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daj95376
Joined: 23 Aug 2008
Posts: 3854
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 Posted: Fri Dec 18, 2009 4:51 pm Post subject: Puzzle XY 09/12/18 |
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| Code: | +-----------------------+
| 5 . . | . 7 8 | . . . |
| . 6 . | . . . | . 8 . |
| . . 8 | 3 . . | . 7 . |
|-------+-------+-------|
| . . 6 | 4 . 5 | 7 . . |
| 1 . . | . 8 3 | 4 6 . |
| 4 . . | 6 2 1 | . . 5 |
|-------+-------+-------|
| . . . | 5 6 . | 8 . . |
| . 5 2 | . 3 . | . 9 . |
| . . . | . . 7 | . . 6 |
+-----------------------+
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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: Sat Dec 19, 2009 4:07 am Post subject: |
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I really wondered on this puzzle for a total of six steps with deletions of four different digits.
My first three steps were standard patterns: a xy-wing 2-45, an ER on 9, a kite on 2. Then all that I could find were three long AICs by extending the vertex of potential xy-wings.
I may go back later and try this one again. It was fun but I would like to solve it using more standard patterns.
Ted |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Sun Dec 20, 2009 2:35 pm Post subject: |
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| Code: | <25+4> XY-Wing r3c7/r1c8+r3c5 <> 4 r3c9
c68r7 Skyscraper <> 2 r1c4,r2c7
r9c6 2-String Kite <> 9 r2c3
r19 X-Wing <> 9 r2c4
-4r2c3 3r2c3 3r9c7 4r9c2 [ W-Wing ] <> 4 r3c2,r9c3 -or-
-9r1c3 3r1c3 3r7c9 9r7c1 [ W-Wing ] <> 9 r3c1,r9c3 -or-
-3r1c3 9r1c3 9r7c1 3r7c9 [gM-Wing ] <> 3 r1c9 -or-
-3r9c2 4r9c2 4r2c3 3r2c7 [gM-Wing ] <> 3 r9c7 -or-
BUG+3
(3)r1c2 - (3=4)r2c3 => r3c2<>4
(3)r9c3 - (3=4)r2c3 => r3c2<>4
(2)r3c2 => r3c2<>4
+-----------------------------------------------------+
| 5 12+3 39 | 19 7 8 | 6 24 34 |
| 7 6 34 | 12 45 29 | 35 8 19 |
| 29 14+2 8 | 3 45 6 | 25 7 19 |
|-----------------+-----------------+-----------------|
| 23 23 6 | 4 9 5 | 7 1 8 |
| 1 9 5 | 7 8 3 | 4 6 2 |
| 4 8 7 | 6 2 1 | 9 3 5 |
|-----------------+-----------------+-----------------|
| 39 7 1 | 5 6 29 | 8 24 34 |
| 6 5 2 | 8 3 4 | 1 9 7 |
| 8 34 49+3 | 29 1 7 | 23 5 6 |
+-----------------------------------------------------+
# 29 eliminations remain
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Sun Dec 20, 2009 3:30 pm Post subject: |
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I can't fully reconstruct my original solution but, after reviewing it, I am sure that I simply missed something useful in clean-up. I do not recall seeing a BUG+3 situation.
Ted |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Sun Dec 20, 2009 6:17 pm Post subject: |
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| tlanglet wrote: | I can't fully reconstruct my original solution but, after reviewing it, I am sure that I simply missed something useful in clean-up. I do not recall seeing a BUG+3 situation.
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Ted,
You did not mention an X-Wing on <9>. Without it, there's a BUG+4 ... that still works for r3c2<>4 ... and cracks the puzzle.
Regards, Danny |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Mon Dec 21, 2009 5:39 am Post subject: |
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| Danny, in your grid you might notice the M-Wing on 39 in boxes 17 which takes out the 3 from r1c9 and finishes it off. Prior to that I played three ERs, XY-Wing (254) and an X-Wing (4). |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Mon Dec 21, 2009 7:45 am Post subject: |
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| Marty R. wrote: | | Danny, in your grid you might notice the M-Wing on 39 in boxes 17 which takes out the 3 from r1c9 and finishes it off. Prior to that I played three ERs, XY-Wing (254) and an X-Wing (4). |
I believe my solution above indicates (but doesn't use) 2x W-Wing and 2x gM-Wing that (individually) crack the puzzle. However, my solution missed your X-Wing <4>.
I'm impressed that manual solvers can find (the very useful) W-Wing, but I'm doubly impressed that manual solvers can find the gM-Wing. Congratulations! |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Mon Dec 21, 2009 4:24 pm Post subject: |
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| Quote: | | I believe my solution above indicates (but doesn't use) 2x W-Wing and 2x gM-Wing that (individually) crack the puzzle. |
Oops, I missed that.
What's the difference between an M-Wing and gM-Wing? |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Mon Dec 21, 2009 5:07 pm Post subject: |
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| Marty R. wrote: | | What's the difference between an M-Wing and gM-Wing? |
Keith's definition for the M-Wing is open to interpretation. His examples have strong links where there are weak inferences (-). This may be just a coincidence, but later discussion in his thread (and elsewhere in Solving Techniques) imply that the generalized form doesn't have this constraint.
| Code: | M-Wing: (Y=X)a - (X)b ... = (X-Y)r = (Y)s strong link at weak inferences
gM-Wing: (Y=X)a - (X)b ... = (X-Y)r = (Y)s no constraint at weak inferences
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Mon Dec 21, 2009 7:54 pm Post subject: |
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| daj95376 wrote: | | Marty R. wrote: | | What's the difference between an M-Wing and gM-Wing? |
Keith's definition for the M-Wing is open to interpretation. His examples have strong links where there are weak inferences (-). This may be just a coincidence, but later discussion in his thread (and elsewhere in Solving Techniques) imply that the generalized form doesn't have this constraint.
| Code: | M-Wing: (Y=X)a - (X)b ... = (X-Y)r = (Y)s strong link at weak inferences
gM-Wing: (Y=X)a - (X)b ... = (X-Y)r = (Y)s no constraint at weak inferences
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Thanks Danny,
I don't want to carry this much father, but looking very carefully at the notation, with both lines the same, I can only conclude, at least from a mathematical standpoint, that gM = M.  |
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oaxen
Joined: 10 Jul 2006
Posts: 96
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| Posted: Wed Dec 23, 2009 10:09 am Post subject: |
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a "9" in r9c4 makes it a one stepper.
Dear Danny. Do you before publishing have any chance to check that your puzzles can't be solved in one step with the simplified Oaxen technique?
Merry Christmas and thanks for all the fun you have given me
with your puzzles
Lars |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Wed Dec 23, 2009 3:14 pm Post subject: |
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| Marty R. wrote: | | I don't want to carry this much father, but looking very carefully at the notation, with both lines the same, I can only conclude, at least from a mathematical standpoint, that gM = M. |
Hello Marty,
After some thought on your post, I realized that it could be restated as follows.
Eureka Notation: Specifies strong/weak inferences, but does not account for additional constraints like a strong link being necessary for a weak inference in a particular technique.
This has resulted in several discussions in several threads when such techniques are used.
Regards, Danny |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Wed Dec 23, 2009 3:25 pm Post subject: |
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| oaxen wrote: | a "9" in r9c4 makes it a one stepper.
Dear Danny. Do you before publishing have any chance to check that your puzzles can't be solved in one step with the simplified Oaxen technique?
Merry Christmas and thanks for all the fun you have given me
with your puzzles
Lars |
Hello Lars,
I'm happy to hear that you are enjoying my puzzles!
No, I don't check for backdoor singles before posting my puzzles. There are two reasons.
1) The backdoor singles logic is in my previous solver and is (deliberately) not present in my current solver. Testing each puzzle with my old solver would require extra effort that I don't see as beneficial.
2) The reason it isn't beneficial is because I try to post puzzles whose solutions require a limited number of advanced techniques for manual solvers to tackle. As a consequence, almost all of my puzzles have multiple backdoor singles present after the initial basics. So, looking for them constitutes looking for the obvious.
Merry Christmas (Happy Holidays) and Regards, Danny |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Wed Dec 23, 2009 10:43 pm Post subject: Backdoor singles |
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My mistake! Send it to the wrong location.
Ted |
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