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 

Kicking the x-wing up a notch...

 
Post new topic   Reply to topic    dailysudoku.com Forum Index -> Other puzzles
View previous topic :: View next topic  
Author Message
AZ Matt



Joined: 03 Nov 2005
Posts: 63
Location: Hiding under my desk in Phoenix AZ USA

PostPosted: Fri Aug 25, 2006 9:31 pm    Post subject: Kicking the x-wing up a notch... Reply with quote

Here's a good puzzle. Plenty of advanced techniques to work through. It really helped me work out my advanced x-wing solving techniques, and I will use it as an example of the technique I have used to solve many extreme puzzles.

Code:
1..8.239.
3...4...2
..6......
.7..3.9..
.6.4.5.7.
..3.1..5.
......6..
6...7...1
.851.6..7


So using basic techniques, I get to here:

Code:
1    4  7     8    6  2    3    9   5
3    5  89    79   4  179  178  6   2
289  29 6     3    5  179  178  6   48

5    7  124   26   3  8    9    124 46
289  6  1289  4    29 5    128  7   3
2489 29 3     2679 1  79   248  5   486

7    1  24    5    8  3    6    24  9
6    3  29    29   7  4    5    8   1
249  8  5     1    29 6    24   3   7


I first look for x-wings, mainly because I think of it as the next "basic" solving technique, and as a consequence I am also looking for swordfish and what I call imbalanced patterns -- patterns that don't permit an organized placement of one number in the cells for which it is a candidate.

The swordfish on the <2> in columns 4, 7, and 8 is fairly easy to spot (the r4c34 and the r8c34 are just crying out to be an x-wing), but doesn't yield much.

Now if I were one who looked for every solving technique all the time, I would have spotted potential in the <29> swirling around in boxes 5, 7 and 8. But I am not that person. I didn't find any x-wings, but I am still fishing around (so to speak), and here's what I see.

I look for strong links and I see that the <9> has only two candidate cells in each of rows 8 and 9, columns 2 and 5, and boxes 7 and 8. Looks like a good candidate for fishing. On a grid it looks like this (there are no canditates in boxes 3, 6, and 9):

Code:
... ...
..9 9.9
99. ..9

... ...
9.9 .9.
99. 9.9
... ...
..9 9..
9.. .9.


Now, I will try to simplify my fishing technique. I look for potential x-wings in the pattern and spot many (at least six). The one thing I note is that only the r5c3 has insufficient partners to form a potential x-wing. An imbalance. And sure enough, simply by looking at the interplay of row 5 and rows 8 and 9, it is easy to see that r5c3 cannot be <9>. Testing it out, I also discover that I can eliminate the nine as a candidate in r3c1 and r6c1.

Usually, when I make a discoverylike this, the puzzle is nearly over. Not even close here. As the downhill mountain road sign says -- "Truckers -- You are not down yet!!!"

I enjoyed this puzzle so much I did it twice, and discovered you can get the same information I got from a remote pair on the <29>, removing the <9> from r5c3. This makes a swordfish possible on <9>, eliminating it from r3c1 and r6c1.

Anyway, I have caught a lot of fish this way. I have given up on keeping track of the names, though I would be curious if this one has a name ("Nisho"?).

And I thought I'd share the puzzle.
Back to top
View user's profile Send private message
Marty R.



Joined: 12 Feb 2006
Posts: 5179
Location: Rochester, NY, USA

PostPosted: Sat Aug 26, 2006 12:34 am    Post subject: Reply with quote

Matt, you've got some sort of typo what with two 6s in box 3.

Code:
1    4  7     8    6  2    3    9   5
3    5  89    79   4  179  178  6   2
289  29 6     3    5  179  178  6   48

5    7  124   26   3  8    9    124 46
289  6  1289  4    29 5    128  7   3
2489 29 3     2679 1  79   248  5   486

7    1  24    5    8  3    6    24  9
6    3  29    29   7  4    5    8   1
249  8  5     1    29 6    24   3   7
Back to top
View user's profile Send private message
David Bryant



Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado

PostPosted: Sat Aug 26, 2006 12:37 pm    Post subject: Here's a corrected grid ... Reply with quote

Here's the corrected version of Matt's grid, Marty.
Code:
1    4  7     8    6  2    3    9   5
3    5  89    79   4  179  178  6   2
289  29 6     3    5  179  1478 14  48

5    7  124   26   3  8    9    124 46
289  6  1289  4    29 5    128  7   3
2489 29 3     2679 1  79   248  5   486

7    1  24    5    8  3    6    24  9
6    3  29    29   7  4    5    8   1
249  8  5     1    29 6    24   3   7

Matt:

I'm also very fond of the technique you used on the "9"s in this puzzle. The classical name for this technique is "Nishio", and it's usually explained as a sort of proof by contradiction.
Code:
1    4   7     8    6   2    3    9   5
3    5   89    79   4   179  178  6   2
289* 29  6     3    5   179  1478 14  48

5    7   124   26   3   8    9    124 46
289  6   1289  4    29  5    128  7   3
2489 29* 3     2679 1   79   248  5   486

7    1   24    5    8   3    6    24  9
6    3   29*   29   7   4    5    8   1
249  8   5     1    29* 6    24   3   7

r3c1 = 9 ==> r6c2 = 9
r3c1 = 9 ==> r8c3 = 9 ==> r9c5 = 9

See the cells marked "*" above -- clearly we cannot place a "9" in box 5 if these 4 cells contain "9", and therefore r3c1 cannot be a "9".

I noticed a "UR" pattern in the "9"s while I was performing the Nishio analysis -- that was kind of cute, but I think I'll wait untiil later to explain it ... this post is already a bit long. dcb
Back to top
View user's profile Send private message Send e-mail Visit poster's website
AZ Matt



Joined: 03 Nov 2005
Posts: 63
Location: Hiding under my desk in Phoenix AZ USA

PostPosted: Sun Aug 27, 2006 4:21 pm    Post subject: Oops! Reply with quote

Sorry about the slip-up Embarassed .

I usually finish a puzzle a forget about it, but I have done this one three times now, and it seems endless how many (very difficult) ways there are to solve it.
Back to top
View user's profile Send private message
keith



Joined: 19 Sep 2005
Posts: 3184
Location: near Detroit, Michigan, USA

PostPosted: Sun Aug 27, 2006 10:21 pm    Post subject: Reply with quote

Or, there is a remote naked pair on <29>, an X-wing, a Swordfish ...

Keith
Back to top
View user's profile Send private message
ravel



Joined: 21 Apr 2006
Posts: 536

PostPosted: Mon Aug 28, 2006 9:21 am    Post subject: Reply with quote

... or you can solve it with the remote pair, 2 x-wings, 2 xy-wings, xyz-wing.
Really interesting puzzle.
Back to top
View user's profile Send private message
David Bryant



Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado

PostPosted: Mon Aug 28, 2006 4:15 pm    Post subject: Combining "Nishio" with a "UR" Reply with quote

Here's how I solved this puzzle, starting from the position Matt posted.
Code:
1    4   7     8    6   2    3    9   5
3    5   89    79+  4   179  178  6   2
289  29+ 6     3    5   179  1478 14  48
5    7   124   26   3   8    9    124 46
289+ 6   1289  4    29- 5    128  7   3
2489 29  3     2679 1   79+  248  5   486
7    1   24    5    8   3    6    24  9
6    3   29+   29-  7   4    5    8   1
249- 8   5     1    29+ 6    24   3   7

I started my analysis of the "9"s from r9c5.

r9c5 = 9 ==> r8c3 = 9
r9c5 = 9 ==> "9" in box 5 lies in row 6 ==> r5c1 = 9
(r5c1 = 9 & r8c3 = 9) ==> r3c2 = 9

These cells are marked with a "+" sign in the grid. Here's how we find a "UR" by following a chain.

r9c5 = 9 ==> r5c5 = 2 ==> r4c4 = 6 ==> {7, 9} at r6c4

But if this is true we almost have the "deadly pattern" in r26c46, so that r2c6 must be a "1". Therefore

r9c5 = 9 ==> r2c4 = 9 ==> r6c6 = 9

What if r9c5 is not 9?

r9c5 <> 9 ==> (r5c5 = 9 & r8c4 = 9 & r9c1 = 9)

These cells are marked "-" in the grid ... we can apparently eliminate "9" from r3c1, r5c3, r6c1, and r6c4, revealing an X-Wing in c34r28 that also allows us to eliminate the "9" at r2c6. (Keith should like this -- it combines "Nishio" / coloring with a "UR"). Now the grid looks like this.
Code:
1    4   7     8    6  2    3    9   5
3    5   89a   79   4  17   178  6   2
28A  29  6     3    5  179  1478 14  48B
5    7   124a  26   3  8    9    124 46*
289  6   128a  4    29 5    128  7   3
248  29a 3     267  1  79   248  5   486
7    1   24    5    8  3    6    24  9
6    3   29    29   7  4    5    8   1
249  8   5     1    29 6    24   3   7

A straightforward double-implication chain finishes it off.

A1. r3c1 = 2 ==> r6c2 = 2 ==> {1, 4} at r4c3 & {1, 8} at r5c3
A2. r3c1 = 2 ==> r2c3 = 8 ==> r5c3 = 1 ==> r4c3 = 4 ==> r4c9 = 6
B. r3c1 = 8 ==> r3c9 = 4 ==> r4c9 = 6

So r4c9 = 6, and the rest is easy. dcb
Back to top
View user's profile Send private message Send e-mail Visit poster's website
Display posts from previous:   
Post new topic   Reply to topic    dailysudoku.com Forum Index -> Other 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