SE Rating for UR Types 2 & 5 please

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SE Rating for UR Types 2 & 5 please

Postby civiliza » Sun Jul 31, 2011 11:14 am

I have (hopefully) expanded my generator to include Type 2 and Type 5 Unique Rectangles.

As I understand the Sudopedia description, these are a UR deadly pattern with an extra common candidate value in either a common row/column (Type 2) or diagonally opposite (Type 5).

Their effects once detected are similar to half an X wing (Type 2) or an XY Wing (Type 5).

My generator is notoriously unable to generate a given clue type on demand. Until it does produce one I need to know:

a) Does Sudoku Explainer recognise Type 2 and/or Type 5 Unique Rectangles ?
b) What rating does Sudoku Explainer give to each of these techniques ?

Pending any response I will continue running my generator's output through Sudoku Explainer on the assumption that:

a) Sudoku Explainer does recognise UR2's and UR5's
b) The SE rating for both types is the same as for UR Type 1's (which I believe to be 4.5)
c) My generator is correctly detecting/generating these UR's
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Re: SE Rating for UR Types 2 & 5 please

Postby ronk » Sun Jul 31, 2011 11:33 am

civiliza wrote:a) Does Sudoku Explainer recognise Type 2 and/or Type 5 Unique Rectangles ?
b) What rating does Sudoku Explainer give to each of these techniques ?

Explainer recognizes UR Type 2 but not UR Type 5. As you stated, its rating for UR Type 2 is 4.5. IMO the best summary of Explainer ratings is posted here.
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Re: SE Rating for UR Types 2 & 5 please

Postby civiliza » Sun Jul 31, 2011 11:53 am

ronk wrote:Explainer recognizes UR Type 2 but not UR Type 5. As you stated, its rating for UR Type 2 is 4.5. IMO the best summary of Explainer ratings is posted here.


Thank you for that Ronk. I had managed to find the linked posting earlier today, but failed to make sense of it at the time. Once you know what you are looking for, it does indeed confirm the Type 2 UR rating.

Is there a reason Explainer does not recognise Type 5 UR's? Is there a simpler/alternative method that makes Type 5 UR's redundant?

My generator is slow enough as it is, if there is no point in a UR Type 5 routine it would be useful to know.
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Re: SE Rating for UR Types 2 & 5 please

Postby JasonLion » Sun Jul 31, 2011 12:56 pm

It is just a historical accident. Type 5s were discovered later, so were not a common technique around the time SE was written. Type 5s are not all that common, but they have their place.
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Re: SE Rating for UR Types 2 & 5 please

Postby civiliza » Sun Jul 31, 2011 1:44 pm

JasonLion wrote:It is just a historical accident. Type 5s were discovered later, so were not a common technique around the time SE was written. Type 5s are not all that common, but they have their place.


Thanks for confirming tha validity of Type 5 UR's, I didn't know if there was some underlying corollary that made them redundant (in the same way that pointing makes row/box and column/box x-wings (as opposed to the classic row/column x-wing) redundant),

I will continue to use Sudoku Explainer as my main "prover", but until I have proved that I can successfully generate both types, is there another (preferably free - unemployed at the moment) Windows program that can identify Type 5 Unique Rectangles?
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D'oh (row/box X-Wings)

Postby civiliza » Sun Jul 31, 2011 2:40 pm

D'oh, just sussed that Pointing isn't a replacement for row/box (or column/box) X-Wings.

If all the candidates for two rows are in the same box, then that leaves the remaining row in the chute to cover both the remaining boxes.

Since the true value for a row can't simultaneously end up in two different boxes, the whole situation is totally impossible and so row/box (and column/box) X-Wings are likewise impossible.
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Locked set by extension

Postby civiliza » Sun Jul 31, 2011 3:16 pm

Whenever something is impossible, it has implications.

Based on the reasoning just descibed, whenever all the candidates for a digit in one block are in the same two rows, then the digit must also be present in one of the other twelve cells in the two rows.

If I understand the terminology right, said twelve squares are a locked set, Now if only someone can find a use for a twelve square locked set.

EDIT - Sorry, just looked up Locked Sets on Sudopedia, and I obviously did not understand the terminology. What I meant was that there were twelve cells that MUST contain one (and only one) kocation for a particular digit.
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Re: SE Rating for UR Types 2 & 5 please

Postby daj95376 » Sun Jul 31, 2011 4:34 pm

civiliza wrote:My generator is slow enough as it is, if there is no point in a UR Type 5 routine it would be useful to know.

I am only aware of one instance of a UR Type 5 being found (by Bernhard Hobiger), and it needed a specific sequence of steps leading up to the grid containing it. I don't remember the steps, but here's the puzzle.

Code: Select all
75..8...12.96.3.8...8...9.......437.....2.....938.......5...2...8.2.57.34...3..59

If you force your generator to "create" these puzzles, then you can test your UR Type 2 logic.
(They are from a collection posted by Mike Barker.}

Code: Select all
#16 UR+2x (Type 2)
...61......3...5...95....78.....4..5.42.3.76.8..5.....41....62...9...3......96...
..8..69.53..............6.......98..8...6.....561....354.3.........12.7..2..4.1..
.9...4...4..38........5.1.7..4...9.......9..3...2.3.64.8.........671.8.2..2....3.
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Re: SE Rating for UR Types 2 & 5 please

Postby civiliza » Sun Jul 31, 2011 5:34 pm

Looking for UR Type 5's on the internet, I came across isudoku's definition which includes the marginally more common 3 corner Type 5 in which the non-UR value is possible in three of the four UR corners.

I have expanded my code to include this definition.

The eliminations possible when detected are like those of an xyz-wing. (two cells instead of the xy-wing like "pure" version that could potentially eliminate up to four cells).
Last edited by civiliza on Sun Jul 31, 2011 6:45 pm, edited 1 time in total.
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Re: SE Rating for UR Types 2 & 5 please

Postby civiliza » Sun Jul 31, 2011 5:48 pm

daj95376 wrote:I am only aware of one instance of a UR Type 5 being found (by Bernhard Hobiger), and it needed a specific sequence of steps leading up to the grid containing it. I don't remember the steps, but here's the puzzle.

Code: Select all
75..8...12.96.3.8...8...9.......437.....2.....938.......5...2...8.2.57.34...3..59


Interesting - I ran it through Sudoku Explainer to see what it would make of it, and it resorted to Turbot Fishes.

I'll have to try it more slowly and see where the UR5 appears (one of the turbot fish reduces a 4 corner UR down to a three corner Type 5 UR, but I am not sure whether that is what I'm looking for).
Last edited by civiliza on Mon Aug 01, 2011 12:29 am, edited 1 time in total.
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Re: SE Rating for UR Types 2 & 5 please

Postby daj95376 » Sun Jul 31, 2011 10:38 pm

Here's a solution where the UR Type 5 is present ... but not needed.

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

 <15+6>  XY-Wing  r4c4/r4c9+r5c6         <> 6    r5c9

 W-Wing:  (1=6)r8c3 - r1c3 = r1c7 - (6=1)r9c7  =>  r8c8,r9c23<>1

 r248    Swordfish (222)                 <> 1    r3c2,r7c25

 +------------------------------------------------------+
 |  7    5    46   |  9     8    2    |  46   3    1    |
 |  2    14   9    |  6     14   3    |  5    8    7    |
 |  13   346  8    |  14    5    7    |  9    26   24   |
 |-----------------+------------------+-----------------|
 |  8    12   12   |  5     9    4    |  3    7    6    |
 |  6    47   47   |  3     2    1    |  8    9    5    |
 |  5    9    3    |  8     7    6    |  14   12   24   |
 |-----------------+------------------+-----------------|
 |  13   367  5    |  47-1 *46   9    |  2   *46+1 8    |
 |  9    8    16   |  2    *46+1 5    |  7   *46   3    |
 |  4    267  267  |  17    3    8    |  16   5    9    |
 +------------------------------------------------------+
 # 35 eliminations remain

 r78c58  <46> UR Type 5.2233             <> 1    r7c4   extraneous

 r3c7    2-String Kite                   <> 6    r9c2
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Re: SE Rating for UR Types 2 & 5 please

Postby civiliza » Mon Aug 01, 2011 1:15 pm

Yay - My first UR2:

Code: Select all
000007000
200008310
041000002
000000000
060004150
053000409
000043590
004010008
008900020
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Re: SE Rating for UR Types 2 & 5 please

Postby civiliza » Wed Sep 14, 2011 2:05 am

And finally a UR5 - Well, sort of. It's a UR with the same extra value in three of the corners. One definition I have read reckons it's a Type 5 Unique Rectangle, Sudoku Explainer reckons it's a Type 2. Figures !!

Code: Select all
000000000
000520000
000006894
801004300
000200708
000000050
020105003
500000087
900700001
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