Unique Rectangles Gallery

Advanced methods and approaches for solving Sudoku puzzles

Unique Rectangles Gallery

Postby David P Bird » Sat May 13, 2017 1:02 pm

The coverage of Unique Rectangle and Avoidable Rectangle inferences and eliminations is scattered throughout this forum, so recently I worked on a personal gallery of the possible patterns. I have now added annotations etc. to make them suitable for others to understand, and attach the result as an Open Office file.

In 2006 Mike Baker did a tremendous job in compiling a collection <here> of the different UR configurations that he and others could discover or devise, and listing the eliminations that each one produced. At that time the collaborators allocated UR type numbers in the order that they were discovered so they were rather illogical, but they are still in use. Mike did not use these type numbers, but used his own comprehensive system. In 2006 different notation systems were in flux, so diplomatically, he only listed the eliminations that were available. He also excluded deductions that utilise external disrupting nodes, as the members of the team would have been well aware of the implications. These points, together with the terminology he used, make his listing difficult reading.

In the gallery, I have adapted his indexing system and have added AICs to justify the eliminations provided by the patterns. Understanding AICs is therefore a prerequisite to be able to follow the logic involved. The indexing system used is meant to support the listing order, nothing more, as it should be easier for readers if the chain notations are given in preference to quoting pattern numbers.

As usual, I would be grateful for any comments or corrections and would welcome a collection of sample puzzles if anyone has one to complement the gallery. However, please be warned that nowadays I am only able to work piecemeal on Sudoku, so please accept it may take me some time to respond.

UR Gallery.odt
UR Gallery
(25.11 KiB) Downloaded 49 times


David P Bird

TAGdpbUniqueness
David P Bird
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Re: Unique Rectangles Gallery

Postby David P Bird » Tue Jun 06, 2017 9:25 am

Thanks to Gordon Fick for pointing out to me that in the gallery file I've omitted one of Mike Barker's patterns:

Code: Select all
*----------*-----------*
| a*bW . . | a*b*X . . |
| .    . . | .     . . |
| a*bY . . | ab*Z  . . |
*----------*-----------*   
| B    . . | .     . . |

UR.BL2adj.1 Digit (a) bilocal in adjacent sides (r1,c1), (b) bilocal in another side (c4)
Eliminates (b) from the cell where (a) is doubly bilocal
(a)r1c1 = (a#2)r1c4,r3c1 -[UR]- (b#2)r1c1,r3c4 = (b)r1c4,r3PQRc1 => r1c1 <> b

When (a#2)r1c4,r3c1 and (b)r3c4 are true (b) must be true in an external disruptor in c1.
Adding cells (b)r1c4,r3c1 to the final node avoids 'remembering' that they would already be occupied.

Gordon encountered this in this grid (shown after JExocet eliminations have been made)
.7.....4....3...878...9...69...4.6...3...1.....75.....4...2..6......54.9..1.....2 SudokoWiki Weekly Unsolvable 238
Code: Select all
 *----------------------*----------------------*----------------------*
 | 12356  <7>    23569  | 1268   1568   268    | 1359   <4>    135    |
 | 1256   124569 24569  | <3>    156    246    | 159    <8>    <7>    |
 | <8>    1245   2345   | 1247   <9>    247    | 135    1235   <6>    |
 *----------------------*----------------------*----------------------*
 | <9>    1258   258    | 278    <4>    2378   | <6>    12357  135    |
 | 256    <3>    24568  | 26789  678    <1>    | 28     579    45     |
 | 126    12468  <7>    | <5>    368    23689  | 28     139    134    |
 *----------------------*----------------------*----------------------*
 | <4>    59     359    | 179    <2>    379    | 1357   <6>    8      |
 | 2367   268    2368   | 1678   13678  <5>    | <4>    13     <9>    |
 | 3567   5689   <1>    | 4689-7 3678   346789 | 357    35     <2>    |
 *----------------------*----------------------*----------------------*

The chain for eliminating (7)r9c4 is
(4)r9c4 = (4#2)r3c4,r9c6 -[UR]- (7#2)r3c6,r9c4 = (7)r3c4,r9c1568 => r9c4 <> 7

(4) Is locked in the UR cells r9 & c4 and (7) is locked in r3

Taking the memory chain view, if (4)r9c4 is false it must occupy both r3c4 and r9c6 which forces (7) into r3c6. To prevent (7)r9c4 from being true and making the UR, it must be true in an external cell in r9. As the internal UR cells r3c4 & r9c6 also see r9c4, adding them to the final node converts the chain into an AIC.

I'll edit the gallery file in due course.

DPB

[Edit error in grid where (7)r7c7 had been omitted, as revealed by Phil's post below, corrected]
Last edited by David P Bird on Tue Jun 06, 2017 2:08 pm, edited 2 times in total.
David P Bird
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Re: Unique Rectangles Gallery

Postby pjb » Tue Jun 06, 2017 11:58 am

Interesting. After applying singles to the grid as shown, there are only 122 left, and the 7 at r9c4 is already gone. However, the starting grid obtained (174 to go) after basics alone has the hidden UR at r39c46 with the elimination of 7 at r9c4.
Phil
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Re: Unique Rectangles Gallery

Postby David P Bird » Tue Jun 06, 2017 2:07 pm

Sorry Phil,
My grid was wrong. Somehow I had corrupted r7c7 to exclude (7).
I deliberately left the (2)hidden single and the (8)naked single to leave the UR cells fully populated.
In the edited version I've kept the (2)hidden single but have made the eliminations for the (8)naked single as they didn't add anything.

David
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