## looks like a Non-Unique Rectangle - But it's NOT!

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### looks like a Non-Unique Rectangle - But it's NOT!

So I'm solving away, and everything's going well. Then I see what looks like a non-unique rectangle pattern, so I fill in the remaining candidate - and my solver says it's wrong! Huh? The solver tells me my candidate lists are all up to date, so it's not like I forgot to remove a candidate or something... I'm hoping someone can show me why this isn't a non-unique rectangle, so I can avoid making a mistake on future puzzles.

Original puzzle:
Code: Select all
`.1.|7..|5...35|..4|..78..|.3.|..6---+---+---..4|.71|6....3|...|7....7|89.|4..---+---+---5..|.1.|..83..|2..|17...1|..8|.5.`

And the "stuck" state, or rather, the state where I see the non-unique rectangle pattern (R3C3,R3C7,R7C3,R7C7)
Code: Select all
`4     1     6     |  7     8     29    |  5     39    23929    3     5     |  69    26    4     |  8     1     78     7     29    |  1     3     5     |  29    4     6------------------+--------------------+--------------------29    28    4     |  5     7     1     |  6     38    391     89    3     |  4     26    26    |  7     89    56     5     7     |  8     9     3     |  4     2     1------------------+--------------------+--------------------5     4     29    |  39    1     7     |  239   6     83     69    8     |  2     5     69    |  1     7     47     269   1     |  369   4     8     |  39    5     29`
EnderGT

Posts: 69
Joined: 19 February 2008

EnderGT wrote:So I'm solving away, and everything's going well. Then I see what looks like a non-unique rectangle pattern, so I fill in the remaining candidate - and my solver says it's wrong! Huh? The solver tells me my candidate lists are all up to date, so it's not like I forgot to remove a candidate or something... I'm hoping someone can show me why this isn't a non-unique rectangle, so I can avoid making a mistake on future puzzles.

Original puzzle:
Code: Select all
`.1.|7..|5...35|..4|..78..|.3.|..6---+---+---..4|.71|6....3|...|7....7|89.|4..---+---+---5..|.1.|..83..|2..|17...1|..8|.5.`

And the "stuck" state, or rather, the state where I see the non-unique rectangle pattern (R3C3,R3C7,R7C3,R7C7)
Code: Select all
`4     1     6     |  7     8     29    |  5     39    23929    3     5     |  69    26    4     |  8     1     78     7     29    |  1     3     5     |  29    4     6------------------+--------------------+--------------------29    28    4     |  5     7     1     |  6     38    391     89    3     |  4     26    26    |  7     89    56     5     7     |  8     9     3     |  4     2     1------------------+--------------------+--------------------5     4     29    |  39    1     7     |  239   6     83     69    8     |  2     5     69    |  1     7     47     269   1     |  369   4     8     |  39    5     29`

your rectangle is in 4 boxes

only works if it's 2 boxes

Pat

Posts: 3691
Joined: 18 July 2005

I was trying out the puzzles in this forum with my new web program and it gave me this advice to your problem.
Pair found at R5C2 R5C8 for 9 and 8 which eliminates 1 option
X-Wing on 2 at R7C3 R7C7 R3C7 R3C3 eliminates 1 option
X-Wing on 3 at R4C8 R4C9 R1C9 R1C8 eliminates 1 option
R1C6 forced chain at R1C6 shows it cannot hold 9 so it must hold 2
Hope it helps

Mike

http://www.checkmypages.com/sudoku/index.php
mike_bike_kite

Posts: 2
Joined: 25 September 2008

Pat has already answered yr question, so since you're into unique rectangles, here's a way to solve the puzzle.

Code: Select all
`4     1     6     |  7     8     29    |  5     39    23929    3     5     |  69    26    4     |  8     1     78     7     29    |  1     3     5     |  29    4     6------------------+--------------------+--------------------29    28    4     |  5     7     1     |  6     38    391     89    3     |  4     26    26    |  7     89    56     5     7     |  8     9     3     |  4     2     1------------------+--------------------+--------------------5     4     29    | *3-9  1     7      | *239   6     83     69    8     |  2    5     69     |  1     7     47     269   1     | *369  4     8      | *3-9   5     29`

Yet again: X-wing overlay on a UR with diagonal bivalues.
"The diagonal pair must have the x-wing component." ~ Keith

Luke
2015 Supporter

Posts: 435
Joined: 06 August 2006
Location: Southern Northern California

Luke451 wrote:Yet again: X-wing overlay on a UR with diagonal bivalues.
"The diagonal pair must have the x-wing component." ~ Keith

What you have here can also be described as a combintion of two hidden rectangles:

Hidden Rectangle: 3/9 in r7c47,r9c47 => r7c4<>9
Hidden Rectangle: 3/9 in r7c47,r9c47 => r9c7<>9

(Only one of them needs to be performed)
hobiwan
2012 Supporter

Posts: 321
Joined: 16 January 2008
Location: Klagenfurt

From my notes:

Code: Select all
`Unique Rectangle Type 6   (UR + X-Wing in <1>)(diagonal variant of Type 4)+---------------+|   -   -   -   ||  1-2  -  23-1 ||   -   -   -   |+---------------+| 24-1  -  1-2  ||   -   -   -   ||   -   -   -   |+---------------+`
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

Pat wrote:only works if it's 2 boxes

Thank you very much, that is a distinction I was not aware of until now.

EnderGT

Posts: 69
Joined: 19 February 2008

daj95376 wrote:From my notes:...

Thank's, I should have seen that
hobiwan
2012 Supporter

Posts: 321
Joined: 16 January 2008
Location: Klagenfurt

mike_bike_kite wrote:I was trying out the puzzles in this forum with my new web program and it gave me this advice to your problem.

X-Wing on 2 at R7C3 R7C7 R3C7 R3C3 eliminates 1 option
X-Wing on 3 at R4C8 R4C9 R1C9 R1C8 eliminates 1 option

Hi, Mike,
Looks like EnderGT had already cleaned up his x-wings quite nicely. Your "advice" pertains only to the original grid and not the PM under discussion. Maybe you only intended to plug your site?

Moving on: Have I got this right? [r4c8]<>3
Code: Select all
`4     1     6     |  7     8     29    |  5    *39   *23929    3     5     |  69    26    4     |  8     1     78     7     29    |  1     3     5     |  29    4     6------------------+--------------------+--------------------29    28    4     |  5     7     1     |  6    *-38  *391     89    3     |  4     26    26    |  7     89    56     5     7     |  8     9     3     |  4     2     1------------------+--------------------+--------------------5     4     29    |  39    1     7     |  239   6     83     69    8     |  2     5     69    |  1     7     47     269   1     |  369   4     8     |  39    5     29`

This looks like one of them there "avoidable/forbidden/unresolvable rectangles" under much discussion hereabouts lately. [r4c8]<>[3] lest we end up with a deadly pattern.

Luke
2015 Supporter

Posts: 435
Joined: 06 August 2006
Location: Southern Northern California

Luke451 wrote:Have I got this right? [r4c8]<>3
[...]
This looks like one of them there "avoidable/forbidden/unresolvable rectangles" under much discussion hereabouts lately. [r4c8]<>[3] lest we end up with a deadly pattern.

You've got it right. Because none of the four cells r14c89 contain a given, you may "freely reinvent" the missing '9' in r4c8.

AUR(39)r14c89:(r4c8 =8|2= r1c9) -2- r9c9 -9- r4c9 -3- r4c8 ==> r4c8<>3

Although the "reinvented pattern" is an AUR, the deduction does not depend upon an assumption of uniqueness.
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

ronk wrote:... you may "freely reinvent" the missing '9' in r4c8.

I'm more interested in how EnderGT reached the elimination [r4c8]<>9 in the first place. Another good reason to provide the original puzzle.
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

daj95376 wrote:I'm more interested in how EnderGT reached the elimination [r4c8]<>9 in the first place. Another good reason to provide the original puzzle.

He probably used the UR of {89} @ r45c28 to eliminate 9 from r4c28.
udosuk

Posts: 2698
Joined: 17 July 2005

ronk wrote:Although the "reinvented pattern" is an AUR, the deduction does not depend upon an assumption of uniqueness.
Yes, but then you must be able to get rid of the 9 in r4c8 without using uniqueness
eleven

Posts: 1946
Joined: 10 February 2008

eleven wrote:
ronk wrote:Although the "reinvented pattern" is an AUR, the deduction does not depend upon an assumption of uniqueness.
Yes, but then you must be able to get rid of the 9 in r4c8 without using uniqueness

I carefully did not make a claim as to "overall" uniqueness.
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

udosuk wrote:
daj95376 wrote:I'm more interested in how EnderGT reached the elimination [r4c8]<>9 in the first place. Another good reason to provide the original puzzle.

He probably used the UR of {89} @ r45c28 to eliminate 9 from r4c28.

Thanks udosuk! I should have spotted it myself.

Another example of the old claim that you should apply other URs before a UR Type 4.
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

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