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Victor
Joined: 29 Sep 2005
Posts: 207
Location: NI
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 Posted: Sun Dec 09, 2007 8:21 pm Post subject: One that got away |
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... but here's one that's stumped me: help appreciated: M3564480 (5....3...8.9.6.5...1.....2..9.3....23....7.1..2...8.959...45.....4....6.7........)
After basics:
| Code: |
+-------------+-----------------+-------------------+
| 5 467 2 | 14789 789 3 | 146789 478 146789 |
| 8 347 9 | 1247 6 124 | 5 347 1347 |
| 46 1 36 | 5 789 49 | 46789 2 346789 |
+-------------+-----------------+-------------------+
| 1 9 68 | 3 5 46 | 4678 478 2 |
| 3 468 5 | 29 29 7 | 468 1 468 |
| 46 2 7 | 46 1 8 | 3 9 5 |
+-------------+-----------------+-------------------+
| 9 368 1368 | 12678 4 5 | 1278 378 1378 |
| 2 5 4 | 1789 3789 19 | 1789 6 13789 |
| 7 368 1368 | 12689 2389 1269 | 12489 5 13489 |
+-------------+-----------------+-------------------+
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Play this puzzle online at the Daily Sudoku site
Started promisingly - colouring, a sykscraper, a finned X-wing and a UR. But then I can't proceed. |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sun Dec 09, 2007 10:25 pm Post subject: |
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| I would next use remote pairs. A four-cell chain of 46 cells starting at r3c1 will eliminate the 4 from r3c6. Don't know offhand how far that will take you. |
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Victor
Joined: 29 Sep 2005
Posts: 207
Location: NI
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| Posted: Sun Dec 09, 2007 11:54 pm Post subject: |
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| Thanks Marty. Yep, did that (thinking of it as colouring on 4). There's also a skyscraper in 3s, and and a finned X-wing in 4s, and a UR in 29s, but each kills only one candidate. |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Mon Dec 10, 2007 12:46 am Post subject: |
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| after that nifty remote pair, is there an x-wing on 1's??? |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Mon Dec 10, 2007 1:15 am Post subject: |
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| this one has me stumped as well. |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Mon Dec 10, 2007 3:00 am Post subject: |
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Those <4>s are interesting. r59 contains a Finned X-Wing with remote fin that is reflected by the Box 1 ER into r3, killing the <4>s in r3c79. This exposes a r36 Skyscraper.
Alternately, if that coloring elimination of the <4> in r3c6 (which can also be seen as a Sashimi X-Wing) was done first, there is another Finned X-Wing in r39 where the ER in Box 4 kills the <4>s in r5c79. So all four of those <4> can be removed.
Another way to see it is to notice that there is a fundamental contradiction in these mutually destructive X-Wing structures. If the similarly colored <4>s in r3c1 and r5c2 are false, we are left with an impossible pattern of <4>s in c79, marked x below.
| Code: | +-------------+-----------------+-------------------+
| 5 467 2 | 14 78 3 | 146789 478 146789 |
| 8 347 9 | 124 6 24 | 5 347 1347 |
| 46 1 36 | 5 78 9 |x46789 2 x346789 |
+-------------+-----------------+-------------------+
| 1 9 68 | 3 5 46 | 4678 478 2 |
| 3 468 5 | 29 29 7 |x468 1 x468 |
| 46 2 7 | 46 1 8 | 3 9 5 |
+-------------+-----------------+-------------------+
| 9 368 1368 | 2678 4 5 | 1278 378 1378 |
| 2 5 4 | 789 39 1 | 789 6 3789 |
| 7 368 1368 | 2689 239 1269 |x12489 5 x13489 |
+-------------+-----------------+-------------------+ |
So, r3c1 and r5c2 must be true. |
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Victor
Joined: 29 Sep 2005
Posts: 207
Location: NI
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| Posted: Mon Dec 10, 2007 9:14 am Post subject: |
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| Asellus, that's smart stuff, on the edge of my understanding. More homewrok needed I guess. |
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Tue Dec 11, 2007 1:12 pm Post subject: |
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A different view on finned sushi.
From Asellus' grid I did a plot of "4"s to better visualize the finned, ER, and other constellations. This is what it looks like:
| Code: |
+·····+·····+·····+
· o ·o ·o o o·
· · · ·
· o ·o *· o o·
· · |· ·
·* · |·o o·
+|····+····|+·····+
·| · *·o o ·
·| · / · ·
·| * · / ·o o·
·|/ · / · ·
·*-----* · ·
+·····+·····+·····+
· · · ·
· · · ·
· · · ·
· · · ·
· · ·*---*·
+·····+·····+·····+
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When I tried to verify the effect of the finned x-wing in r59 I realized there is a contradiction:
IF r5c2 (the fin) is NOT 4, we get a regular x-wing in r59 (c79), which eliminates all 4s from c79, particularly in r3.
But if r5c2<>4, then by the links r5c2=r6c1-r3c1, the 4 in r3c1 is impossible and we are left without 4 in row 3.
That is a contradiction and r5c2 (and r3c1, r6c4, r2c7) must be 4.
Some time later, I came to this position:
| Code: |
+--------------------------+--------------------------+--------------------------+
| 5 67 2 | 1 78 3 | 46789 478 6789 |
| 8 37 9 | 2 6 4 | 5 37 1 |
| 4 1 36 | 5 78 9 | 678 2 3678 |
+--------------------------+--------------------------+--------------------------+
| 1 9 8 | 3 5 6 | 47 47 2 |
| 3 4 5 | 9 2 7 | 68 1 68 |
| 6 2 7 | 4 1 8 | 3 9 5 |
+--------------------------+--------------------------+--------------------------+
| 9 68 1 | 678 4 5 | 2 378 378 |
| 2 5 4 | 78 3 1 | 89 6 789 |
| 7 368 36 | 68 9 2 | 1 5 4 |
+--------------------------+--------------------------+--------------------------+
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where I used a potential DP to solve the puzzle. But I made a glaring error and have to start thinking again.
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Tue Dec 11, 2007 5:14 pm Post subject: |
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some more thinking (and a little Medusa coloring) revealed an xy-chain from r7c2 to r2c8 which can be completed with one more link to form a complete AIC that eliminates 8 from r7c8:
(3)r7c8=(3-7)r2c8=(7)r2c2-(7=6)r1c2-(6=8)r7c2;r7c8<>8
similar, but slightly different reasoning gives the same result:
if r7c2=8 then r7c8<>8 => r1c8=8.
if r7c2<>8 then r7c2=6 => r1c2=7 => r2c2=3 => r2c8=7 => r4c8=4 => r1c8 = 8.
with r1c8=8 the puzzle finally succumbs |
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ravel
Joined: 21 Apr 2006
Posts: 536
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| Posted: Tue Dec 11, 2007 6:10 pm Post subject: |
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| Code: | *--------------------------------------------------------*
| 5 467 2 |#14 78 3 | 146789 478 146789 |
| 8 347 9 |#124 6 #24 | 5 347 1347 |
| 46 1 36 | 5 78 9 | 4678 2 34678 |
|----------------+----------------+----------------------|
| 1 9 68 | 3 5 #46 | 4678 478 2 |
| 3 468 5 | 29 29 7 | 468 1 468 |
| 46 2 7 |#46 1 8 | 3 9 5 |
|----------------+----------------+----------------------|
| 9 368 168 | 2678 4 5 | 1278 378 1378 |
| 2 5 4 | 789 39 1 | 789 6 3789 |
| 7 368 1368 | 2689 239 26 | 12489 5 13489 |
*--------------------------------------------------------*
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Either r6c4=4 or r12c4=4
r12c4=4 => r2c6=2 => r4c6=6
=> r6c4<>6
| Code: | *-----------------------------------------------*
| 5 67 2 | 1 78 3 | 46789 478 6789 |
| 8 37 9 | 2 6 4 | 5 37 1 |
| 4 1 36 | 5 78 9 | 678 2 3678 |
|-------------+-------------+-------------------|
| 1 9 8 | 3 5 6 | 47 47 2 |
| 3 4 5 | 9 2 7 | 68 1 68 |
| 6 2 7 | 4 1 8 | 3 9 5 |
|-------------+-------------+-------------------|
| 9 68 1 | 678 4 5 | 2 378 378 |
| 2 5 4 | 78 3 1 | 789 6 789 |
| 7 368 36 | 68 9 2 | 1 5 4 |
*-----------------------------------------------*
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UR 68 (type 3) in r35c79 => r1c789<>7
UR 47 (type 4) in r14c78 => r1c78<>7
UR 68 in r79c24: either r9c3=6 or (r8c4=8 =>) r9c4=6
=> r9c2<>6
Strong link for 3 in c8:
r2c8=3 => r2c2=7 => r1c2=6 => r7c2=8
=> r7c8<>8 |
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Tue Dec 11, 2007 6:37 pm Post subject: |
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| ravel wrote: |
r12c4=4 => r2c6=2 => r4c6=6
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I can't follow you on this one, ravel. r2c6=2 implies r9c6=6 => r4c6=4.
Thanks for pointing out the URs. I just knew something could be done about them but looked in all the wrong places. Seems I am more gifted for chains... |
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ravel
Joined: 21 Apr 2006
Posts: 536
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| Posted: Wed Dec 12, 2007 8:21 am Post subject: |
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[quote="nataraj"] | ravel wrote: | | I can't follow you on this one, ravel. r2c6=2 implies r9c6=6 => r4c6=4 |
Cant either  Where are my glasses ? |
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ravel
Joined: 21 Apr 2006
Posts: 536
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| Posted: Wed Dec 12, 2007 3:17 pm Post subject: |
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Here is a possible patch to my mistake, a bit complicated:
Either r4c6=6 or
r4c6=4 => (r3c6<>4 AND r3c8<>4 => r12c8=4 => r3c79<>4) => r3c1=4 => r6c1=6
=> r4c3<>6,r6c4<>6
| Code: | +-------------+-----------------+--------------------+
| 5 467 2 | 14789 789 3 | 146789 #478 146789 |
| 8 347 9 | 1247 6 124 | 5 #347 1347 |
|#46 1 36 | 5 789 #49 |#46789 2 #346789 |
+-------------+-----------------+--------------------+
| 1 9 -68 | 3 5 #46 | 4678 #478 2 |
| 3 468 5 | 29 29 7 | 468 1 468 |
|#46 2 7 | 4-6 1 8 | 3 9 5 |
+-------------+-----------------+--------------------+
| 9 368 1368 | 12678 4 5 | 1278 378 1378 |
| 2 5 4 | 1789 3789 19 | 1789 6 13789 |
| 7 368 1368 | 12689 2389 1269 | 12489 5 13489 |
+-------------+-----------------+--------------------+ |
Eureka notation ?
After using the kite to eliminate 4 in r3c6 its simpler. |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Wed Dec 12, 2007 5:06 pm Post subject: |
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A bit complicated, indeed. First, I believe what you meant to write is:
Either r4c6=6 or
r4c6=4 => r3c6<>4 AND (r4c8<>4 => r12c8=4 => r3c79<>4) => r3c1=4 => r6c1=6
=> r4c3<>6,r6c4<>6
This is a branching AIC. Since you asked for it, here's the Eureka as I would write it. I believe you will see that it is virtually the same (apart from placing the victims at the beginning and end of the notation) as the sequence above:
| Code: | (4)r4c8=(4)r12c8-(4)r3c79
/ \
(6)r4c3|r6c4-(6=4)r4c6- =(4)r3c1-(4=6)r6c1-(6)r4c3|r6c4;
\ /
(4)r3c6
r4c3|r6c4 <> 6 |
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ravel
Joined: 21 Apr 2006
Posts: 536
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| Posted: Wed Dec 12, 2007 6:22 pm Post subject: |
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Thanks again.
Without the branch i already had it right |
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