## Times superfiendish '09.Mar.6 -- Almost x-wing

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### Times superfiendish '09.Mar.6 -- Almost x-wing

The Time super fiendish last Friday (6th March) ended up after simple elimination with R8 and R9 as follows:

Code: Select all
`| x  x  68  | 628  x  x  |  x  x  62 || x  x  68  | x   62  x  | 628 x  x  |`

This is amost an x-wing in 6 and 6 in R9C5 is eliminated because,
r9c3=6 => r9c5=2
r9c3=8 => r8c3=6 => r8c9=2 => r9c7=6 => r9c5=2 (corrected typo)

In this particular puzzle this pattern could be found without PM and once we have 6 eliminated from r9c5 the rest of the puzzle solves with simple elimination.

My question is: what's the name of the general technique that this pattern is part of?

the original puzzle:

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

Richard
Last edited by richardm on Tue Mar 10, 2009 11:26 am, edited 1 time in total.
richardm

Posts: 53
Joined: 27 December 2006

### Re: Almost x-wing

richardm wrote:This is amost an x-wing in 6 and 6 in R9C5 is eliminated because,
r9c3=6 => r9c5=2
r9c3=8 => r8c3=6 => r8c9=2 => r9c7=6 => r9c5=6
.
.
.
My question is: what's the name of the general technique that this pattern is part of?
It looks to me that you've used a double implication chain (you need to correct the 2nd chain to r9c5=2)

tarek
Last edited by tarek on Sun Mar 08, 2009 3:38 am, edited 1 time in total.

tarek

Posts: 2761
Joined: 05 January 2006

### Re: Almost x-wing

richardm wrote:The Time super fiendish last Friday (6th March) ended up after simple elimination with R8 and R9 as follows:

Code: Select all
`| x  x  68  | 628  x  x  |  x  x  62 || x  x  68  | x   62  x  | 628 x  x  |`

This is amost an x-wing in 6 and 6 in R9C5 is eliminated

There is something there, but I see it as a W-wing. You've got two cells with (26) linked by the conjugate 6's in box 7. That means that any (2) that can see both the (26) cells can be eliminated, =>r8c4,r9c7<>2.

That leads to the eliminations you found. I don't think I see an almost X-wing yet, as I know it.

Luke
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Location: Southern Northern California

A better title for this thread would have been 'Question about Mar 6 Fiendish.'
thanks, i've adjusted the title
-- Moderator (Pat)
DonM
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Joined: 13 January 2008

### Re: Almost x-wing

tarek wrote:It looks to me that you've used a double implication chain

I think that is the answer Richard was looking for. May I ask, is a "double implication chain" also known as a forcing chain (as differentiated from a NL or AIC)? I have never learned about certain forcing chains because I gathered some time ago that there is a stigma associated with their use.

Curious, my choice, because "stigma" has never deterred me from using uniqueness techniques.....

Luke
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Location: Southern Northern California

They are forcing chains ....

Because each candicate from the start cell will result in the same ending thus FORCING it.

tarek

tarek

Posts: 2761
Joined: 05 January 2006

### Re: Almost x-wing

Luke451 wrote:
tarek wrote:It looks to me that you've used a double implication chain

I think that is the answer Richard was looking for. May I ask, is a "double implication chain" also known as a forcing chain (as differentiated from a NL or AIC)? I have never learned about certain forcing chains because I gathered some time ago that there is a stigma associated with their use.

Curious, my choice, because "stigma" has never deterred me from using uniqueness techniques.....

Not so curious. This type of forcing chain involves a rather random exercise: pick a random bivalue cell and test each possible value until a conflict occurs. On the other hand uniqueness techniques are based on hard core application of uniqueness logic (not too mention that IMO these days there is no guessing when it comes to whether the puzzle has one solution). Long story short, I think the overwhelming acceptance of uniqueness techniques these days removes any last vestige of stigma, although I've never accepted the uniqueness stigma label anyway.
DonM
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Posts: 475
Joined: 13 January 2008

### Re: Almost x-wing

tarek wrote:
richardm wrote:This is amost an x-wing in 6 and 6 in R9C5 is eliminated because,
r9c3=6 => r9c5=2
r9c3=8 => r8c3=6 => r8c9=2 => r9c7=6 => r9c5=2
.
.
.
My question is: what's the name of the general technique that this pattern is part of?
It looks to me that you've used a double implication chain.

I'm not convinced that it's a DIC. The key letter in this abbreviation is the C. However, the only way he can deduce r9c7=6 is if the r9c3=8 assignment has the downstream effect of r9c7<>8. I see this as a forcing network variant.
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

### Re: Almost x-wing

richardm wrote:This is amost an x-wing in 6 and 6 in R9C5 is eliminated because,
r9c3=6 => r9c5=2
r9c3=8 => r8c3=6 => r8c9=2 => r9c7=6 => r9c5=6

A shorter version:
Code: Select all
`r9c3=6 => r9c5=2r9c3=8 => r8c4=8 => r9c5=2`

The move written as Nice Loop:
Discontinuous Nice Loop r9c5 -6- r9c3 -8- r8c3 =8= r8c4 =2= r9c5 => r9c5<>6
hobiwan
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Location: Klagenfurt

### Re: Almost x-wing

daj95376 wrote:
tarek wrote:
richardm wrote:This is amost an x-wing in 6 and 6 in R9C5 is eliminated because,
r9c3=6 => r9c5=2
r9c3=8 => r8c3=6 => r8c9=2 => r9c7=6 => r9c5=2
.
.
.
My question is: what's the name of the general technique that this pattern is part of?
It looks to me that you've used a double implication chain.

I'm not convinced that it's a DIC. The key letter in this abbreviation is the C. However, the only way he can deduce r9c7=6 is if the r9c3=8 assignment has the downstream effect of r9c7<>8. I see this as a forcing network variant.

Just a little bit of memory...
aran

Posts: 334
Joined: 02 March 2007

### Re: Almost x-wing

DonM wrote:
Luke451 wrote:
tarek wrote:It looks to me that you've used a double implication chain

I think that is the answer Richard was looking for. May I ask, is a "double implication chain" also known as a forcing chain (as differentiated from a NL or AIC)? I have never learned about certain forcing chains because I gathered some time ago that there is a stigma associated with their use.

Curious, my choice, because "stigma" has never deterred me from using uniqueness techniques.....

Not so curious. This type of forcing chain involves a rather random exercise: pick a random bivalue cell and test each possible value until a conflict occurs. On the other hand uniqueness techniques are based on hard core application of uniqueness logic (not too mention that IMO these days there is no guessing when it comes to whether the puzzle has one solution). Long story short, I think the overwhelming acceptance of uniqueness techniques these days removes any last vestige of stigma, although I've never accepted the uniqueness stigma label anyway.

On uniqueness techiques : IMO these provide a touch of class, and a degree of variety. Stigma is the last word I ever would have applied to them.

On forcing chains : as Hobiwan showed for the example above, and as is true for any forcing chain, these can always be presented as a discontinuous loop starting on "x-" (ie "true"=>) (DLx-) where x is the eliminated candidate.
But then any elimination however obtained can be presented as a DLx- where x is the eliminated candidate.

For that reason I seldom and almost never consider any logic starting with : if x is true what happens.

Lastly, one could note that the final step in a DLx- is always : x-x. (eg suppose loop began 5- in r1c9, then it will end for example : ......4r3c5-6r3c1=5r1c1-5r1c9 (highlighted the x-x ending).
This can equally be interpreted as a contradiction (two 5s row 1).
In Dlx- the solver closes the loop rather than calling out "contradiction" but it is exactly the same thing.
In other words, to be in favour of DLx- and opposed to contradiction would be a contradictory position
Personally I am not much in favour of DLx- and not particularly opposed to contradiction.
aran

Posts: 334
Joined: 02 March 2007

Of all the moves presented, I see Luke's w-wing as the most elegant. However I don't think it is the intended move for this puzzle, as it's still supposed to be solved pencilmarkless.

Here is a pencilmarkless approach:

After singles:

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

Focus on the digit 2, for c469, only r258c469 (*) can have 2. As a result, 2 can't appear elsewhere on r258 (this is called a swordfish). In particular, r5c27 (#) can't have 2, and are forced to be [68].

udosuk

Posts: 2698
Joined: 17 July 2005

daj95376 wrote:
tarek wrote:
richardm wrote:
Code: Select all
`-------+-------+------ 2 3 4 | . . . | 1 . .  9 5 . | . 1 4 | 7 3 .  1 7 . | 3 . 5 | . 9 4 `

This is amost an x-wing in 6 and 6 in R9C5 is eliminated because,
r9c3=6 => r9c5=2
r9c3=8 => r8c3=6 => r8c9=2 => r9c7=6 => r9c5=2

My question is: what's the name of the general technique that this pattern is part of?
It looks to me that you've used a double implication chain.

I'm not convinced that it's a DIC. The key letter in this abbreviation is the C. However, the only way he can deduce r9c7=6 is if the r9c3=8 assignment has the downstream effect of r9c7<>8. I see this as a forcing network variant.

yes, what richardm used is a "net" rather than a "chain"
he could instead use a "chain"
e.g.
Code: Select all
`r8c3=6 --> r8c9=2 --> r9c5=2r9c3=6 --> r9c5=2`
as udosuk said, the puzzle is of course meant to be solved by the Swordfish

Pat

Posts: 3676
Joined: 18 July 2005

Unfortunately, the term, 'forcing chain' seems to be the source of a lot of confusion and the following Forcing Net definition from Sudopedia seems to indicate why:

A Forcing Net shows a contradiction or a verity which is caused by testing a candidate. Also known as Generalized Forcing Chain. The term Contradiction Net is also used when the Forcing Net is used to derive a contradiction. Unlike a Forcing Chain, which requires a single stream of implications, a Forcing Net allows branching and merging, making it a lot more complicated than a single chain. Whenever possible, players avoid this solving technique.

So, Pat & Daj are correct that what RichardM used is a Forcing Net (in this case showing a 'verity' as per the definition above), but I think the fact that it is 'also known as a Generalized Forcing Chain' continues to confuse things. I mention this because what is really a forcing net is often defined/described as a forcing chain in tutorials. Just one example:

http://www.palmsudoku.com/pages/techniques-10.php

Edited to further clarify so that people can decide which side of the 'forcing chain' vs. 'forcing net' vs. 'something else' fence they're on.
Last edited by DonM on Mon Mar 09, 2009 1:32 am, edited 3 times in total.
DonM
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Posts: 475
Joined: 13 January 2008

DonM wrote:forcing net is often defined/described as a forcing chain in tutorials.
So, Pat & Daj are correct that what RichardM used is a Forcing Net

No; they are quite wrong.
aran

Posts: 334
Joined: 02 March 2007

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