dailysudoku.com Forum Index dailysudoku.com
Discussion of Daily Sudoku puzzles
 
 FAQFAQ   SearchSearch   MemberlistMemberlist   UsergroupsUsergroups   RegisterRegister 
 ProfileProfile   Log in to check your private messagesLog in to check your private messages   Log inLog in 

OCT 25 VH

 
Post new topic   Reply to topic    dailysudoku.com Forum Index -> Daily Sudoku puzzles
View previous topic :: View next topic  
Author Message
Johan



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

PostPosted: Thu Oct 25, 2007 12:09 am    Post subject: OCT 25 VH Reply with quote

Two advanced steps for this one.

1. ER for digit <3> in Box 6, the ERI in R6C7 can see one of the strong links on <3> in C2, which eliminates <3> in R7C7.

2. XY-wing with [19] pivot in R6C9 eliminating <3> in R7C2, collapsing the puzzle.

The grid after basic steps :

Code:

+-------------+---------+--------------+
| 8   7  2    | 1  6 3  | 4    9   5   |
| 9   14 146  | 5  2 48 | 68   3   7   |
| 36  5  346  | 48 9 7  | 1    68  2   |
+-------------+---------+--------------+
| 367 2  1367 | 9  4 5  | 367  167 8   |
| 5   8  69   | 3  7 1  | 69   2   4   |
| 4   13 1379 | 2  8 6  | 379  5   139 |
+-------------+---------+--------------+
| 2   34 5    | 6  1 48 | 3789 78  39  |
| 37  6  347  | 48 5 9  | 2    18  13  |
| 1   9  8    | 7  3 2  | 5    4   6   |
+-------------+---------+--------------+
Back to top
View user's profile Send private message Send e-mail
George Woods



Joined: 28 Mar 2006
Posts: 304
Location: Dorset UK

PostPosted: Thu Oct 25, 2007 11:29 am    Post subject: an alternative solution Reply with quote

I found a solution based on the 13 in box 4 . Seeking a possible remote pair with the 13 in box9 it became evident that r6c2 if 1 brings a 39 pair to bear down on r8c9 and if 3 again denies 3 to this cell so r8c9 must be 1 .........
Back to top
View user's profile Send private message
Earl



Joined: 30 May 2007
Posts: 677
Location: Victoria, KS

PostPosted: Thu Oct 25, 2007 2:09 pm    Post subject: Oct 25 VH Reply with quote

I have seldom used so many techniques in one puzzles - an x-wing, a kite, two xyz-wings and an xy wing. But they were all evident and the puzzle opened quickly. Perhaps someone found a single move that unlocked it, which is always neater.

Earl
Back to top
View user's profile Send private message Send e-mail
sdq_pete



Joined: 30 Apr 2007
Posts: 119
Location: Rotterdam, NL

PostPosted: Thu Oct 25, 2007 2:13 pm    Post subject: Reply with quote

There's an X-wing on 6 in R25.
Thereafter, X-wing on 8 in R38. Then I saw a Finned X-wing on 3 in C29 (victim R7C7) and finally the XY-wing on 139 with pivot R6C9.

Peter
Back to top
View user's profile Send private message Visit poster's website
Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

PostPosted: Thu Oct 25, 2007 3:42 pm    Post subject: Reply with quote

Quote:
Perhaps someone found a single move that unlocked it, which is always neater.


Earl, the W-Wing on 13 in boxes 4 and 9 knocks out the 1 from r6c9 and that solves the puzzle. Clearly, this puzzle is like so many others in that many different techniques can be used depending on how and where one looks.
Back to top
View user's profile Send private message
Earl



Joined: 30 May 2007
Posts: 677
Location: Victoria, KS

PostPosted: Thu Oct 25, 2007 4:44 pm    Post subject: Oct 25 VH Reply with quote

Marty,

Is that W-wing valid in Johan's grid?

Earl
Back to top
View user's profile Send private message Send e-mail
Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

PostPosted: Thu Oct 25, 2007 4:51 pm    Post subject: Re: Oct 25 VH Reply with quote

Earl wrote:
Marty,

Is that W-wing valid in Johan's grid?

Earl

Yes.

The 3 in r7c2 and the 3s in r7c79 do the trick. Even though it's not a strong link, it either has to be the 3 in r7c2 or either one in box 9, since the other 13 is in box 9. I think it was Asellus who I can thank for that, as it was he who first pointed it out that I saw.

Code:
+-------------+---------+--------------+
| 8   7  2    | 1  6 3  | 4    9   5   |
| 9   14 146  | 5  2 48 | 68   3   7   |
| 36  5  346  | 48 9 7  | 1    68  2   |
+-------------+---------+--------------+
| 367 2  1367 | 9  4 5  | 367  167 8   |
| 5   8  69   | 3  7 1  | 69   2   4   |
| 4   13 1379 | 2  8 6  | 379  5   139 |
+-------------+---------+--------------+
| 2   34 5    | 6  1 48 | 3789 78  39  |
| 37  6  347  | 48 5 9  | 2    18  13  |
| 1   9  8    | 7  3 2  | 5    4   6   |
+-------------+---------+--------------+
Back to top
View user's profile Send private message
duffy



Joined: 13 Sep 2007
Posts: 26
Location: Toronto Canada

PostPosted: Thu Oct 25, 2007 6:55 pm    Post subject: Reply with quote

Underlining Marty's observation about multiple solution paths, here is Johan's grid after utilizing the x-wing Peter noted:
Code:
+-------------+---------+--------------+
| 8   7  2    | 1  6 3  | 4    9   5   |
| 9  @14 146  | 5  2 48 | 68   3   7   |
| 36  5  34   | 48 9 7  | 1    68  2   |
+-------------+---------+--------------+
| 367 2 #137  | 9  4 5  | 37   167 8   |
| 5   8  69   | 3  7 1  | 69   2   4   |
| 4   13 1379 | 2  8 6  | 379  5   139 |
+-------------+---------+--------------+
| 2   34 5    | 6  1 48 | 3789 78  39  |
| 37  6  347  | 48 5 9  | 2    18  13  |
| 1   9  8    | 7  3 2  | 5    4   6   |
+-------------+---------+--------------+
My key moves then were to remove all 3's from box 4, except the one in r6c2, by way of two xy-wings pivoted at the marked @ and # locations: the first clears the ones in c3 of that box, and the subsequent one clears the one in c1.
Laughing
Don D.
Back to top
View user's profile Send private message
cgordon



Joined: 04 May 2007
Posts: 769
Location: ontario, canada

PostPosted: Thu Oct 25, 2007 7:51 pm    Post subject: Reply with quote

Like Earl - I threw the book at this one - starting with an X-wing on 4s (R38), which I felt clever spotting - then 2 more easier to spot x-wings - then the ER already mentioned - then an xyz (pivot R4C3) - then, after much staring, the 13,19,39 xy-wing with pivot R6C9. Though it appears I could have just thrown a couple of pages at it, instead of the whole book. Still -a challenge for sure!
Back to top
View user's profile Send private message
KSipher



Joined: 24 Sep 2006
Posts: 38

PostPosted: Thu Oct 25, 2007 11:09 pm    Post subject: Reply with quote

Would anyone be willing to explain the empty rectangle in box 6? I've searched the web for explanations of the empty rectangle but I still can't see it. Perhaps if it was explained specifically for this sudoku, I might be able to see it.

Thanks so much! I've learned so much from this group!
Kathy
Back to top
View user's profile Send private message AIM Address
keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

PostPosted: Fri Oct 26, 2007 12:18 am    Post subject: Reply with quote

Code:
+----------------+----------------+-----------------+
| 8    7    2    | 1    6    3    | 4     9    5    |
| 9    14   146  | 5    2    48   | 68    3    7    |
| 36   5    346  | 48   9    7    | 1     68   2    |
+----------------+----------------+-----------------+
| 367  2    1367 | 9    4    5    | 367a  167  8    |
| 5    8    69   | 3    7    1    | 69    2    4    |
| 4    13e  1379 | 2    8    6    | 379b  5    139c |
+----------------+----------------+- ---------------+
| 2    34f  5    | 6    1    48   | 3789d 78   39   |
| 37   6    347  | 48   5    9    | 2     18   13   |
| 1    9    8    | 7    3    2    | 5     4    6    |
+----------------+----------------+-----------------+

"Empty Rectangle" is also called a "hinge". The relevant digit is <3>.

Look at the hinge: The L shape formed by the candidates for <3> in B6. a, b, c.

Note that one leg of the hinge can be extended to another cell, d, which also has a candidate <3>. Note also the strong link on <3> in C2: e, f.

e aligns with one arm of the hinge. f aligns with the target, d. There are two possibilities:

1. f is true, d must be false.

2. f is not true. e is true. b, c, are not true, a is true, d must be false.

Either way, d is false.

The better view is that

2. f is not true. e is true. The <3> in B6 does not lie in the horizontal arm of the hinge, it must be in the vertical arm.

Take a look at:

----- Empty Rectangles http://www.sudoku.com/boards/viewtopic.php?t=3251

Best wishes,

Keith


Last edited by keith on Fri Oct 26, 2007 12:48 am; edited 1 time in total
Back to top
View user's profile Send private message
Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

PostPosted: Fri Oct 26, 2007 12:33 am    Post subject: Reply with quote

Maybe it's just me, but I couldn't get the hang of Empty Rectangles until I read this description. Now I use them regularly.

http://www.intosudoku.com/Doc/EmptyRectangles.html
Back to top
View user's profile Send private message
keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

PostPosted: Fri Oct 26, 2007 12:47 am    Post subject: Reply with quote

I took a look at the link I posted. With all due respect, I think it's confusing.

Here is the basic idea:

Code:
 .  .  .  | .  .  .  | .  .  .
 .  .  .  | .  .  .  | .  .  .
 .  .  .  | .  .  .  | .  .  .
----------+----------+----------
 .  #  .  | .  .  .  | .  .  .
 #  #  #  | .  .  @  | .  .  .
 .  #  .  | .  .  .  | .  .  .
----------+----------+----------
 .  .  .  | .  .  .  | .  .  .
 .  %  .  | .  .  %  | .  .  .
 .  .  .  | .  .  .  | .  .  .

Elements:

1. A block where the candidates occur only in one row and one column is easy to spot. For example, # in B4. This is the hinge.

2. Another candidate, the target, in the same row (or column) as one arm of the hinge. This is @ above.

3. A strong link that aligns with the other arm of the hinge and with the target. This is % above.

Logic:

One of the % cells is true. Either way, the target, @, is not true.

Keith

PS: Only two of the # cells need to be present, so long as they are not in the same row or column. Another not very clear explanation is here: http://www.sudopedia.org/wiki/Empty_Rectangle


Last edited by keith on Fri Oct 26, 2007 1:09 am; edited 2 times in total
Back to top
View user's profile Send private message
KSipher



Joined: 24 Sep 2006
Posts: 38

PostPosted: Fri Oct 26, 2007 1:05 am    Post subject: Reply with quote

Oh wow. I get it. I followed thru Keith's explanation and was still somewhat confused, then I followed Marty's link and then I finally got it. But I wondered if I would ever be able to actually identify a ER myself. But then I went back and saw Keith's second reply and it made it so much clearer! Thanks to both of you.

Kathy Smile
Back to top
View user's profile Send private message AIM Address
Asellus



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

PostPosted: Fri Oct 26, 2007 1:14 am    Post subject: Reply with quote

A couple of comments on the solutions used above...

(1) That ER elimination of <3> in Box 6: This can also be seen as a Sashimi Swordfish in Rows 3, 4 and 8. R8C9 is the fin and R8C7 is the "missing <3> part" of the Swordfish. Or, in this case, you could describe it as an ordinary Finned Swordfish with the fin in a "remote Box."

(2) The {13} W-Wing is activated by the ER in Box 7, speaking of ERs. ERs do provide a strong link. However, the link is between the two "arms" of the "hinge" rather than between two cells. (Some describe this as "group coloring.") There is always an external strong link involved in a W-Wing.

As an additional advanced comment: if the pivot cell in an ER "hinge" is occupied by an ER candidate digit, then the link created by the ER is what is called a "strongly inferential link" instead of the ordinary strong link. The difference is that, in such a link, both alternatives can be true. If the pivot cell is true, then both arms of the ER are true. It doesn't matter in either of the cases above. The ER target cell in "(1)" still must be false. For the W-Wing in "(2)", if the hinge pivot cell were present (it isn't in this case) and true, then both {13} cells would be <1>. But, that's okay: the W-Wing <1> eliminations are still valid.
_____

Edited to clarify that (1) is talking about the <3> elimination, not that the ER and Sashimi Fish are the same things.
Back to top
View user's profile Send private message Visit poster's website
cgordon



Joined: 04 May 2007
Posts: 769
Location: ontario, canada

PostPosted: Fri Oct 26, 2007 12:07 pm    Post subject: Reply with quote

I'm a big fan of ERs because I find patterns easier to spot that numbers, e.g. xy-wings. So if I'd like to just add to Kieth's post that the hinges can be shaped like + (as in his example) or a T or an L as shown below. It's also worth mentioning that ALL the bits of the +, T and L DON'T have to be present. See the partial T example below.

T shape hinge
Code:

+-------+-------+-------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-------+-------+-------+
| # # # | . . @ | . . . |
| . # . | . . . | . . . |
| . # . | . . . | . . . |
+-------+-------+-------+
| . . . | . . . | . . . |
| . % . | . . % | . . . |
| . . . | . . . | . . . |
+-------+-------+-------+


L shape hinge
Code:

+-------+-------+-------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-------+-------+-------+
| # # # | . . @ | . . . |
| # . . | . . . | . . . |
| # . . | . . . | . . . |
+-------+-------+-------+
| . . . | . . . | . . . |
| % . . | . . % | . . . |
| . . . | . . . | . . . |
+-------+-------+-------+


PARTIAL T hinge
Code:

+-------+-------+-------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-------+-------+-------+
| # . . | . . @ | . . . |
| . . . | . . . | . . . |
| . # . | . . . | . . . |
+-------+-------+-------+
| . . . | . . . | . . . |
| . % . | . . % | . . . |
| . . . | . . . | . . . |
+-------+-------+-------+
Back to top
View user's profile Send private message
storm_norm



Joined: 18 Oct 2007
Posts: 1741

PostPosted: Fri Oct 26, 2007 7:06 pm    Post subject: Reply with quote

if you follow the "sudoku players forum", someone posted this puzzle there.
Back to top
View user's profile Send private message
storm_norm



Joined: 18 Oct 2007
Posts: 1741

PostPosted: Fri Oct 26, 2007 7:10 pm    Post subject: link Reply with quote

here is the link

http://www.sudoku.com/boards/viewtopic.php?t=5693[/url]
Back to top
View user's profile Send private message
Asellus



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

PostPosted: Fri Oct 26, 2007 9:03 pm    Post subject: Reply with quote

Thanks, storm_norm! It's definitely worth taking a look at that other forum thread.

There is an interesting use of an otherwise useless XYZ-Wing extended by that B6 ER to make an elimination.

And, Ruud provides Eureka notation for the B6 ER elimination of that <3>, which I'll copy here:

(1=3)r6c2 - (3)r7c2 = (3)r8c13 - (3=1)r8c9 => r6c9<>1

Pursuant to my comment above, if the "pivot" cell R8C2 in the ER "hinge" also contained a <3> candidate, then the notation would be:

(1=3)r6c2 - (3)r78c2 = (3)r8c123 - (3=1)r8c9 => r6c9<>1

The pivot cell <3> occurs on both sides of the (inferential) strong link.

Ruud also points out that this elimination is also viewable as an ALS chain.
Back to top
View user's profile Send private message Visit poster's website
keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

PostPosted: Sat Oct 27, 2007 2:36 pm    Post subject: Reply with quote

These things are becoming pretty easy to spot!

Code:
+----------------+----------------+----------------+
| 8    7    2    | 1    6    3    | 4    9    5    |
| 9    14#  146  | 5    2    48@  | 68   3    7    |
| 36   5    346  | 48@  9    7    | 1    68   2    |
+----------------+----------------+----------------+
| 367  2    1367%| 9    4    5    | 367  167% 8    |
| 5    8    69   | 3    7    1    | 69   2    4    |
| 4   -13   1379 | 2    8    6    | 379  5    139  |
+----------------+----------------+----------------+
| 2    34   5    | 6    1    48   | 3789 78   39   |
| 37   6    347  | 48@  5    9    | 2    18#% 13   |
| 1    9    8    | 7    3    2    | 5    4    6    |
+----------------+----------------+----------------+

In the <48> chain @, the ends have the same value. You can make an extended XY-wing with the cells marked #. One of R2C2 and R8C8 is <1>.

Coloring on <1>, %, says that if R8C8 is <1>, so is R4C3. So, R6C2 cannot be <1>, it must be <3>, and the puzzle is solved.

Keith
Back to top
View user's profile Send private message
Display posts from previous:   
Post new topic   Reply to topic    dailysudoku.com Forum Index -> Daily Sudoku puzzles All times are GMT
Page 1 of 1

 
Jump to:  
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