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Earl
Joined: 30 May 2007
Posts: 677
Location: Victoria, KS
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 Posted: Sat Aug 16, 2008 2:45 pm Post subject: August 16 DB |
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The August 16 DB can be solved with various techniques. I used two xy-wings then a UR with a virtual cell (34). Coloring will also do it. But I could not find a single magic bullet.
| Code: |
+-------+-------+-------+
| . 5 3 | . 1 . | 4 . . |
| 6 . . | 2 . . | . . . |
| . 1 2 | . 8 . | 9 . . |
+-------+-------+-------+
| 5 . . | 9 . . | 2 . 1 |
| . 2 . | . . . | . 9 . |
| 1 . 4 | . . 2 | . . 7 |
+-------+-------+-------+
| . . 5 | . 7 . | 8 6 . |
| . . . | . . 8 | . . 9 |
| . . 7 | . 9 . | 1 5 . |
+-------+-------+-------+
|
Play this puzzle online at the Daily Sudoku site
Earl |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Sat Aug 16, 2008 5:58 pm Post subject: |
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Earl, I also noticed several options but all required two steps minimum to solve the puzzle.
A Type 4 UR on <56> was available after basics or it became a Type 1 after a xy-wing on <347>. As you indicated, coloring or kites were also very effective.
Ted |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Sat Aug 16, 2008 6:26 pm Post subject: Re: August 16 DB |
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| Earl wrote: | | I used two xy-wings then a UR with a virtual cell (34). |
Earl, I have not been able to locate the UR <34> even after a couple of xy-wings on <347>. Would you provide some details, and include info on the "virtual cell <34>"?
Thanks .........
Ted |
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ravel
Joined: 21 Apr 2006
Posts: 536
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| Posted: Sat Aug 16, 2008 6:49 pm Post subject: |
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Here is a one stepper:
| Code: | *--------------------------------------------------------------------*
| 8 5 3 | 7 1 9 | 4 2 6 |
| 6 47 9 | 2 345 345 | 357 1 8 |
| 4-7 1 2 | 346 8 3456 | 9 #37 35 |
|----------------------+----------------------+----------------------|
| 5 37 68 | 9 346 347 | 2 *348 1 |
|#37 2 68 | 1348 3456 13457 |@356 9 @345 |
| 1 9 4 | 38 56 2 | 56 *38 7 |
|----------------------+----------------------+----------------------|
| 9 34 5 | 134 7 134 | 8 6 2 |
| 34 6 1 | 5 2 8 | 37 347 9 |
| 2 8 7 | 346 9 346 | 1 5 34 |
*--------------------------------------------------------------------*
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The w-wing 37 is connected by a grouped strong link for 3 in box 6 (either one of the *'s or one of the @'s must be 3).
So 7 can be eliminated from r3c1.
(btw this link is also part of an ER, which eliminates 3 in r8c8) |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sat Aug 16, 2008 7:31 pm Post subject: |
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| ravel wrote: | Here is a one stepper:
| Code: | *--------------------------------------------------------------------*
| 8 5 3 | 7 1 9 | 4 2 6 |
| 6 47 9 | 2 345 345 | 357 1 8 |
| 4-7 1 2 | 346 8 3456 | 9 #37 35 |
|----------------------+----------------------+----------------------|
| 5 37 68 | 9 346 347 | 2 *348 1 |
|#37 2 68 | 1348 3456 13457 |@356 9 @345 |
| 1 9 4 | 38 56 2 | 56 *38 7 |
|----------------------+----------------------+----------------------|
| 9 34 5 | 134 7 134 | 8 6 2 |
| 34 6 1 | 5 2 8 | 37 347 9 |
| 2 8 7 | 346 9 346 | 1 5 34 |
*--------------------------------------------------------------------*
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The w-wing 37 is connected by a grouped strong link for 3 in box 6 (either one of the *'s or one of the @'s must be 3).
So 7 can be eliminated from r3c1.
(btw this link is also part of an ER, which eliminates 3 in r8c8) |
Grouped strong links are a little too advanced for me. However, the 34 W-Wing in boxes 79, with pincer coloring, eliminates the 3 in r5c9. That exposes the W-Wing on 37 in boxes 39 which finishes the puzzle, a two-stepper. |
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ravel
Joined: 21 Apr 2006
Posts: 536
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| Posted: Sat Aug 16, 2008 9:05 pm Post subject: |
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| Marty R. wrote: | | Grouped strong links are a little too advanced for me. |
I am sure, no. I know, you can use the empty rectangle in box 6 for the ER elimination. So you also can connect the w-wing with it.
Wasn't there already a thread about ER-w-wings ? |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Sun Aug 17, 2008 4:39 am Post subject: |
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Marty,
I second ravel! Grouped links really aren't hard to grasp and ERs are the most well-known example. In terms of "activating" a W-Wing, all you need to know is that an ER provides a strong link (in this case between a row fragment and a column fragment within a box: If <3> is not in r5 of b6, then it must be in c8 of b6, and vice-versa). Since both <3>s of the two 37 cells can "see" the <3> ER, we have our W-Wing. |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sun Aug 17, 2008 5:21 am Post subject: |
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| It's late and I'll try to digest that on Sunday. |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sun Aug 17, 2008 3:49 pm Post subject: |
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OK, I can see how the 3s in b6 act as a strong link to connect the 37 cells.
Is there a concise definition of a grouped link?
I don't understand how the ER fits into this scenario.
I assume that Ravel saw the 37 cells, looked at b6 and saw the W-Wing connection without looking at ERs. |
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ravel
Joined: 21 Apr 2006
Posts: 536
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| Posted: Sun Aug 17, 2008 6:53 pm Post subject: |
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| Marty R. wrote: | | Is there a concise definition of a grouped link? |
This is the best i remember, a post by Asellus.
Added:
Note the differences between ER-w-wing, grouped kite and ER. E.g.:
| Code: | . . . | . . . |
-7 . . | . 37 . |
. . . | . . . |
----------------------
. . . | . 3 . |
37 . . | 3 3 3 |
. . . | . 3 . | |
ER-w-wing only needs an empty rectangle (if the 3 is not in the row of the box, it must be in the column of the box and vice vera), that one of the pairs must be 7
| Code: | . . . | . . . |
-3 . . | . 3 . |
. . . | . . . |
----------------------
. . . | . 3 . |
3 . . | 3 . 3 |
. . . | . 3 . | |
A grouped kite - there must not be other 3's in row 5 or column 5 - needs a weak link (if the 3 is in the row of the box, it cant be in the column of the box and vice versa).
[Edit:] Corrected strong to weak. All cells but the middle cell may contain a 3.
| Code: | 3 . . | . -3 . |
. . . | . . . |
----------------------
. . . | . 3 . |
3 . . | 3 3 3 |
. . . | . 3 . | |
ER: The 3's in column 1 must be conjugated.
| Quote: | | I assume that Ravel saw the 37 cells, looked at b6 and saw the W-Wing connection without looking at ERs. |
Yes, but in future i will do  (though they seem to be not much common as w-wing connections).
Last edited by ravel on Mon Aug 18, 2008 7:24 am; edited 1 time in total |
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Earl
Joined: 30 May 2007
Posts: 677
Location: Victoria, KS
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| Posted: Mon Aug 18, 2008 2:07 am Post subject: Aug 16 DB |
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Ted,
Regarding the (34) virtual cell for the (56) UR.
1) an xy-wing eliminates a 3 from R8C8.
2) an xy-wing then eliminates a 3 from R3C9.
The remaining candidates in R5C9 are then 34
3) The UR (56) has possible candidates in R 5 of 3, or 34.
Since only 3 or 4 are possible solutions in R5 for the UR,
(34) becomes as virtual cell which along with the 34 in R5C9
eliminates the 3 from R5C1 and solves the puzzle.
Hope this helps.
Earl |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Mon Aug 18, 2008 4:13 am Post subject: |
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Earl,
Thanks for the detailed solution; it it did the trick.
My first step after basics was to use the UR <56> as a Type 4 due to the strong link on <6> in col7 to delete the <5> in r5c5. By using the two xy-wings first, you treated the UR as a Type 3 to make your deletions.
I guess that this is another case of different sequences using/needing different logic to solve the puzzle.
Again, thanks for the time and effort.
Ted |
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ravel
Joined: 21 Apr 2006
Posts: 536
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| Posted: Mon Aug 18, 2008 7:51 am Post subject: |
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When i looked at my post above again, i saw, that for the kite sample i mixed "strong" and "weak". In the row and column there must be a strong (grouped) link, in the box a weak one.
The point is, that with grouped links a strong link is not necessariliy a weak one too.
An empty recatangle gives you a strong link, but not a weak one, if the crossing cell is part of both groups.
| Code: | e 3 e 3 3 3
3 3 3 3 e 3
e 3 e 3 3 3 |
The left box is a grouped strong link in the box with maximum 3's (e for empty/not 3), the right one a weak link between row 2 and column 2 of the box. |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Sun Aug 24, 2008 7:37 am Post subject: |
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Ravel,
are you ending your posting career on this site at 999 posts?? |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Wed Aug 27, 2008 10:56 pm Post subject: |
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| storm_norm wrote: | Ravel,
are you ending your posting career on this site at 999 posts?? |
Perhaps (and I hope) not. It used to be that the PHP software had a bug / design flaw, in that it stopped incrementing the count of messages posted beyond 999.
By the way, South Africa has signs all over counting down the days to the soccer world cup. On the day we arrived, my son pointed out that the count was 666. Not, we thought, a good omen.
Keith |
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