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daj95376
Joined: 23 Aug 2008
Posts: 3854
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 Posted: Wed Sep 22, 2010 5:55 am Post subject: Puzzle 10/09/22: A BBDB |
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| Code: | +-----------------------+
| 8 . . | . 9 2 | . . . |
| . 7 2 | 6 . . | . 9 8 |
| . 4 6 | . 8 5 | 3 . 1 |
|-------+-------+-------|
| . 8 . | 1 . . | . 7 . |
| 2 . 9 | . 7 . | 8 1 . |
| 1 . 7 | . . 8 | . . . |
|-------+-------+-------|
| . . 8 | . 5 . | 9 4 . |
| . 9 . | 8 1 . | 2 5 7 |
| . 2 5 | . . . | . 8 . |
+-----------------------+
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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: Wed Sep 22, 2010 2:52 pm Post subject: |
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AUR (34)r48c13 Internal SIS: r4c1=5,r8c1=6; r8c6,r9c1<>6
| Code: |
(6)r8c1=(5)r4c1-(5=6)r4c7-(6)r4c5=(6)r9c5; r8c6,r9c1<>6
\ /
-(5=6)r6c2-(6)r6c5 |
x-wing(6)r24c17; r6c7<>6
Ted |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Wed Sep 22, 2010 10:06 pm Post subject: |
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| Ted: nice use of an AUR in a simple network! |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Thu Sep 23, 2010 12:08 am Post subject: |
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| tlanglet wrote: | AUR (34)r48c13 Internal SIS: r4c1=5,r8c1=6; r8c6,r9c1<>6
| Code: |
(6)r8c1=(5)r4c1-(5=6)r4c7-(6)r4c5=(6)r9c5; r8c6,r9c1<>6
\ /
-(5=6)r6c2-(6)r6c5 |
x-wing(6)r24c17; r6c7<>6
Ted |
Ted, is it possible to briefly explain that thing? I realize there has to be a 5 or 6 and I can easily see that if the 6 is true, then r8c6 and r9c1<>6. At that point I'm lost, plus for the X-Wing I see 5s, not 6s in those cells. |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Thu Sep 23, 2010 2:26 am Post subject: |
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| Marty R. wrote: | | tlanglet wrote: | AUR (34)r48c13 Internal SIS: r4c1=5,r8c1=6; r8c6,r9c1<>6
| Code: |
(6)r8c1=(5)r4c1-(5=6)r4c7-(6)r4c5=(6)r9c5; r8c6,r9c1<>6
\ /
-(5=6)r6c2-(6)r6c5 |
x-wing(6)r24c17; r6c7<>6
Ted |
Ted, is it possible to briefly explain that thing? I realize there has to be a 5 or 6 and I can easily see that if the 6 is true, then r8c6 and r9c1<>6. At that point I'm lost, plus for the X-Wing I see 5s, not 6s in those cells. |
Marty,
I am happy to attempt an explanation, but no one has ever accused me of being brief.
You indicated that you could see the result if r8c1=6, so lets look at the situation if r4c1=5.
First look at the branch in row4. If r4c1=5 then r4c7=6, then r4c5<>6; this only tells us that r4c5<>6
Now look at the second branch in box4. If r4c1=5 then r6c2=6, then r6c5<>6. So now we know that if r4c1=5 then both r4c5 and r6c5 <>6 which makes r9c5=6 since it is the only remaining digit 6 in col5. We now have two pincers on digit 6, one as a result of r4c1=5 and the other is the original AUR where r8c1=6 to prevent the DP.
Hope this helps. If not, I will try again or maybe someone else with better terminology and understanding would give it a go. If this description is of help, it may then be possible for you to interpret the chain notation I originally posted. The first statement, (6)r8c1=(5)r4c1, simply indicates that either r8c1=6 or r4c1=5 must be true to prevent the DP.
Finally, the x-wing is on digit 5 not digit 6. I assume it was a senior moment, to much wine last evening, a combination of both or simply a screw-up.
Ted |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Thu Sep 23, 2010 5:09 am Post subject: |
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OK, that's easy enough to follow. You referred to that as an SIS. There must've been a pattern you spotted to proceed as you did. Is there some generalization that one can use to indicate that similar action should be taken?
(I know, give him an inch and he takes a foot). |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Thu Sep 23, 2010 12:16 pm Post subject: |
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| Marty R. wrote: | OK, that's easy enough to follow. You referred to that as an SIS. There must've been a pattern you spotted to proceed as you did. Is there some generalization that one can use to indicate that similar action should be taken?
(I know, give him an inch and he takes a foot). |
Marty, the SIS, Strong Inference Set, I used as the bases for the step was the internal digit constraints of the AUR: r8c1=6 and r4c1=5. One of those conditions must be true to prevent the DP.
I did not spotted a pattern other than the AUR itself. Given the SIS based on the AUR, I just starting following the inferences to see what would happen in the same manner I believe you handle AURs to determine an invalidity or other result. With only two constraints in the SIS, I usually try to get them to both be the same digit, which is what happened in this puzzle; I got the r4c1=5 term to force a digit 6 condition which then lead to the deletion.
Ted |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Thu Sep 23, 2010 3:45 pm Post subject: |
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| Thanks very much. Just one more question. If you just followed the normal steps for an "either/or", what, exactly, is an SIS? Is it a technique or just a new name for something we already know? |
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peterj
Joined: 26 Mar 2010
Posts: 974
Location: London, UK
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| Posted: Thu Sep 23, 2010 5:32 pm Post subject: |
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| Marty R. wrote: | | Is it a technique or just a new name for something we already know? |
As far as I can tell (!) you can consider it synonymous for "strong link" (but it's quicker to type!) - unless you want to get involved in murky world of transfer matrix, cover sets etc. |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Thu Sep 23, 2010 5:54 pm Post subject: |
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I'm under the impression that it stands for Strong Inference Set, but I think Strong Inference Sequence is slightly more accurate. A 5-SIS chain is a sequence of five strong inferences separated by four weak inferences.
| Code: | XY-Chain as a trivial example of a 5-SIS chain
+-----------------------------------------------------------------------+
| 4 8 37 | 1 c39 b79 | 2 6 5 |
| 135 2 137 | a67 8 567 | 9 13 4 |
| 135 6 9 | 24 d34 245 | 8 13 7 |
|-----------------------+-----------------------+-----------------------|
| 8 479 246 | 5 469 4679 | 1 249 3 |
| 139 5 134 | 349 2 8 | 7 49 6 |
| 369 479 2346 | 34679 1 4679 | 5 249 8 |
|-----------------------+-----------------------+-----------------------|
| 2 1 5 | 8 e46 3 | 46 7 9 |
| 7 49 46 | 9-6 5 1 | 3 8 2 |
| 69 3 8 | 249-6 7 2469 | 46 5 1 |
+-----------------------------------------------------------------------+
# 65 eliminations remain
SI SI SI SI SI
(6=7)r2c4 - (7=9)r1c6 - (9=3)r1c5 - (3=4)r3c5 - (4=6)r7c5 => r89c4<>6
WI WI WI WI
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There's also Weak Inference Set, but I think Weak Inference Sequence is slightly more accurate. A 6-WIS chain is a sequence of six weak inferences separated by five strong inferences. It's also a discontinuous loop.
| Code: | WI WI WI WI WI WI
(6)r89c4 - (6=7)r2c4 - (7=9)r1c6 - (9=3)r1c5 - (3=4)r3c5 - (4=6)r7c5 - (6)r89c4
SI SI SI SI SI
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I've also seen WIS used in conjunction with SIS, but I find one or the other to be redundant.
Regards, Danny
Note: a strong inference is always represented by a strong link, but a weak inference can be represented by either a strong link or a weak link. (Sudopedia) In this example, the weak inference on <7> is represented by a weak link in [b2], but the weak inference on <9> is represented by strong links in [b2] and [r1].
BTW: This XY-Chain cracks one of tomorrow's puzzles. _  _ |
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peterj
Joined: 26 Mar 2010
Posts: 974
Location: London, UK
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| Posted: Thu Sep 23, 2010 8:36 pm Post subject: |
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Nah, it's not an xy-chain or a discontinuous loop or SIS-thingy - it's an m-wing with a pseudocell... 
| Code: | m-wing(69) ; (6=7)r2c4-(7=9)r1c6 - r1c5=(9-6)r4c5=r7c5
A 4-SIS solution or "proof" in the SIS world idiom.. |
I just get the sense that these hard-ish puzzles have sort of "discontinuities" in the strong links/SIS that crack them - there are multiple manifestations of this core irregularity that we solvers see as specific patterns. Some are happy to note the strong links and "the rules of Sudoku" does the rest. I am still not good enough at applying those rules to not want them spelled out - in my case happy with Eureka/AIC notation. |
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