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An other type of Unique Rectangle ?

 
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mage

Joined: 29 Nov 2005
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Location: France

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PostPosted: Sat Feb 25, 2006 4:15 pm    Post subject: An other type of Unique Rectangle ? Reply with quote

I have seen that the following UR-like configuration has been dicussed under AUR's (Almost UR's), in conjunction with nice loops :
Code:
  +---------+--------+
  | ab  . . | abY . .| Its a kind of hybrid between type 3 and 3B UR.
  | ... . . | ... . .| Apart that either X must be in abX or Y in abY,
  | abX . . | ab  . .| there is usually not much to do with it alone.
  +---------+--------+


But consider the case where X=Y, noted Z here :
Code:
  +---------+--------+
  | ab  @ @ | abZ . .| Its a kind of type 2/2B UR hybrid .
  | ... . . | ... . .| To avoid the deathly pattern, Z must be in one of the 2 abZ cells.
  | abZ . . | ab  @ @| We have then a sort of XY-wing and the @ marqued cells cannot be Z.
  +---------+--------+

Is there anything wrong in this logic, or can we call this a type 2C or 5 UR, .... or have I re-invented the wheel ?

Mage
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rkral

Joined: 21 Oct 2005
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PostPosted: Sat Feb 25, 2006 8:21 pm    Post subject: Re: An other type of Unique Rectangle ? Reply with quote

mage wrote:
Is there anything wrong in this logic, or can we call this a type 2C or 5 UR, .... or have I re-invented the wheel ?

Your logic is impeccable. While I've seen a handful of references to this pattern as UR type 5, I've only seen one reference to it as a type 2 variant.

Of the two choices, I prefer type 5 because it's most consistent with the assignments for types 2, 3, and 4 (n). For those types, the "extra" non-UR candidates are either both in one box (type nA) ... or they are not (type nB).

Only one cell has extra candidate(s) for type 1, so the A & B distinction doesn't apply. For this (proposed) type 5, the extra candidates are on a diagonal ... so they can't possibly be in one box ... so the A & B distinction again doesn't apply. And none of the other types have C variant.

For programmed solvers, I suspect it's more efficient to test for type 2 and (the proposed) type 5 URs with the same code, but that shouldn't affect the logic. We need MadOverlord around to update his Standardizing the Uniqueness descriptions thread on the Players' Forums.

Ron
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Carcul

Joined: 29 Dec 2005
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PostPosted: Sun Feb 26, 2006 10:58 am    Post subject: Reply with quote

Hi Mage.

Yes, your logic is ok, although that type of AUR is extremely rare (I haven't come across anyone until now) which is a pity. Good work. Very Happy

Regards, Carcul
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mage

Joined: 29 Nov 2005
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PostPosted: Sun Feb 26, 2006 11:59 am    Post subject: Reply with quote

Thanks rkral and Carcul.

Hope Madoverlord will find some time to update his valuable Standardizing post.

Mage
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vidarino

Joined: 10 Feb 2006
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PostPosted: Mon Feb 27, 2006 8:18 am    Post subject: Reply with quote

Carcul wrote:
Hi Mage.

Yes, your logic is ok, although that type of AUR is extremely rare (I haven't come across anyone until now) which is a pity. Good work. Very Happy

Regards, Carcul


Not *that* rare. I posted an example of one just yesterday, on the Players' Forum, right here. Smile

Vidar
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rkral

Joined: 21 Oct 2005
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PostPosted: Mon Feb 27, 2006 11:38 am    Post subject: Reply with quote

vidarino wrote:
Carcul wrote:
Yes, your logic is ok, although that type of AUR is extremely rare (I haven't come across anyone until now)

Not *that* rare. I posted an example of one just yesterday, on the Players' Forum

I'm with Carcul on this one. Scanning both the top1465 and "Gordon Royle's library of 36,628 puzzles with 17 clues", my solver found only three. The scenario was that all other techniques (other than guessing) had first crack at the puzzle after any alteration of the grid.

So I'm considering recanting my support of the 'type 5' name for this pattern in favor of 'type 2C'.

Ron
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vidarino

Joined: 10 Feb 2006
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PostPosted: Mon Feb 27, 2006 11:47 am    Post subject: Reply with quote

rkral wrote:

I'm with Carcul on this one. Scanning both the top1465 and "Gordon Royle's library of 36,628 puzzles with 17 clues", my solver found only three. The scenario was that all other techniques (other than guessing) had first crack at the puzzle after any alteration of the grid.


Hmm, okay, you might be right after all. The reason they didn't seem too uncommon for me was that I was scanning a pregenerated collection of puzzles on which various uniqueness tricks could be employed. Probably not very representative of the average puzzles, in other words. Smile

Quote:
So I'm considering recanting my support of the 'type 5' name for this pattern in favor of 'type 2C'.


I concur. I haven't bothered distinguishing between them at all, so currently my solver simply identifies them as "Uniqueness Rectangle type 2/5".

Vidar
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