Looking for a rectangle

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Looking for a rectangle

Postby QiGuy » Tue Feb 22, 2011 7:07 pm

Here's the original grid:
Code: Select all
8..|...|7.1
.3.|...|.5.
.27|..8|..3
..6|79.|...
4..|...|..7
...|.83|5..
9..|2..|14.
.7.|...|.6.
2.5|...|..8


I got this far:

Code: Select all
8 45 49|3 56 569|7 2 1
6 3 19|19 27 27|8 5 4
15 2 7|15 4 8|6 9 3
135 158 6|7 9 15|4 38 2
4 158 138|56 1256 1256|9 38 7
7 9 2|4 8 3|5 1 6
9 68 38|2 367 67|1 4 5
13 7 134|8 135 145|2 6 9
2 146 5|69 16 469|3 7 8


I have the feeling there is a rectangle that I should be looking at: r1c56, r5c56? Can't find any other patterns that seem to help. Can anyone give me a clue? (Sorry about the pencilmark grid -- I thought the software would square it up).
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Postby Pat » Fri Feb 25, 2011 8:36 am

QiGuy wrote:
Here's the original grid:
Code: Select all
 *-----------*
 |8..|...|7.1|
 |.3.|...|.5.|
 |.27|..8|..3|
 |---+---+---|
 |..6|79.|...|
 |4..|...|..7|
 |...|.83|5..|
 |---+---+---|
 |9..|2..|14.|
 |.7.|...|.6.|
 |2.5|...|..8|
 *-----------*

I got this far:
Code: Select all
 *-----------*
 |8..|3..|721|
 |63.|...|854|
 |.27|.48|693|
 |---+---+---|
 |..6|79.|4.2|
 |4..|...|9.7|
 |792|483|516|
 |---+---+---|
 |9..|2..|145|
 |.7.|8..|269|
 |2.5|...|378|
 *-----------*

 *-----------------------------------------------------------*
 | 8     45    49    | 3     56    569   | 7     2     1     |
 | 6     3     19    | 19    27    27    | 8     5     4     |
 | 15    2     7     | 15    4     8     | 6     9     3     |
 |-------------------+-------------------+-------------------|
 | 135   158   6     | 7     9     15    | 4     38    2     |
 | 4     158   138   | 56    1256  1256  | 9     38    7     |
 | 7     9     2     | 4     8     3     | 5     1     6     |
 |-------------------+-------------------+-------------------|
 | 9     68    38    | 2     367   67    | 1     4     5     |
 | 13    7     134   | 8     135   145   | 2     6     9     |
 | 2     146   5     | 69    16    469   | 3     7     8     |
 *-----------------------------------------------------------*
I have the feeling there is a rectangle that I should be looking at: r15c56?
Can't find any other patterns that seem to help.
Can anyone give me a clue?

( neat formatting provided by Angus Johnson's Simple Sudoku )

try r19c26

·:· spoiler ·:· wrote:·:·
    if r1c2 = 4
    then the 4 for r9 is at r9c6,
    so 9 for that column is in r1

    ( nothing left for r1c3 )
·:·
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Re: Looking for a rectangle

Postby QiGuy » Thu Mar 03, 2011 3:48 pm

Spoiler: I've been trying to do something constructive with your clue. I can't find a unique rectangle in the four cells you have directed me to. There might be an XY Wing there, but I can't eliminate the 1 in r9c2 or the 9s in r19c6. I guess I need more clue.
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Re: Looking for a rectangle

Postby daj95376 » Thu Mar 03, 2011 5:02 pm

QiGuy wrote:Spoiler: I've been trying to do something constructive with your clue. I can't find a unique rectangle in the four cells you have directed me to. There might be an XY Wing there, but I can't eliminate the 1 in r9c2 or the 9s in r19c6. I guess I need more clue.

Pat knew there wasn't a potential <56> UR in your cells r15c56 because r5c4=56 prevents the UR from happening. She was simply providing another, non-UR, rectangular pattern that was helpful.
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Re:

Postby aran » Fri Mar 04, 2011 1:06 pm

Code: Select all
-----------------------------------------------------------*
 | 8     45    49    | 3     56    569   | 7     2     1     |
 | 6     3     19    | 19    27    27    | 8     5     4     |
 | 15    2     7     | 15    4     8     | 6     9     3     |
 |-------------------+-------------------+-------------------|
 | 135   158   6     | 7     9     15    | 4     38    2     |
 | 4     158   138   | 56    1256  1256  | 9     38    7     |
 | 7     9     2     | 4     8     3     | 5     1     6     |
 |-------------------+-------------------+-------------------|
 | 9     68    38    | 2     367   67    | 1     4     5     |
 | 13    7     134   | 8     135   145   | 2     6     9     |
 | 2     146   5     | 69    16    469   | 3     7     8     |
 *-----------------------------------------------------------*
*
Using Uniqueness : avoidance 267r257c56 =>3r7c5=6r5c4
3r7c5=6r5c4-(6=9)r9c4-r9c6=r1c6-(9=4)r1c3-(4=13)r8c13-3r8c5=3r7c5 =>r7c5=3 ste
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Re: Looking for a rectangle

Postby JeJ » Tue Mar 08, 2011 6:29 pm

You are looking for something more complicated than it is actually there. Try a skyscraper on 5.
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Postby Pat » Thu Mar 10, 2011 9:20 am

JeJ wrote:skyscraper on 5

yes, and it briefly seems to help;
then you see it was just a red herring
and is not relevant for solving this puzzle
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Re:

Postby JeJ » Thu Mar 10, 2011 2:56 pm

Pat wrote:
JeJ wrote:skyscraper on 5

yes, and it briefly seems to help;
then you see it was just a red herring
and is not relevant for solving this puzzle

The eliminations you did might have been wrong, because with the placement you obtain in r4c6 you can later find the next clue a W-wing.
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Postby Pat » Fri Mar 11, 2011 8:23 am

JeJ wrote:with the placement you obtain in r4c6
you can later find the next clue a W-wing


okay my phrasing was a bit too strong

  • the path in my first post
    uses an implication-stream of 5 cells;

  • your way (solving r4c6 first)
    reduces this to an implication-stream of only 4 cells
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Re: Looking for a rectangle

Postby QiGuy » Fri Mar 11, 2011 2:33 pm

Some of the techniques described in this thread I'm not familiar with (W wings, skyscrapers), so I'm no further ahead in trying to figure this puzzle out. Is there a consensus among you as to how to proceed from where I am? I have an understanding of basic techniques, X, XY wings, uniqueness principles, but I don't know where to go from where I am in this puzzle.
Also, I have difficulty with this notation: "Using Uniqueness : avoidance 267r257c56 =>3r7c5=6r5c4
3r7c5=6r5c4-(6=9)r9c4-r9c6=r1c6-(9=4)r1c3-(4=13)r8c13-3r8c5=3r7c5 =>r7c5=3 ste" aran. Is there a standard form of notation that I can refer to in order to translate and understand the suggestion?
Thanks -- this site is great, by the way.
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Re: Looking for a rectangle

Postby JeJ » Fri Mar 11, 2011 7:47 pm

Pat wrote:
JeJ wrote:with the placement you obtain in r4c6
you can later find the next clue a W-wing


okay my phrasing was a bit too strong

  • the path in my first post
    uses an implication-stream of 5 cells;

  • your way (solving r4c6 first)
    reduces this to an implication-stream of only 4 cells


I still don't see a problem with the method I mentioned, since after the W-wing, you can proceed and find the next clue, an XY-chain and crack the whole puzzle.

QiGuy wrote:Some of the techniques described in this thread I'm not familiar with (W wings, skyscrapers), so I'm no further ahead in trying to figure this puzzle out. Is there a consensus among you as to how to proceed from where I am? I have an understanding of basic techniques, X, XY wings, uniqueness principles, but I don't know where to go from where I am in this puzzle.
Also, I have difficulty with this notation: "Using Uniqueness : avoidance 267r257c56 =>3r7c5=6r5c4
3r7c5=6r5c4-(6=9)r9c4-r9c6=r1c6-(9=4)r1c3-(4=13)r8c13-3r8c5=3r7c5 =>r7c5=3 ste" aran. Is there a standard form of notation that I can refer to in order to translate and understand the suggestion?
Thanks -- this site is great, by the way.

Some puzzles can't be solved with the most basic techniques, so if you don't use some more advanced ones (like the ones mentioned here), you won't be able to solve some puzzles.
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Postby Pat » Sun Mar 13, 2011 9:29 am

QiGuy wrote:Some of the techniques described in this thread I'm not familiar with (W wings, skyscrapers),
so I'm no further ahead in trying to figure this puzzle out.
Is there a consensus among you as to how to proceed from where I am?

why consensus?
there are different ways

this suits me --
    r1c2 = 4 → r9c6 = 4 → r1c6 = 9 → r1c3 = 4 → r1c2 not 4
Code: Select all
 *-----------------------------------------------------------*
 | 8     45    49    | 3     56    569   | 7     2     1     |
 | 6     3     19    | 19    27    27    | 8     5     4     |
 | 15    2     7     | 15    4     8     | 6     9     3     |
 |-------------------+-------------------+-------------------|
 | 135   158   6     | 7     9     15    | 4     38    2     |
 | 4     158   138   | 56    1256  1256  | 9     38    7     |
 | 7     9     2     | 4     8     3     | 5     1     6     |
 |-------------------+-------------------+-------------------|
 | 9     68    38    | 2     367   67    | 1     4     5     |
 | 13    7     134   | 8     135   145   | 2     6     9     |
 | 2     146   5     | 69    16    469   | 3     7     8     |
 *-----------------------------------------------------------*
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Re: Looking for a rectangle

Postby QiGuy » Mon Mar 14, 2011 6:18 pm

Now THAT I get. Thanks, Pat.
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