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daj95376
Joined: 23 Aug 2008
Posts: 3854
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 Posted: Sat Nov 14, 2009 7:16 pm Post subject: Puzzle NR 09/11/14 (B) |
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Alert: XYZ-Wing present in my solver's solution.
| Code: | +-----------------------+
| 2 . . | 3 6 . | . . . |
| . 1 . | . 4 2 | . 6 . |
| . . 3 | 1 . 7 | . . . |
|-------+-------+-------|
| 3 . 6 | . . 9 | 5 2 . |
| 4 9 . | . . 5 | 6 3 . |
| . 8 2 | 7 3 . | . 4 . |
|-------+-------+-------|
| . . . | 6 7 . | 4 . . |
| . 3 . | 2 9 4 | . 1 . |
| . . . | . . . | . . . |
+-----------------------+
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Play this puzzle online at the Daily Sudoku site |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Sun Nov 15, 2009 7:27 pm Post subject: |
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Still another puzzle with various options. I used three fun steps:
xy-wing 7-89 with vertex in r9c8, which opens up a
chain found by extending the vertex of a potential xy-wing:
(5=3)r2c9 - (3=7)r2c7 - (7)r2c13 = (7)r1c3 - (7=5)r8c3; r8c9<>5 which opens a chain:
| Code: | *--------------------------------------------------*
| 2 5 49 | 3 6 8 | 179 79 149 |
| 8 1 7 | 9 4 2 | 3 6 5 |
| 69 46 3 | 1 5 7 | 29 8 249 |
|----------------+----------------+----------------|
| 3 7 6 | 4 1 9 | 5 2 8 |
| 4 9 1 | 8 2 5 | 6 3 7 |
| 5 8 2 | 7 3 6 | 19 4 19 |
|----------------+----------------+----------------|
| 19 2 8 | 6 7 13 | 4 5 39 |
| 7 3 5 | 2 9 4 | 8 1 6 |
| 169 46 49 | 5 8 13 | 279 79 239 |
*--------------------------------------------------* |
| Code: | - (9)r9c9
/ \
(2=9)r3c7 - (9=7)r1c8 - (7=9)r9c8 = (2)r9c9; r3c9, r9c7<>2
\ /
- (9=3)r7c9 - (3)r9c9
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Ted |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Sun Nov 15, 2009 10:04 pm Post subject: |
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| tlanglet wrote: | ... which opens a network:
| Code: | *--------------------------------------------------*
| 2 5 49 | 3 6 8 | 179 79 149 |
| 8 1 7 | 9 4 2 | 3 6 5 |
| 69 46 3 | 1 5 7 | 29 8 249 |
|----------------+----------------+----------------|
| 3 7 6 | 4 1 9 | 5 2 8 |
| 4 9 1 | 8 2 5 | 6 3 7 |
| 5 8 2 | 7 3 6 | 19 4 19 |
|----------------+----------------+----------------|
| 19 2 8 | 6 7 13 | 4 5 39 |
| 7 3 5 | 2 9 4 | 8 1 6 |
| 169 46 49 | 5 8 13 | 279 79 239 |
*--------------------------------------------------* |
| Code: | (9)r9c9
/ \
(2=9)r3c7 - (9=7)r1c8 - (7=9)r9c8 - = (2)r9c9; r3c9,r9c7<>2
\ /
(9=3)r7c9 - (3)r9c9
__________________________________________________________________________________
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Ted: Nice example of a SIN (Single Implication Network). I'm often amazed at how they make short work of difficult puzzles.
Recently, I became interested in an extension to the basic Eureka notation. It's called a "chain", but a lot of things are called chains now that I think are networks. If we take your cells and play them in this format, we get:
| Code: | (2=9)r3c7 - (9=7)r1c8 - (7=9)r9c8 - (93=2)r79c9; r3c9,r9c7<>2
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Suddenly, a network is a chain (in some people's eyes)!
Note: the (7=9)r9c8 - (93=2)r79c9 can be written as ALS[(7)r9c8 = (2)r9c9]r9c8,r79c9, but I've claimed ignorance of ALS usage for too long to admit that one exists here. 
[Edit: changed <39> to <93> so the linking digit was first.]
Last edited by daj95376 on Mon Nov 16, 2009 2:09 am; edited 3 times in total |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Sun Nov 15, 2009 10:55 pm Post subject: |
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| daj95376 wrote: |
Recently, I became interested in an extension to the basic Eureka notation. It's called a "chain", but a lot of things are called chains now that I think are networks. If we take your cells and play them in this format, we get:
| Code: | (2=9)r3c7 - (9=7)r1c8 - (7=9)r9c8 - (39=2)r79c9; r3c9,r9c7<>2
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Suddenly, a network is a chain (in some people's eyes)!
Note: the (7=9)r9c8 - (39=2)r79c9 can be written as ALS[(7)r9c8 = (2)r9c9]r9c8,r79c9, but I've claimed ignorance of ALS usage for too long to admit that one exists here. |
I considered using the ALS but wanted to post the network since that was something I had not previously attempted. Your suggested notation is shorter and simpler, and to me it tells the story.
Also, I would be interested in reading about the Eureka extensions. Do you have a link to any postings on this topic?
Ted |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Mon Nov 16, 2009 2:00 am Post subject: |
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[Addendum: Sudopedia indicates that my chain above needed a slight adjustment. I updated my post so the 9s are next to each other.]
| tlanglet wrote: | I considered using the ALS but wanted to post the network since that was something I had not previously attempted. Your suggested notation is shorter and simpler, and to me it tells the story.
Also, I would be interested in reading about the Eureka extensions. Do you have a link to any postings on this topic?
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I wish!!! Here's an example of what's being done in the way of Eureka notation.
| Code: | +-----------------------------------------------------------------------+
| 478 4789 1 | 28 3 248 | 6789 679 5 |
| 3458 6 458 | 7 48 9 | 2 38 1 |
| 2 3789 789 | 1 5 6 | 3789 79 4 |
|-----------------------+-----------------------+-----------------------|
| 578 35789 2 | 3589 1 578 | 38 4 6 |
| 34568 34589 45689 | 35689 4689 458 | 1 2 7 |
| 1 478 4678 | 2368 4678 2478 | 5 38 9 |
|-----------------------+-----------------------+-----------------------|
| 4567 457 3 | 569 2 57 | 679 1 8 |
| 5678 2 5678 | 5689 6789 1 | 4 5679 3 |
| 9 1 5678 | 4 678 3 | 67 567 2 |
+-----------------------------------------------------------------------+
# 110 eliminations remain
(NQ7468)r6c2358 = (NT578)r4c167 - (XW5)r45c24) = (QFXW5)r453c2.r4523c4 - (5=7)r7c6 => r6c6<>7
_____________________________________________________________________________________________
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a) If there's not a <7468> naked quad in r6c2358, then there is a <578> naked triple in r4c167
b) This prevents an X-Wing for <5> in r45c24
c) at this point, I get lost ... and don't want to know even if someone were to explain it!
As for that r6c6<>7 elimination ...
| Code: | (75=8)r47c6 - r4c7 = r6c8 - (8=467)r6c235 => r6c6<>7 -or-
(75=8)r47c6 - r4c7 = (8-3)r6c8 = (3-2)r6c4 = (2)r6c6 => r6c6<>7
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... which I derived by simply rewriting a short SIN that my solver found.
[Addendum] Alternately, I see it as a network based on the candidates in r4c6:
| Code: | (5)r4c6 - (5=7)r7c6 - ( 7)r6c6
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(7)r4c6 - ( 7)r6c6
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(8)r4c6 - r4c7 = (8-3)r6c8 = (3-2)r6c4 = (2-7)r6c6
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A friend suggests an ALS-XY:
| Code: | r6c6 -7- als:r6c2358 -3- r4c7 -8- als:r47c6 -7- r6c6 --> r6c6<>7
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Sheez: So many typos to correct!
Last edited by daj95376 on Mon Nov 16, 2009 10:03 am; edited 4 times in total |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Mon Nov 16, 2009 5:35 am Post subject: |
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I used:
XY (798)
XYZ (578)
X (9)
XY (279)
Alternatively, a BUG+1 was available in lieu of the last XY. |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Mon Nov 16, 2009 9:13 am Post subject: |
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| My solver found an extraneous X-Wing (5) initially; otherwise, it's solution matches Marty's. |
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