1 27 | 79 34 5 |
+--------------------------+--------------------------+--------------------------+
| 1278 146 14678 | 39 2578 39 | 24568 4568 267 |
| 5 89 789 | 6 278 4 | 238 38 1 |
| 278 3 4678 | 127 2578 127 | 24568 9 267 |
+--------------------------+--------------------------+--------------------------+
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This is where it gets much harder. Useless xy-wing...
| Code: |
+--------------------------+--------------------------+--------------------------+
| 138 2 134568 | 139 46 139 | 13568 7 369 |
| 9 16 1367 | 5 27 8 | 1236 136 4 |
| 1378 1456 134568 | 12379 46 12379 | 13568 13568 2369 |
+--------------------------+--------------------------+--------------------------+
| 4 15 29 | 27 3 56 | 79 16 8 |
| 138 7 1358 | 48 9 56 | 1346 2 36 |
| 6 89 2389 | 48 1 27 | 79 34 5 |
+--------------------------+--------------------------+--------------------------+
| 27 146 146 | 39 58 39 | 4568 4568 27 |
| 5 89 789 | 6 27 4 | 238 38 1 |
| 278 3 46 | 127 58 127 | 4568 9 267 |
+--------------------------+--------------------------+--------------------------+
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play online[/code]
some chains. a UR. hm. don't know where it leads, must hurry (lunch) |
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Sat Apr 26, 2008 11:53 am Post subject: |
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ok, back to "work" now.
Te useless xy-wing 38-34-48 caught my attention. It can be transported with the 89-89 combination in col 2 to pincers r8c2 and r8c8, removing 8 from r8c3 and r8c7. But I did not see that immediately, instead found this:
xy-chain 34-48-89 (row 6) -89-38 (row 8), which eliminates 3 from col 8 in rows 2 and 3, most notably r2c8, which together with r2c2 and r4c8, respectively, makes a naked pair 16 both in row 2 and col 8.
After cleanup and some basic steps, x-wing on 1 and multi-coloring on 3 are two options to get us into the final stretch home.
Not an easy one by any measure. |
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ravel
Joined: 21 Apr 2006
Posts: 536
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| Posted: Sat Apr 26, 2008 12:18 pm Post subject: |
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Nice pattern and interesting puzzle.
Before getting a single number i could use an arsenal of techniques including hidden/naked pairs and triples, x-wings, UR, kite, w-wing, half M-wing ...
From about nataraj's second grid i solved it with the UR 27 in r79c19 (r9c1=8 or r9c9=6):
r9c9=6 => r9c3=4
r9c1=8 => r6c2=8 => r6c4=4, then r5c7=4 => r7c8=4 => r9c3=4
The rest was easy. |
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sheryl
Joined: 24 Sep 2007
Posts: 64
Location: New York
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| Posted: Sat Apr 26, 2008 1:34 pm Post subject: |
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nataraj, you wrote: | Quote: | xy-chain 34-48-89 (row 6) -89-38 (row  , which eliminates 3 from col 8 in rows 2 and 3, most notably r2c8, which together with r2c2 and r4c8, respectively, makes a naked pair 16 both in row 2 and col 8. |
i was under the impression that an xy chain had to eliminate a candidate in the same manner that an xy wing did. what i mean is that an xy wing the pincers have to see the same candidate. in this chain, both pincers end up in the same column, the 34 starts the cain in col. 8 and the 38 ends the cain in col. 8. I did not know that that was allowed. |
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Sat Apr 26, 2008 2:55 pm Post subject: |
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| sheryl wrote: | | i was under the impression that an xy chain had to eliminate a candidate in the same manner that an xy wing did. what i mean is that an xy wing the pincers have to see the same candidate. in this chain, both pincers end up in the same column, the 34 starts the cain in col. 8 and the 38 ends the cain in col. 8. I did not know that that was allowed. |
Sheryl, your impression is correct. The priciple is always that both pincers have to "see" a common candidate. Otherwise the pattern is useless. In our case they both see all candidates in column 8.
Why is this different in an xy-wing?
Because of the way an xy-wing is constructed (only 3 cells), when the pincers are in the same house, the pivot cell is in the same house, too, and all three cells form a naked triple or the pincer cells remove the other candidatess by simple box/line interaction. That's why you never find an xy-wing with pincers in the same column - or maybe I should say that one finds them quite often but the pattern is not called xy-wing but naked triple or box/line intreraction (a.k.a. pointing pairs). |
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sheryl
Joined: 24 Sep 2007
Posts: 64
Location: New York
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| Posted: Sat Apr 26, 2008 3:03 pm Post subject: |
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okay, thanks. it still seems wrong, but i shall take your word for it!  |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sat Apr 26, 2008 3:45 pm Post subject: |
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| sheryl wrote: | | okay, thanks. it still seems wrong, but i shall take your word for it! |
Good idea, to take nataraj's word for it, he knows of what he speaks.
But what seems wrong? The chain does start and end in c8, but so what? The chain proves that either r6c8 or r8c8 must be = 3. There's no right or wrong about it and it's an inescapable fact; in this particular puzzle the 3 in c8 must be in one of those two cells, so just proceed and eliminate the other 3s which we've proven can't exist in their current locations. |
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sheryl
Joined: 24 Sep 2007
Posts: 64
Location: New York
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| Posted: Sat Apr 26, 2008 4:00 pm Post subject: |
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| Quote: | | But what seems wrong? The chain does start and end in c8, but so what? The chain proves that either r6c8 or r8c8 must be = 3. There's no right or wrong about it and it's an inescapable fact; in this particular puzzle the 3 in c8 must be in one of those two cells, so just proceed and eliminate the other 3s which we've proven can't exist in their current locations. |
the reason it seems wrong is that it is so different from an xy wing which can't be in the same house. this is an xy chain so one would think it works the same way as an xy wing but is a chain instead of a wing but obviously one would be wrong! to think that. |
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sheryl
Joined: 24 Sep 2007
Posts: 64
Location: New York
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| Posted: Sat Apr 26, 2008 4:14 pm Post subject: |
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nataraj:
| Quote: | | Te useless xy-wing 38-34-48 caught my attention. It can be transported with the 89-89 combination in col 2 to pincers r8c2 and r8c8, removing 8 from r8c3 and r8c7. But I did not see that immediately, instead found this: |
can you explain how this works, please? i know the xy wing which doesn't remove anything. how does it affect the 89s in col. 2? |
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Sat Apr 26, 2008 4:36 pm Post subject: |
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| sheryl wrote: | nataraj:
| Quote: | | Te useless xy-wing 38-34-48 caught my attention. It can be transported with the 89-89 combination in col 2 to pincers r8c2 and r8c8, removing 8 from r8c3 and r8c7. But I did not see that immediately, instead found this: |
can you explain how this works, please? i know the xy wing which doesn't remove anything. how does it affect the 89s in col. 2? |
Glad to.
38 in r8c8 and 48 in r6c4 are connected by 34 in r6c8, forming an xy-wing. This xy-wing says that when r8c8 is not 8, then r6c4 is (and vice versa).
Unfortunately, as you've pointed out, there are no cells that have a candidate 8 and see both r8c8 and r6c4.
Now comes the transport: if r6c4=8, then ("weak" link in row 6) r6c2 is not 8 and ("strong" link in column 2) r8c2=8.
Let's take both the xy-wing and the transport together:
If r8c8 is not 8 then r6c4=8 (xy-wing) and (transport) r8c2=8.
All cells that see both r8c8 and r8c2 cannot contain 8.
Another example of an xy-chain with both ends in the same house ... |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sat Apr 26, 2008 4:52 pm Post subject: |
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| sheryl wrote: | | Quote: | | But what seems wrong? The chain does start and end in c8, but so what? The chain proves that either r6c8 or r8c8 must be = 3. There's no right or wrong about it and it's an inescapable fact; in this particular puzzle the 3 in c8 must be in one of those two cells, so just proceed and eliminate the other 3s which we've proven can't exist in their current locations. |
the reason it seems wrong is that it is so different from an xy wing which can't be in the same house. this is an xy chain so one would think it works the same way as an xy wing but is a chain instead of a wing but obviously one would be wrong! to think that. |
I wonder if the fact that both techniques have "XY" at the start of the name gives an impression or more similarity than there really is. As has been stated earlier, you can have something in one house which meets the criteria of an XY-Wing: an XY cell which sees both an XZ and YZ cell. However, that is a naked triple and all other candidates XYZ in that house are eliminated, not just Z, as is the case with an XY-Wing.
In the case of the XY-Chain, there are four houses in that short chain; it just so happens that the chain starts and ends in the same house. |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Sat Apr 26, 2008 8:11 pm Post subject: |
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| Marty R. wrote: | | sheryl wrote: | | Quote: | | But what seems wrong? The chain does start and end in c8, but so what? The chain proves that either r6c8 or r8c8 must be = 3. There's no right or wrong about it and it's an inescapable fact; in this particular puzzle the 3 in c8 must be in one of those two cells, so just proceed and eliminate the other 3s which we've proven can't exist in their current locations. |
the reason it seems wrong is that it is so different from an xy wing which can't be in the same house. this is an xy chain so one would think it works the same way as an xy wing but is a chain instead of a wing but obviously one would be wrong! to think that. |
I wonder if the fact that both techniques have "XY" at the start of the name gives an impression or more similarity than there really is. As has been stated earlier, you can have something in one house which meets the criteria of an XY-Wing: an XY cell which sees both an XZ and YZ cell. However, that is a naked triple and all other candidates XYZ in that house are eliminated, not just Z, as is the case with an XY-Wing.
In the case of the XY-Chain, there are four houses in that short chain; it just so happens that the chain starts and ends in the same house. |
I would love to give this technique a different name because it is actually more powerful than a typical xy-chain which usually makes eliminations with two pincers cells.
here is the bottom portion of the grid after the x-wing on 2 and 7
| Code: | 6 #89 2389 |#48 1 27 | 79 #34 5
-------------------------------------------------------------
1278 146 14678 | 39 2578 39 | 24568 4568 267
5 #89 789 | 6 278 4 | 238 #38 1
278 3 4678 | 127 2578 127 | 24568 9 267 |
this configuration of this xy-chain actually contains pincers on all sides of the "loop". Susser calls it a "simple forcing loop".
looks more like a rectangle to me. |
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Sat Apr 26, 2008 8:40 pm Post subject: |
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| storm_norm wrote: | this configuration of this xy-chain actually contains pincers on all sides of the "loop". Susser calls it a "simple forcing loop".
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So it must be an xy-loop ... 
"Ma, I accidentally stepped on a xy-loop"
-
"Go clean your boots!" |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Sat Apr 26, 2008 8:44 pm Post subject: |
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| nataraj wrote: | | storm_norm wrote: | this configuration of this xy-chain actually contains pincers on all sides of the "loop". Susser calls it a "simple forcing loop".
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So it must be an xy-loop ...
"Ma, I accidentally stepped on a xy-loop"
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"Go clean your boots!" |
xy-loop works for me |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Sat Apr 26, 2008 9:27 pm Post subject: |
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Just in case it's not clear to some folks out there, an XY Loop is powerful: every link in the loop becomes a strong link. So, that XY Loop is much more than just the XY Wing with transported pincer that nataraj mentions, and it eliminates more than just the <8>s in r8c37. It also eliminates the <8> in r6c3 and the <3>s in r23c8!
And, it would eliminate any other <4>s in r6 (if there were any), and any other <9>s in c2 (if there were any).
XY Loops don't turn up that often. But, they are nice when they do.
By the way, the same principle holds for an ALS (Chain) Loop or for any sort of AIC Loop. |
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Sat Apr 26, 2008 9:38 pm Post subject: |
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| Asellus wrote: | Just in case it's not clear to some folks out there, an XY Loop is powerful
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Shame on me for not recogizing it for what it was.
And kudos to Norm who did! |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Sun Apr 27, 2008 2:41 pm Post subject: |
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| nataraj wrote: |
This is where it gets much harder. Useless xy-wing...
| Code: |
+--------------------------+--------------------------+--------------------------+
| 138 2 134568 | 139 46 139 | 13568 7 369 |
| 9 16 1367 | 5 27 8 | 1236 136 4 |
| 1378 1456 134568 | 12379 46 12379 | 13568 13568 2369 |
+--------------------------+--------------------------+--------------------------+
| 4 15 29 | 27 3 56 | 79 16 8 |
| 138 7 1358 | 48 9 56 | 1346 2 36 |
| 6 89 2389 | 48 1 27 | 79 34 5 |
+--------------------------+--------------------------+--------------------------+
| 27 146 146 | 39 58 39 | 4568 4568 27 |
| 5 89 789 | 6 27 4 | 238 38 1 |
| 278 3 46 | 127 58 127 | 4568 9 267 |
+--------------------------+--------------------------+--------------------------+
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play online[/code]
some chains. a UR. hm. don't know where it leads, must hurry (lunch) |
Starting from the code posted by Nataraj, I found 2 swordfish, one on<3> in r268c378 and on <1> in r247c238, plus more basics including hidden sets to solve the puzzle.
Ted |
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sheryl
Joined: 24 Sep 2007
Posts: 64
Location: New York
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| Posted: Sun Apr 27, 2008 3:33 pm Post subject: |
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| CAN someone explain to me: how did this come up as posted today" when we did it a few days ago?? |
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