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Empty rectangles

 
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Marty R.



Joined: 12 Feb 2006
Posts: 5119
Location: Rochester, NY, USA

PostPosted: Sat Sep 15, 2007 2:48 pm    Post subject: Empty rectangles Reply with quote

Code:

+-----------------+-----------------+------------------+
| 3     1   2489  | 479  279  6     | 5    29    289   |
| 24568 569 24689 | 459  2359 3459  | 1368 12369 7     |
| 256   569 7     | 8    1    359   | 4    2369  2369  |
+-----------------+-----------------+------------------+
| 1     8   26    | 67   4    37    | 9    5     236   |
| 2456  7   2469  | 569  359  8     | 136  12346 12346 |
| 456   569 3     | 1    59   2     | 68   7     468   |
+-----------------+-----------------+------------------+
| 9     2   5     | 3    8    147   | 167  146   146   |
| 67    3   16    | 4579 579  14579 | 2    8     149   |
| 78    4   18    | 2    6    179   | 137  139   5     |
+-----------------+-----------------+------------------+

Play this puzzle online at the Daily Sudoku site

This is a very unusual puzzle from the site it comes from in that the commonly discussed techniques are not available based on what I can see. So I thought I'd take my first shot at ERs. I made a few eliminations but ended up with duplicates, so I wondered if I was misusing the ER logic.

Is r1c3 an ERI? There is a strong link on 2 in c5. Can the 2 in r2c5 be removed?

Is r2c7 an ERI? There is a strong link on 3 in c5. Can the 3 in r5c5 be removed?

Using the same ERI, there is a strong link on 8 in r6. Can the 8 in r6c9 be removed?

When an ERI and strong link share a line, are there circumstances where the other end of the strong link can't be eliminated?
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TKiel



Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI

PostPosted: Sat Sep 15, 2007 4:28 pm    Post subject: Reply with quote

Havard wrote:
you can eliminate a candidate at the point where the other end of the strong link and the ERI intersect.


The elimination never happens in the cells of the strong link and it never happens in the box where the ER occurs.
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Marty R.



Joined: 12 Feb 2006
Posts: 5119
Location: Rochester, NY, USA

PostPosted: Sat Sep 15, 2007 4:50 pm    Post subject: Reply with quote

TKiel wrote:
Havard wrote:
you can eliminate a candidate at the point where the other end of the strong link and the ERI intersect.


The elimination never happens in the cells of the strong link and it never happens in the box where the ER occurs.


Thank you Tracy, obviously I was pretty confused. Havard's term "other end of the strong link" wasn't clear to me. However, going back to the ERI in r2c7 and the strong link on 3 in c5: could the 3 in r5c7 be removed or would r5 also have to have the strong link on 3 for it to be removed?
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TKiel



Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI

PostPosted: Sat Sep 15, 2007 8:39 pm    Post subject: Reply with quote

No, if r2c7 were an ERI, then row 5 would not have to have a strong link for the exclusion to be valid, but I don't think there is an ER in box 3.

Code:

 *--------------------------------------------------------------------*
 | 3      1      2489   | 479    279    6      |  X      X      X     |
 | 24568  569    24689  | 459    2359   3459   |  .      .      X     |
 | 256    569    7      | 8      1      359    |  X      .      .     |
 |----------------------+----------------------+----------------------|
 | 1      8      26     | 67     4      37     |  X      X      .     |
 | 2456   7      2469   | 569    359    8      |  .      .      .     |
 | 456    569    3      | 1      59     2      |  X      X      .     |
 |----------------------+----------------------+----------------------|
 | 9      2      5      | 3      8      147    | 167    146    146    |
 | 67     3      16     | 4579   579    14579  | 2      8      149    |
 | 78     4      18     | 2      6      179    | 137    139    5      |
 *--------------------------------------------------------------------*


The X's represent the non-candidate cells in box 3, but they do not form a rectangle of four cells, so no ER exclusion is possible.

In box 6, the X's also represent the non-candidate cells for <3>. In this case there is a rectangle. So row 5 becomes one of the ERL's and column 9 the other, with the ERI at r5c9. One end of the strong link on <3> in column 5 lines up with the r5c9. So the intersection is at r2c9, which unfortunately does not have a <3>.


Last edited by TKiel on Sat Sep 15, 2007 9:09 pm; edited 1 time in total
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Marty R.



Joined: 12 Feb 2006
Posts: 5119
Location: Rochester, NY, USA

PostPosted: Sat Sep 15, 2007 9:09 pm    Post subject: Reply with quote

Thank you Tracy, you answered my key question. However, I wonder if we're on the same wave length about box 3. The grid and the diagram with the X's and 3's don't seem to mesh. Is that not a rectangle in box 3, r13c89?
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TKiel



Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI

PostPosted: Sat Sep 15, 2007 9:18 pm    Post subject: Reply with quote

Quote:
Is that not a rectangle in box 3, r13c89?


R3c89 contain <3>, so they can't be part of the cells that form the Empty Rectangle.
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Johan



Joined: 25 Jun 2007
Posts: 206
Location: Bornem Belgium

PostPosted: Sun Oct 21, 2007 10:16 pm    Post subject: Reply with quote

Code:

+----------------+-----------+-----------+
| 9    1    457  | 2   8 47  | 6   57 3  |
| 47   2    6    | 5   3 1   | 47  9  8  |
| 3457 3457 8    | 47  6 9   | 147 2  15 |
+----------------+-----------+-----------+
| 1357 6    357  | 9   4 2   | 37  8  15 |
| 145  45   2    | 3   7 8   | 9   15 6  |
| 37   8    9    | 1   5 6   | 237 4  27 |
+----------------+-----------+-----------+
| 6    9    57   | 478 1 457 | 278 3  27 |
| 8    47   147  | 6   2 3   | 5   17 9  |
| 2    357  1357 | 78  9 57  | 178 6  4  |
+----------------+-----------+-----------+


This is my first attempt on ER's
The puzzle comes from Gaby Vanhegan's site and is rated fiendish.
The posted grid is after basic steps, and could be solved by xy-wing, reading Harvard's topic from ER's i assume there is a ER in box 6 for digit <7>
The ERI is in R6C7(i think), one of the strong links on <7> in R2 can see the ERI, so i eliminated <7> in R6C1, because R6C1 can see the ERI and one of the two strong links on<7> in R2.

Is this elimination ER-logic or did i make a lucky guess?
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Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA

PostPosted: Mon Oct 22, 2007 1:02 am    Post subject: Reply with quote

Johan,

Yes, that is a correct ER elimination.

This happens to be a double ER: Before making your elimination, note that Box 4 also contains an ER on <7> that eliminates the <7> in R4C7.

By the way, both of these eliminations can also be seen as Finned X-Wings: one in R24; the other in R26.
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Johan



Joined: 25 Jun 2007
Posts: 206
Location: Bornem Belgium

PostPosted: Mon Oct 22, 2007 11:34 am    Post subject: Reply with quote

Asellus,

Thanks for confirming the elimination i made was based on ER logic and

not a shot in the dark.

Blinded by the first ER elimination i discovered, i missed the ER you

mentioned in Box 4 completely.
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