| View previous topic :: View next topic |
| Author |
Message |
Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
|
 Posted: Sat Sep 15, 2007 2:48 pm Post subject: Empty rectangles |
 |
|
| 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? |
|
| Back to top |
|
 |
TKiel
Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI
|
| Posted: Sat Sep 15, 2007 4:28 pm Post subject: |
|
|
| 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. |
|
| Back to top |
|
|
Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
|
| Posted: Sat Sep 15, 2007 4:50 pm Post subject: |
|
|
| 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? |
|
| Back to top |
|
|
TKiel
Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI
|
| Posted: Sat Sep 15, 2007 8:39 pm Post subject: |
|
|
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 |
|
| Back to top |
|
|
Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
|
| Posted: Sat Sep 15, 2007 9:09 pm Post subject: |
|
|
| 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? |
|
| Back to top |
|
|
TKiel
Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI
|
| Posted: Sat Sep 15, 2007 9:18 pm Post subject: |
|
|
| 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. |
|
| Back to top |
|
|
Johan
Joined: 25 Jun 2007
Posts: 206
Location: Bornem Belgium
|
| Posted: Sun Oct 21, 2007 10:16 pm Post subject: |
|
|
| 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? |
|
| Back to top |
|
|
Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
|
| Posted: Mon Oct 22, 2007 1:02 am Post subject: |
|
|
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. |
|
| Back to top |
|
|
Johan
Joined: 25 Jun 2007
Posts: 206
Location: Bornem Belgium
|
| Posted: Mon Oct 22, 2007 11:34 am Post subject: |
|
|
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. |
|
| Back to top |
|
|
|
|
You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot vote in polls in this forum
|
Powered by phpBB © 2001, 2005 phpBB Group
|
FAQ
Search
Memberlist
Usergroups
Register
Profile
Log in to check your private messages
Log in
