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What can we call this?
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Marty R.



Joined: 12 Feb 2006
Posts: 5121
Location: Rochester, NY, USA

PostPosted: Thu Jul 01, 2010 9:33 pm    Post subject: What can we call this? Reply with quote

It's the case where a pincer situation is created from a UR.

Suppose we have something like:

Code:

+-------+-----------+-------+
| . . . | 457 . 459 | . . . |
| . . . | .   . .   | . . . |
| . . . | .   . .   | . . . |
+-------+-----------+-------+
| . . . | .   . .   | . . . |
| . . . | 45  . 45  | . . . |
| . . . | .   . .   | . . . |
+-------+-----------+-------+
| . . . | .   . .   | . . . |
| . . . | .   . .   | . . . |
| . . . | .   . .   | . . . |
+-------+-----------+-------+

Play this puzzle online at the Daily Sudoku sitehave:

This UR may or not qualify as a Type 4, it doesn't matter. The DP can be killed with a 7 or 9. If the 7 proves a 9 somewhere or if the 9 proves a 7, we have a pincer situation.

Can anyone suggest some terminology?
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tlanglet



Joined: 17 Oct 2007
Posts: 2461
Location: Northern California Foothills

PostPosted: Fri Jul 02, 2010 12:14 pm    Post subject: Reply with quote

Marty,

I also have wondered how to post this situation; to date I have beat around the bush and simply stated the end result.

Also, I believe your question could be expanded to include the case where the two pincer force or delete a totally different digit.

It would be surprising to me if some terminology has not already been suggested, but if not I offer the term "transport" as a general term for AIC type extensions since coloring is associated with a single digit.

Ted
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Fri Jul 02, 2010 2:52 pm    Post subject: Re: What can we call this? Reply with quote

[Withdrawn: I don't understand Marty's objective.]

Last edited by daj95376 on Mon Jul 05, 2010 2:37 am; edited 1 time in total
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Marty R.



Joined: 12 Feb 2006
Posts: 5121
Location: Rochester, NY, USA

PostPosted: Fri Jul 02, 2010 4:58 pm    Post subject: Reply with quote

Quote:
I'm not absolutely sure of your point, but I might write:

Danny, as far as I know, every technique, even though it can be expressed via notation, has a name and I was wondering what a name for this could be. When I've used it I've said that I used the UR to create a pincer situation and that doesn't sound very good to me.
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keith



Joined: 19 Sep 2005
Posts: 3150
Location: near Detroit, Michigan, USA

PostPosted: Fri Jul 02, 2010 8:46 pm    Post subject: Reply with quote

Marty,

The UR creates a "pseudocell" that acts like a single cell 79. So, suppose you have:
Code:
+-------+-----------+--------+
| . . . | 457 . 459 | . 67 . |
| . . . | .   . .   | . .  . |
| . . . | .   . .   | . .  . |
+-------+-----------+--------+
| . . . | .   . .   | . .  . |
| . . . | 45  . 45  | . .  . |
| . . . | .   . .   | . .  . |
+-------+-----------+--------+
| . . . | .   . .   | . .  . |
| . . . | .   . 69  | . -6 . |
| . . . | .   . .   | . .  . |
+-------+-----------+--------+

The pseudocell is now the hinge of an XY-wing -679. I would say: "The UR forms a pseudocell 79, leading to an XY-wing -679 that eliminates 6 in R8C8."

Ted,

I don't like the term "transport" in this case. We use transport to describe the extension of a pincer to another cell of the same value. For example, we have an XY-wing with pincers 6:

69 - 79 - 67

We extend the right pincer by:

69 - 79 - 67 - a7 = b7

7 in 67 causes 7 in b7. a and b are any candidates.

Marty is looking for a term to say "9 in 79 causes 7 in some other cell".

Opinionated best wishes,

Keith
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Sat Jul 03, 2010 3:42 pm    Post subject: Reply with quote

[Withdrawn: I don't understand Marty's objective.]

Last edited by daj95376 on Mon Jul 05, 2010 2:38 am; edited 1 time in total
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Marty R.



Joined: 12 Feb 2006
Posts: 5121
Location: Rochester, NY, USA

PostPosted: Sat Jul 03, 2010 6:33 pm    Post subject: Reply with quote

daj95376 wrote:
Marty,

Sudopedia describes your scenario as a Unique Rectangle and Forcing Chains under the topic Uniqueness Tests.

Sorry I took so long to research it.

Regards, Danny

Danny, no apologies necessary.

However, I respectfully disagree. In the Sudopedia example, a standard Forcing Chain is shown, as either the 2 or the 3 force r5c2<>7. If in that example they used what I was talking about, then pincers would have been established and either 2s or 3s would have been eliminated.

If my example is to be called Unique Rectangle and Forcing Chain, then an XY-Chain would also have to be called a Forcing Chain, IMHO.

Regards,
Marty
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ronk



Joined: 07 May 2006
Posts: 397

PostPosted: Sat Jul 03, 2010 7:43 pm    Post subject: Reply with quote

Marty R. wrote:
If my example is to be called Unique Rectangle and Forcing Chain, then an XY-Chain would also have to be called a Forcing Chain, IMHO.

According to Jeff's 2006 Forcing chains: Terminology and Definition, it appears an xy-chain is a forcing chain. I personally avoid the forcing chain term, however, because it seems to have a negative connotation for some people.

Marty R. wrote:
In the Sudopedia example, a standard Forcing Chain is shown, as either the 2 or the 3 force r5c2<>7. If in that example they used what I was talking about, then pincers would have been established and either 2s or 3s would have been eliminated.

That sounds like you want to make a distinction because the strong infererence due to an AUR is at end of a chain, rather than mid-chain. IMHO we shouldn't make our pencils that sharp.
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keith



Joined: 19 Sep 2005
Posts: 3150
Location: near Detroit, Michigan, USA

PostPosted: Sat Jul 03, 2010 8:39 pm    Post subject: Reply with quote

Marty,

Here's an example.
Code:
BB070310sh
+-------+-------+-------+
| . . 1 | 7 . 3 | 4 . . |
| . 3 . | . 5 . | . 1 . |
| 5 . . | 4 . 1 | . . 3 |
+-------+-------+-------+
| 6 . 3 | . . . | 7 . 1 |
| . 8 . | . . . | . 6 . |
| 4 . 5 | . . . | 8 . 2 |
+-------+-------+-------+
| 3 . . | 1 . 8 | . . 7 |
| . 7 . | . 6 . | . 8 . |
| . . 9 | 2 . 7 | 1 . . |
+-------+-------+-------+

Play this puzzle online at the Daily Sudoku site

Yes, the UR is also a Type 4. But, the pseudocell makes an XY-wing.

Keith
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Marty R.



Joined: 12 Feb 2006
Posts: 5121
Location: Rochester, NY, USA

PostPosted: Sat Jul 03, 2010 8:48 pm    Post subject: Reply with quote

Quote:
That sounds like you want to make a distinction because the strong infererence due to an AUR is at end of a chain, rather than mid-chain. IMHO we shouldn't make our pencils that sharp.

Well, I'm not sure I'm following this 100%; I never read about mid-chains vs. ends of chains. However, if we shouldn't make that distinction when a pseudo cell from a UR is the starting point, does that mean that we also shouldn't make the distinction when the starting point is a single cell, which we routinely call XY-Chains?
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Sat Jul 03, 2010 9:30 pm    Post subject: Reply with quote

[Withdrawn: I don't understand Marty's objective.]

Last edited by daj95376 on Mon Jul 05, 2010 2:38 am; edited 1 time in total
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tlanglet



Joined: 17 Oct 2007
Posts: 2461
Location: Northern California Foothills

PostPosted: Sat Jul 03, 2010 9:48 pm    Post subject: Reply with quote

Marty: I may have misunderstood your original post. I assumed you were considering the individual digits, not the combined pseudocell. Consider the following example.

Code:

+-------+-----------+--------+
| . . . | 457 . 459 | . 19.  |
| . . . | .   . .   | . . .  |
| . . . | 37  . .   | . . .  |
+-------+-----------+--------+
| . . . | .   . .   | . . .  |
| . . . | 45  . 45  | . . .  |
| . . . | .   . .   | . . .  |
+-------+-----------+--------+
| . . . | .   . .   | . . .  |
| . . . | .   . .   | . . .  |
| . . . | -3 . .    | . 13 . |
+-------+-----------+--------+
-
7 in r1c4 makes r3c4=7 {or (7)r1c7 - (7=3)r3c4}
9 in r1c6 makes r1c8=1 which makes r9c8=3 {or (9)r1c6 - (9=1)r1c8 - (1=3)r9c8}
These two pincers result in r9c4<>3
I perform this type of process to determine the implications of the individual digits regularly and would like to have a name for the process.

Danny: I like your suggestion of making individual statements for each digit, except I have already been questioned why I provide so much detail about my steps.

Keith: I understood that "coloring" is the term used for extending a digit to a cell of the same value. If so, do we need two terms for that process?

Also, if the AUR implications are used as a pseudocell, them I agree 100% with your suggestion to simply state that fact: "The UR forms a pseudocell 79, leading to an XY-wing -679 that eliminates 6 in R8C8."

Well, I only had a nickel but I spent dime so it is time to quit.

Ted
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ronk



Joined: 07 May 2006
Posts: 397

PostPosted: Sun Jul 04, 2010 2:32 pm    Post subject: Reply with quote

Marty R. wrote:
Well, I'm not sure I'm following this 100%; I never read about mid-chains vs. ends of chains.

Nothing to read here. Either the derived AUR strong inference is at the end of a chain or it isn't. The AICs for the examples posted by daj95376 and keith (above) illustrate the difference.

Code:
+-------+-----------+--------+
| . . . | 457 . 459 | . 67 . |
| . . . | .   . .   | . .  . |
| . . . | .   . .   | . .  . |
+-------+-----------+--------+
| . . . | .   . .   | . .  . |
| . . . | 45  . 45  | . .  . |
| . . . | .   . .   | . .  . |
+-------+-----------+--------+
| . . . | .   . .   | . .  . |
| . . . | .   . -9  | . 69 . |
| . . . | .   . .   | . .  . |
+-------+-----------+--------+

[(9)r1c6 = (7)r1c4]AUR:r15c46 - (7=6)r1c8 - (6=9)r8c8 => r8c6<>9

Code:
+-------+-----------+--------+
| . . . | 457 . 459 | . 67 . |
| . . . | .   . .   | . .  . |
| . . . | .   . .   | . .  . |
+-------+-----------+--------+
| . . . | .   . .   | . .  . |
| . . . | 45  . 45  | . .  . |
| . . . | .   . .   | . .  . |
+-------+-----------+--------+
| . . . | .   . .   | . .  . |
| . . . | .   . 69  | . -6 . |
| . . . | .   . .   | . .  . |
+-------+-----------+--------+

(6=9)r8c6 - [(9)r1c6 = (7)r1c4]AUR:r15c46 - (7=6)r1c8 => r8c6<>6

Compared to others, I probably overload the 'AUR' term. For me, if the exclusion is not due to a useful UR Type 1, Type 2, ... Type 6, it's an AUR.

Marty R. wrote:
However, if we shouldn't make that distinction when a pseudo cell from a UR is the starting point, does that mean that we also shouldn't make the distinction when the starting point is a single cell, which we routinely call XY-Chains?

Huh? For an xy-chain, all the "nodes" are single cells.
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Marty R.



Joined: 12 Feb 2006
Posts: 5121
Location: Rochester, NY, USA

PostPosted: Sun Jul 04, 2010 7:25 pm    Post subject: Reply with quote

Quote:
Marty R. wrote:
However, if we shouldn't make that distinction when a pseudo cell from a UR is the starting point, does that mean that we also shouldn't make the distinction when the starting point is a single cell, which we routinely call XY-Chains?

Huh? For an XY-chain, all the "nodes" are single cells.

Bear with me, I'm very weak at discussing this stuff and don't know what a "node' is in this regard.

It has been suggested that what I did was a Unique Rectangle and Forcing Chain, whereas what I think I did was similar to an XY-Chain. I'm just asking if what I did by establishing pincers should be called a UR and Forcing Chain, then why shouldn't we call a more typical XY-Chain a Forcing Chain as well.
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ronk



Joined: 07 May 2006
Posts: 397

PostPosted: Sun Jul 04, 2010 8:56 pm    Post subject: Reply with quote

Marty R. wrote:
Quote:
Marty R. wrote:
However, if we shouldn't make that distinction when a pseudo cell from a UR is the starting point, does that mean that we also shouldn't make the distinction when the starting point is a single cell, which we routinely call XY-Chains?

Huh? For an XY-chain, all the "nodes" are single cells.

Bear with me, I'm very weak at discussing this stuff and don't know what a "node' is in this regard.

A 'node' is a single cell or a group of cells. Grouped cells can be 1) of like candidates as for an empty rectangle (ER) pattern, 2) of unlike candidates as for an almost locked set (ALS), or (usually unlike) candidates as for a pseudo-cell of a uniqueness pattern (UP).

Sudopedia has a definition for Node that could use some work IMO. It also says 'node' may apply to a candidate, a POV most appropriate for AIC notation and other 3-D representations.

Marty R. wrote:
It has been suggested that what I did was a Unique Rectangle and Forcing Chain, whereas what I think I did was similar to an XY-Chain. I'm just asking if what I did by establishing pincers should be called a UR and Forcing Chain, then why shouldn't we call a more typical XY-Chain a Forcing Chain as well.

So application of the 'forcing chain' term to your example is your actual concern. If so, I'm empathetic. Since the previous examples are based on a pseudo-cell, you could trial balloon something like ...

'xy-chain with a UR-based pseudo-cell' ... or even 'pseudo-xy-chain.'
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Marty R.



Joined: 12 Feb 2006
Posts: 5121
Location: Rochester, NY, USA

PostPosted: Sun Jul 04, 2010 11:17 pm    Post subject: Reply with quote

Quote:
So application of the 'forcing chain' term to your example is your actual concern.

Exactly. I'm sure it's not all that simple, but my understanding of a Forcing Chain was when any of multiple options made the same eliminations(s), as opposed to creating a pincer situation.
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ronk



Joined: 07 May 2006
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PostPosted: Sun Jul 04, 2010 11:26 pm    Post subject: Reply with quote

Marty R. wrote:
Quote:
So application of the 'forcing chain' term to your example is your actual concern.

Exactly. I'm sure it's not all that simple, but my understanding of a Forcing Chain was when any of multiple options made the same eliminations(s), as opposed to creating a pincer situation.

Isn't that what "pincers" do too?
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Marty R.



Joined: 12 Feb 2006
Posts: 5121
Location: Rochester, NY, USA

PostPosted: Sun Jul 04, 2010 11:53 pm    Post subject: Reply with quote

ronk wrote:
Marty R. wrote:
Quote:
So application of the 'forcing chain' term to your example is your actual concern.

Exactly. I'm sure it's not all that simple, but my understanding of a Forcing Chain was when any of multiple options made the same eliminations(s), as opposed to creating a pincer situation.

Isn't that what "pincers" do too?

I don't know. In a Forcing Chain, it might go, "what if this cell is a 2?" "What if this cell is a 5"? If they make a common elimination, it's a success. An XY-Chain with pincers seems like something different.

At any rate, they're certainly perceived as different. Many top players here talk about the XY-Chains that they used in a solution, while nobody mentions Forcing Chains. Perhaps they're the same, or somewhat overlapping, but one definitely has more cachet than the other.
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ronk



Joined: 07 May 2006
Posts: 397

PostPosted: Mon Jul 05, 2010 1:39 am    Post subject: Reply with quote

Marty R., the 'forcing chain' term is not part of my sudoku vocabulary, so I'm not really sure of its definition.

That said, I think it has a 'cachet' at least equal to elimination-by-contradiction ... including uncovering a deadly pattern by blindly asserting a candidate.
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keith



Joined: 19 Sep 2005
Posts: 3150
Location: near Detroit, Michigan, USA

PostPosted: Mon Jul 05, 2010 2:41 am    Post subject: Reply with quote

ronk wrote:
Marty R. wrote:
Quote:
So application of the 'forcing chain' term to your example is your actual concern.

Exactly. I'm sure it's not all that simple, but my understanding of a Forcing Chain was when any of multiple options made the same eliminations(s), as opposed to creating a pincer situation.

Isn't that what "pincers" do too?
The usual connotation (at least on this site is:

If A and B are two mutually exclusive (complementary) choices.

Forcing: A choice of A or B forces a result C in another cell. Therefore, C is true.

Pincers: A choice of A forces C in a cell, @. A choice of B forces C in a different cell, #. @ # are pincers; any cell that sees both cannot be C.

I think the problem that some people have is that pincers often result from recognizable patterns - XY-wing, W-wing, M-wing, etc.

Forcing results, however, are generally not associated with patterns.

So, forcing results are seen to be trial and error, much more so than pincers.

(And, I agree, the result in a "pinched" cell is a force, but pincers have multiple peers where eliminations can be made.)

I am not really one for this philosophy angle. Like other notable solitary pursuits, do it (solve Sudoku) in the way that gives you most pleasure. It's up to you, my opinion does not matter, even if I happen to have one.

Keith
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