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gindaani
Joined: 06 Mar 2009
Posts: 79
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 Posted: Fri Mar 06, 2009 6:01 pm Post subject: What is this called? |
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This is from the Mar 6 playr.co.uk Fiendish, which you can play Here.
After the basics and an x-chain I have:
| Code: |
+-----------+------------+---------+
| 13 124 7 | 8 34 9 | 12 5 6 |
| 9 12 8 | 45 57 6 | 12 3 47 |
| 36 5 46 | 2 1 347 | 8 9 47 |
+-----------+------------+---------+
| 5 7 9 | 34 34 2 | 6 8 1 |
| 4 8 1 | 7 6 5 | 9 2 3 |
| 2 6 3 | 1 9 8 | 7 4 5 |
+-----------+------------+---------+
| 16 14 2 | 346 8 34 | 5 7 9 |
| 7 3 5 | 9 2 1 | 4 6 8 |
| 8 9 46 | 56 57 47 | 3 1 2 |
+-----------+------------+---------+
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Play this puzzle online at the Daily Sudoku site
if r9c6=4 => r7c6=3, r3c6=7 => r3c9=4 => r3c3<>4 => r9c3=4
Since there cannot be two 4s in r9, the original premise is wrong, and therefore r9c6<>4. That solves the puzzle.
So what is this called?
Is there another solution I missed?
Thanks!
(Fixed typo, thanks Asellus)
Last edited by gindaani on Mon Mar 09, 2009 7:15 pm; edited 3 times in total |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Fri Mar 06, 2009 6:33 pm Post subject: |
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I'm not sure, but it could be the start of a Forcing Chain which led to a contradiction, or invalid solution, that allowed you to solve r9c6.
There is a Type 1 Unique Rectangle on 12 in boxes 1 and 3 which might solve it as well. There's also a W-Wing on 47 linked by the 4s in column 3.
I don't know what terminology you might know or not know, so feel free to ask if there are more questions. |
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gindaani
Joined: 06 Mar 2009
Posts: 79
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| Posted: Fri Mar 06, 2009 6:50 pm Post subject: |
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The UR and W-wing both solve the puzzle. I usually ignore URs. Not sure how I missed the W-wing, it looks pretty obvious now. 
I do this sort of chain a lot when I don't see something else quickly. It is a forcing chain that leads to a contradiction. I was hoping it had a neat little name like everything else. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sat Mar 07, 2009 1:25 am Post subject: |
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There is another W-wing 47 connected by 7 in C5. With pincer coloring, it makes an elimination.
There is a 4-cell chain that takes out 3 in R3C6 - 36 16 14 34.
Keith |
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gindaani
Joined: 06 Mar 2009
Posts: 79
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| Posted: Sat Mar 07, 2009 2:02 am Post subject: |
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| So how do you find those chains (xy-chain)? Do you start at every pair until you find one (or dont), or is there some way of spotting them? |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sat Mar 07, 2009 3:02 am Post subject: |
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| gindaani wrote: | | So how do you find those chains (xy-chain)? Do you start at every pair until you find one (or dont), or is there some way of spotting them? |
I began to find them as sort of an extension of an XY-wing. In this case, notice that you can collapse 36 16 14 34 in a number of ways. Suppose you are looking for an XY-wing, and notice 36 16. So, you are looking for 13 to complete the wing. Together, 14 and 34 behave like a "pseudo-cell" 13.
So, if I can't find any XY-wings, I look at pairs of cells like WZ and WY. Together they make XZ, can I fit that in a pattern?
Or, if an XY-wing is a 3-cell chain
XZ - XY - YZ, with pincers Z,
the 4-cell chain is
XZ - XY - WY - WZ, with pincers Z.
It took me some practice, a couple of weeks, but I now find these not much harder to spot than XY-wings.
I hope this helps,
Keith |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Sat Mar 07, 2009 6:08 am Post subject: |
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| gindaani wrote: | | So what is this called? |
First, noting that "r7c6=4" should really be "r7c6=3", you could call it an "XYZ-Wing with Transport". The XYZ-Wing is on 347 in r3c69 and r7c6. By itself, this is useless because of the geometry: there are no common peers of those three cells so no <4> eliminations. However, the two <4>s in r3c69 (considered together as a group) can be transported to r9c3 (via r3c3). Then, r7c6 and r3c3 work together as pincers to eliminate <4> from r9c6.
You could work it the other way and transport r7c6 to r9c3 (via r9c6) and eliminate <4> from r3c3. The <4> at r9c3 and the grouped <4>s at r3c69 are the pincers in that case.
Sometimes what look like useless wing patterns can be useful if a pincer can be transported. |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Sat Mar 07, 2009 11:09 am Post subject: |
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| Asellus wrote: | | gindaani wrote: | | So what is this called? |
First, noting that "r7c6=4" should really be "r7c6=3", ... |
Thanks Asellus! Your correction opened my eyes.
To me, gindaani is using an Error Net / SIN (Single Implication Network) because not all assignments follow from the preceeding step as in a "chain". |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Mon Mar 09, 2009 6:19 pm Post subject: |
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Asellus, you have again exposed me to another solution technique; thanks!
Looking at the posted code, I believe I found still another view of the xyz-wing with transport. The xyz-wing is r39c6 and pseudo-cell <34> in r3c13. Then transport <4> in r9c6 to r3c3 via r9c3 to delete <4> in r3c9.
Ted |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Mon Mar 09, 2009 7:07 pm Post subject: |
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| tlanglet wrote: | Looking at the posted code, I believe I found still another view of the xyz-wing with transport. The xyz-wing is r39c6 and pseudo-cell <34> in r3c13. Then transport <4> in r9c6 to r3c3 via r9c3 to delete <4> in r3c9.
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Ted: If you consider just the transport on <4>, you have ...
(7)r3c6 - (7=4)r9c6 - (4)r9c3 = (4)r3c3 - (4=7)r3c9 => [r3c6]<>7 |
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gindaani
Joined: 06 Mar 2009
Posts: 79
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| Posted: Mon Mar 09, 2009 7:18 pm Post subject: |
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| What syntax is that? And/or can you put that in words? |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Mon Mar 09, 2009 7:51 pm Post subject: |
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| gindaani wrote: | | What syntax is that? And/or can you put that in words? |
It is called Eureka notation. It says:
If you assume r3c6=7,
then r9c6 <>7, it is 4,
then r9c3 <> 4
then r3c3 = 4,
then r3c9 <> 4, it is 7.
This would create an invalid condition since two <7s> would be in row 3; so r3c6 <>7.
Hope this helps........
Ted |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Tue Mar 10, 2009 4:43 am Post subject: |
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| daj95376 wrote: | Ted: If you consider just the transport on <4>, you have ...
(7)r3c6 - (7=4)r9c6 - (4)r9c3 = (4)r3c3 - (4=7)r3c9 => [r3c6]<>7 |
Yes, Marty already pointed out this W-Wing.
And yes, gindaani was using forcing (SIN, etc.) in the original description of the <4> elimination. I just wanted to show that resort to forcing wasn't necessary.
As for Eureka notation, the "if this is true, then that is false, etc." approach is one way to understand it. Better, in my opinion, is to learn to see it in terms of the inferences and Alternate Implication Chains (AIC). The terms and concepts involved are explained in various places online (such as Sudopedia). [Note: I hasten to add that someone still getting started in advanced sudoku solving techniques should probably focus most of all on learning the common "wings" and other techniques, and then ease into learning about these implications, etc.]
Meanwhile, I would revise the notation above slightly then explain the notated chain this way:
(7)r3c6 - (7=4)r9c6 - (4)r9c3=(4)r3c3 - (4=7)r3c9 - (7)r3c6; r3c6<>7
Looking at the blue part of the notation, the <7> and <4> in r9c6 have a strong inference (cannot both be false), denoted by the "=" symbol, because they form a bivalue cell. The two <4>s in r9c3 and r3c3 have a strong inference because they are the only two <4>s in column 3. And again, in r3c9, we have a bivalue cell for another strong inference.
The <4>s in r9c6 and r9c3 have a weak inference (cannot both be true), denoted by the "-" symbol, because they share a house, row 9 in this case. Similarly, the <4>s in r3c3 and r3c9 have a weak inference in row 3.
The inferences ("implications") in the blue section alternate strong-weak-strong-weak-strong, or "= - = - =". In such a chain of alternating implications (AIC), the implications propagate. So, the <7>s that are connected to the two ends, at r9c6 and r3c9, by strong inferences themselves have a strong inference between them. That is, they cannot both be false. Any <7> that can "see" both of these <7>s (or more generally, any <7>s with a weak inference to both of these) cannot be true. The (non-blue) <7> at r3c6 shown attached by a weak inference on both ends, thus cannot be true. This conclusion is stated explicitly after the semicolon. (Some people use "=>" in place of the semicolon. But I don't like having a "=" sign in the notation that does not mark a strong inference so prefer the semicolon.)
It's not as easy to describe as the "If... then..." approach! But, it is ultimately a more revealing and useful way to see the notation. This description is not complete: several additional things could be mentioned. But, it paints an adequate introductory picture, I believe. |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Tue Mar 10, 2009 5:14 am Post subject: |
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| Asellus wrote: | | daj95376 wrote: | Ted: If you consider just the transport on <4>, you have ...
(7)r3c6 - (7=4)r9c6 - (4)r9c3 = (4)r3c3 - (4=7)r3c9 => [r3c6]<>7 |
Yes, Marty already pointed out this W-Wing.
Meanwhile, I would revise the notation above slightly then explain the notated chain this way:
(7)r3c6 - (7=4)r9c6 - (4)r9c3=(4)r3c3 - (4=7)r3c9 - (7)r3c6; r3c6<>7
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Marty: My apologies for not catching that my chain overlapped your W-Wing.
Asellus: Yes, your additional link in my chain makes more sense. If I'd meant to identify the W-Wing, then I would have only used the part you highlighted in blue.
However, my thoughts were focused on Ted's XYZ-Wing correlation and the stream from the assumption [r3c6]=7. |
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