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daj95376
Joined: 23 Aug 2008
Posts: 3854
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 Posted: Fri Nov 13, 2009 5:48 pm Post subject: Puzzle NR 09/11/13 BBDB |
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| Code: | +-----------------------+
| 7 1 . | 6 2 9 | 5 . . |
| 2 . . | 4 . 5 | . . . |
| . . 5 | . 8 . | . . 2 |
|-------+-------+-------|
| 6 2 . | 3 . . | . 5 . |
| 3 . 1 | . 9 . | . . . |
| 9 5 . | . . 2 | . 4 3 |
|-------+-------+-------|
| 1 . . | . . . | 3 . . |
| . . . | 9 . 3 | . 2 . |
| . . 2 | . . 1 | . . . |
+-----------------------+
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Play this puzzle online at the Daily Sudoku site |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Fri Nov 13, 2009 8:49 pm Post subject: |
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here is a solution which uses almost-x-wings in every step
| Code: | .---------------------.---------------------.---------------------.
| 7 1 3 | 6 2 9 | 5 8 4 |
| 2 689 689 | 4 3 5 | 679 1 679 |
| 4 69 5 | 1 8 7 | 69 3 2 |
:---------------------+---------------------+---------------------:
| 6 2 478 | 3 147 48 | 1789 5 1789 |
| 3 478 1 | 5 9 468 | 2 67 678 |
| 9 5 78 | 78 16 2 | 16 4 3 |
:---------------------+---------------------+---------------------:
| 1 4679 4679 | 2 4567 468 | 3 67 5678 |
| 58 467 467 | 9 4567 3 | 14678 2 15678 |
| 58 3 2 | 78 4567 1 | 4678 9 5678 |
'---------------------'---------------------'---------------------' |
1...[x-wing(8)r57c69] = (8)r5c2 - (8)r6c3 = (8)r6c4; r4c6 <> 8
2...[x-wing(1)r46c57] = (1-9)r4c9 = (9)r4c7 - (9=6)r3c7 - (6=1)r6c7; r8c7 <> 1
3...(7)r9c45 = [x-wing(7)r29c79] - (7)r5c9 = (7)r5c8 - (7=6)r7c8 - (6)r7c6 = (6)r5c6 - (6=1)r6c5 - (1=7)r4c5; r78c5 <> 7
4...[x-wing(8)r89c17] = (8)r4c7 - (8)r8c7 = (8)r8c1 - (8=5)r9c1 - (5)r9c9 = (5-8)r7c9 = (8)r7c6; r9c4 <> 8
step 4 is really stretching the chain out just to make it work.
step 4 could easily be this...
(8)r8c7 = (8)r8c1 - (8=5)r9c1 - (5)r9c9 = (5)r7c9; r7c9 <> 8
this post is in response to Myth Jellies thread on how set cover candidates closely resemble naked sets/subsets/als etc etc etc... and since Danny was also involved in the discussion I thought I would post this entirely almost x-wing approach to a puzzle which he has generated.
the thread is here.
http://www.sudoku.com/boards/viewtopic.php?t=14765&start=0 |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Sat Nov 14, 2009 12:07 am Post subject: |
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| storm_norm wrote: | here is a solution which uses almost-x-wings in every step
1...[x-wing(8)r57c69] = (8)r5c2 - (8)r6c3 = (8)r6c4; r4c6 <> 8
2...[x-wing(1)r46c57] = (1-9)r4c9 = (9)r4c7 - (9=6)r3c7 - (6=1)r6c7; r8c7 <> 1
3...(7)r9c45 = [x-wing(7)r29c79] - (7)r5c9 = (7)r5c8 - (7=6)r7c8 - (6)r7c6 = (6)r5c6 - (6=1)r6c5 - (1=7)r4c5; r78c5 <> 7
4...[x-wing(8)r89c17] = (8)r4c7 - (8)r8c7 = (8)r8c1 - (8=5)r9c1 - (5)r9c9 = (5-8)r7c9 = (8)r7c6; r9c4 <> 8
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Hmmm. When almost X-Wings are used as in your (1,2,4), then they also meet the definition of a Kraken X-Wing -- remote fin cell(s) produce one or more eliminations in common with the X-Wing. However, your (3) uses the X-Wing as part of the chain. Interesting, but I'll have to review the definition of an almost X-Wing! |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Sat Nov 14, 2009 12:49 am Post subject: |
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I am looking forward to reviewing Norm's post but in the meantime here is my 5 step solution.
1: I started with a basic x-wing on 6 in r57c68,
2: Next I found a fun w-wing 78 in r5c9 & r9c4 with strong link 8 in row7 that makes a deletion; a transport then makes a second deletion; then after cleanup, another pincer transport makes two more deletions. FUN sequence.
3: xy-wing -478 with vertex 78 in r6c3, pincer 48 in r5c2 and pincer47 is a pseudocell in box5 makes two deletions,
4: x-wing 8 in r57c69,
5: xy-wing -567 with vertex 67 in r7c8, pincer 56 in r9c9, pincer 47 a pseudocell in row7 to complete the puzzle.
Danny, thanks again the the fine puzzles....
Ted |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Sat Nov 14, 2009 12:53 am Post subject: |
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| Quote: | | When almost X-Wings are used as in your (1,2,4), then they also meet the definition of a Kraken X-Wing -- remote fin cell(s) produce one or more eliminations in common with the X-Wing |
yes, I think my step 1 is also a finned swordfish of some sort. I was just ignoring all other fish and or fins when creating the almost x-wings. I basically wanted to put them in a chain instead of trying to decipher which fish/fin they would be categorized under. |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Sat Nov 14, 2009 1:47 am Post subject: |
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| tlanglet wrote: | Danny, thanks again the the fine puzzles....
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Hello Ted,
I'm glad you are enjoying my puzzles. Others seem happy as well. Good!!!
Regards, Danny |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Sat Nov 14, 2009 1:50 am Post subject: |
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here are the steps...
1...[x-wing(8)r57c69] = (8)r5c2 - (8)r6c3 = (8)r6c4; r4c6 <> 8
2...[x-wing(1)r46c57] = (1-9)r4c9 = (9)r4c7 - (9=6)r3c7 - (6=1)r6c7; r8c7 <> 1
3...(7)r9c45 = [x-wing(7)r29c79] - (7)r5c9 = (7)r5c8 - (7=6)r7c8 - (6)r7c6 = (6)r5c6 - (6=1)r6c5 - (1=7)r4c5; r78c5 <> 7
4...[x-wing(8)r89c17] = (8)r4c7 - (8)r8c7 = (8)r8c1 - (8=5)r9c1 - (5)r9c9 = (5-8)r7c9 = (8)r7c6; r9c4 <> 8
this is the break down of where the almost x-wings are at each step.
my step one involves the 8's almost x-wing
| Code: | +-----------------+-----------------+-------------------+
| 7 1 3 | 6 2 9 | 5 8 4 |
| 2 689 689 | 4 3 5 | 679 1 679 |
| 4 69 5 | 1 8 7 | 69 3 2 |
+-----------------+-----------------+-------------------+
| 6 2 478 | 3 147 48 | 1789 5 1789 |
| 3 47(8) 1 | 5 9 46(8) | 2 67 67(8) |
| 9 5 78 | 78 16 2 | 16 4 3 |
+-----------------+-----------------+-------------------+
| 1 4679 4679 | 2 4567 46(8) | 3 67 567(8) |
| 58 467 467 | 9 4567 3 | 14678 2 15678 |
| 58 3 2 | 78 4567 1 | 4678 9 5678 |
+-----------------+-----------------+-------------------+ |
in the grid above you can see that if the 8 in r5c2 is false then the x-wing(8)r57c69 is true.
step 2 is the 1's almost x-wing | Code: | +--------------+--------------+------------------+
| 7 1 3 | 6 2 9 | 5 8 4 |
| 2 8 69 | 4 3 5 | 679 1 679 |
| 4 69 5 | 1 8 7 | 69 3 2 |
+--------------+--------------+------------------+
| 6 2 78 | 3 7(1) 4 | 89(1) 5 89(1) |
| 3 4 1 | 5 9 68 | 2 67 678 |
| 9 5 78 | 78 6(1) 2 | 6(1) 4 3 |
+--------------+--------------+------------------+
| 1 679 469 | 2 4567 68 | 3 67 5678 |
| 58 67 46 | 9 4567 3 | 14678 2 15678 |
| 58 3 2 | 78 4567 1 | 4678 9 5678 |
+--------------+--------------+------------------+ |
if the 1 in r4c9 is false, then the x-wing(1)r46c57 is true.
step 3 is the almost x-wing 7's
| Code: | +--------------+------------------+--------------------+
| 7 1 3 | 6 2 9 | 5 8 4 |
| 2 8 69 | 4 3 5 | 69(7) 1 69(7) |
| 4 69 5 | 1 8 7 | 69 3 2 |
+--------------+------------------+--------------------+
| 6 2 78 | 3 17 4 | 189 5 89 |
| 3 4 1 | 5 9 68 | 2 67 678 |
| 9 5 78 | 78 16 2 | 16 4 3 |
+--------------+------------------+--------------------+
| 1 679 469 | 2 4567 68 | 3 67 5678 |
| 58 67 46 | 9 4567 3 | 4678 2 1 |
| 58 3 2 | 8(7) 456(7) 1 | 468(7) 9 568(7) |
+--------------+------------------+--------------------+ |
if the group of 7's in r9c45 is false, then the x-wing(7)r29c79 is true.
step 4 is the almost x-wing on 8's
| Code: | +----------------+--------------+------------------+
| 7 1 3 | 6 2 9 | 5 8 4 |
| 2 8 69 | 4 3 5 | 679 1 679 |
| 4 69 5 | 1 8 7 | 69 3 2 |
+----------------+--------------+------------------+
| 6 2 78 | 3 17 4 | 19(8) 5 89 |
| 3 4 1 | 5 9 68 | 2 67 678 |
| 9 5 78 | 78 16 2 | 16 4 3 |
+----------------+--------------+------------------+
| 1 679 469 | 2 456 68 | 3 67 5678 |
| 5(8) 67 46 | 9 456 3 | 467(8) 2 1 |
| 5(8) 3 2 | 78 4567 1 | 46(8) 9 568 |
+----------------+--------------+------------------+ |
if the 8 in r4c7 is false, then the x-wing(8)r89c17 is true
I orginally had a different almost x-wing. that is the reason for the edit.
Last edited by storm_norm on Sat Nov 14, 2009 3:59 am; edited 5 times in total |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Sat Nov 14, 2009 1:55 am Post subject: |
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| storm_norm wrote: | | Quote: | | When almost X-Wings are used as in your (1,2,4), then they also meet the definition of a Kraken X-Wing -- remote fin cell(s) produce one or more eliminations in common with the X-Wing |
yes, I think my step 1 is also a finned swordfish of some sort. I was just ignoring all other fish and or fins when creating the almost x-wings. I basically wanted to put them in a chain instead of trying to decipher which fish/fin they would be categorized under. |
Hello Norm,
I didn't check the puzzle for different fish. Other than X-Wings and XY-Wings, the only other advanced step my solver needed was an Empty Rectangle for r4c6<>8.
I understand that you had a purpose in mind and that it was productive. It must have been fun hunting down all those patterns!
Thanks for including the PMs for each step. Initially, I had fun tracking down when you applied each step.
Regards, Danny |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Sat Nov 14, 2009 1:59 am Post subject: |
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| Quote: | | I understand that you had a purpose in mind and that it was productive. It must have been fun hunting down all those patterns! |
it was a very nice puzzle to try those almost x-wings |
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Myth Jellies
Joined: 27 Jun 2006
Posts: 64
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| Posted: Sat Nov 14, 2009 8:32 am Post subject: |
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Very creative, Norm   |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Sat Nov 14, 2009 2:12 pm Post subject: |
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Norm ,
I normally look for finned, sashimi and Kraken fish, but do not pursue them to the degree you did here, especially on step 2
| Code: |
step 2 is the 1's almost x-wing
Code:
+--------------+--------------+------------------+
| 7 1 3 | 6 2 9 | 5 8 4 |
| 2 8 69 | 4 3 5 | 679 1 679 |
| 4 69 5 | 1 8 7 | 69 3 2 |
+--------------+--------------+------------------+
| 6 2 78 | 3 7(1) 4 | 89(1) 5 89(1) |
| 3 4 1 | 5 9 68 | 2 67 678 |
| 9 5 78 | 78 6(1) 2 | 6(1) 4 3 |
+--------------+--------------+------------------+
| 1 679 469 | 2 4567 68 | 3 67 5678 |
| 58 67 46 | 9 4567 3 | 14678 2 15678 |
| 58 3 2 | 78 4567 1 | 4678 9 5678 |
+--------------+--------------+------------------+
if the 1 in r4c9 is false, then the x-wing(1)r46c57 is true. |
At first glance, it is obvious that the single candidate for the x-wing, r8c7 is NOT deleted by the Kraken fin: (1)r4c9 - (1)r8c9 = (1)r8c7.
What prompted you to search for another path, which would be in conflict?
If we continue the chain you posted we would get:
2...[x-wing(1)r46c57] = (1-9)r4c9 = (9)r4c7 - (9=6)r3c7 - (6=1)r6c7 - (1)r8c7 = (1)r8c9; r4c9<>1
In this situation, the end result in the same, but I do not look further into these cases because I assume the possibility of a conflict is very low. Did you notice something that suggested the alternate path?
Ted |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Sat Nov 14, 2009 6:15 pm Post subject: |
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Ted,
if I told you that I noticed the strong inference between the 9's in r4c79, would that help you understand what I saw?
this would lead to the strong inference in cell r3c7 {6=9) .
those are the kind of things I look for when forming chains.
I can't say that any ONE thing stood out for me to take that route. it was a matter of noticing the strong inferences involved and making sure they were weakly linked correctly as to make a sensible AIC.
hopefully producing some results along the way.
I can talk all day long about how I go about solving a puzzle. and sometimes I think other solvers who post here see the same things I do. In puzzles such as this one, I don't think that is the issue. I think the greater issue is an agreement that although my solution is a little convoluted, its still valid. After that, I can only hope that the reader is enlightened and helps open his/her view on puzzles.
if my solution was shown to be invalid then I think that is where discussion like this have a good potential of educating the reader and where the rubber truly hits the road.
----
Myth,
thank you. loved the post on skinny fish to ALS, and also see the resemblences. its enough to make me think a x-wing is really a type of locked set spread over two houses instead of one. |
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oaxen
Joined: 10 Jul 2006
Posts: 96
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| Posted: Sun Nov 15, 2009 7:39 pm Post subject: |
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| A "6" in r5c6 makes it a onestepper |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Sun Nov 15, 2009 9:23 pm Post subject: |
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| oaxen wrote: | | A "6" in r5c6 makes it a onestepper |
Your solutions all appear to be based on using a backdoor single derived through a contradiction network. Few people are interested in a solution derived this way! In the case of this puzzle, there are 19 backdoor singles after basics:
| Code: | +-----------------------------------------------------------------------------+
| 7 1 3 | 6 2 9 | 5 8 4 |
| 2 689 689 | 4 3 5 | 679 1 679 |
| 4 69 5 | 1 8 7 | 69 3 2 |
|-------------------------+-------------------------+-------------------------|
| 6 2 478 | 3 147 48 | 1789 5 1789 |
| 3 478 1 | 5 9 468 | 2 67 678 |
| 9 5 78 | 78 16 2 | 16 4 3 |
|-------------------------+-------------------------+-------------------------|
| 1 4679 4679 | 2 4567 468 | 3 67 5678 |
| 58 467 467 | 9 4567 3 | 14678 2 15678 |
| 58 3 2 | 78 4567 1 | 4678 9 5678 |
+-----------------------------------------------------------------------------+
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| Code: | r4c3 = 8 simple SSTS backdoor
r4c5 = 7 simple SSTS backdoor
r4c7 = 1 simple SSTS backdoor
r5c6 = 6 simple SSTS backdoor -- yours
r5c8 = 7 simple SSTS backdoor
r5c9 = 8 simple SSTS backdoor
r6c3 = 7 simple SSTS backdoor
r6c4 = 8 simple SSTS backdoor
r6c5 = 1 simple SSTS backdoor
r6c7 = 6 simple SSTS backdoor
r7c6 = 8 simple SSTS backdoor
r7c8 = 6 simple SSTS backdoor
r7c9 = 7 simple SSTS backdoor
r8c1 = 5 simple SSTS backdoor
r8c7 = 8 simple SSTS backdoor
r9c1 = 8 simple SSTS backdoor
r9c4 = 7 simple SSTS backdoor
r9c5 = 6 simple SSTS backdoor
r9c9 = 5 simple SSTS backdoor
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Regards, Danny |
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oaxen
Joined: 10 Jul 2006
Posts: 96
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| Posted: Mon Nov 16, 2009 10:40 am Post subject: |
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Hello Danny
hatever technique you use, you are looking after some spot where to begin and what seemes to be successful. My method is to eliminate all useless "backdoors", one can easily see if they are useless or not. So it is not directly a simple "guess". |
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arkietech
Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
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| Posted: Mon Nov 16, 2009 12:36 pm Post subject: |
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| oaxen wrote: | Hello Danny
hatever technique you use, you are looking after some spot where to begin and what seemes to be successful. My method is to eliminate all useless "backdoors", one can easily see if they are useless or not. So it is not directly a simple "guess". |
What is a "useless backdoor"?  |
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oaxen
Joined: 10 Jul 2006
Posts: 96
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| Posted: Mon Nov 16, 2009 12:58 pm Post subject: |
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| arkietech wrote: | | oaxen wrote: | Hello Danny
hatever technique you use, you are looking after some spot where to begin and what seemes to be successful. My method is to eliminate all useless "backdoors", one can easily see if they are useless or not. So it is not directly a simple "guess". |
What is a "useless backdoor"? |
I hope the word "backdoor" has the same meaning for us? Anyhow, I need two same numbers in a row or a column. It is easy to figure out that some of the "pairs" will not lead anywhere, but in one of the pairs both numbers give you a lot of eliminations both horisontally as vertically. Most often to a complete solution, a one stepper. As only one of the two numbers can be correct my chain in 50% fails. But that only means that the other number must be correct.
I like you puzzles Danny and most of all when the "one stepper" doesn't work, so I have to start a new "backdoor" in the middle of the game.
My method is efficient. |
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arkietech
Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
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| Posted: Mon Nov 16, 2009 1:47 pm Post subject: |
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To me a "backdoor" is a logical clue that will leave only basic moves to solve the puzzle. I like to find them with logic.
Danny,
Does SSTS include xy-wings? |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Mon Nov 16, 2009 7:31 pm Post subject: |
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| arkietech wrote: | To me a "backdoor" is a logical clue that will leave only basic moves to solve the puzzle. I like to find them with logic.
Danny,
Does SSTS include xy-wings? |
| Code: | ===== ===== ===== ===== Simple Sudoku Hierarchy (SSTS)
- Naked Single
- Hidden Single
- Naked Pair
- Locked Candidate 1
- Locked Candidate 2
- Naked Triple
- Naked Quad
- Hidden Pair
- X-Wing
- Swordfish
- Colors
- Multi-Colors
- Hidden Triple
- XY-Wing
- Hidden Quad
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| Code: | ===== ===== ===== ===== simple SSTS
- Naked Single
- Hidden Single
- Naked Pair
- Locked Candidate 1
- Locked Candidate 2
- Naked Triple
- Naked Quad
- Hidden Pair
- Hidden Triple
- Hidden Quad
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I allow simple SSTS to complete a backdoor single. Others prefer to use just Naked/Hidden Singles. |
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DanChen
Joined: 18 May 2022
Posts: 1
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| Posted: Fri May 20, 2022 8:47 am Post subject: |
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| Actually, recently I find another site with a friendly interface for sudoku players sudoku game. You can play as online as offline. I think it is worth checking. |
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