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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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 Posted: Fri Feb 02, 2018 9:22 am Post subject: Let's try this again |
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A puzzle from a couple of years ago:
| Code: | +-------+-------+-------+
| . 1 . | 2 3 . | . . . |
| 2 . 4 | 1 5 . | 6 . . |
| . 7 . | . . . | . . . |
+-------+-------+-------+
| . . . | 4 . . | . 1 . |
| 8 6 . | . . . | 5 . 9 |
| . . . | . . . | 3 . 7 |
+-------+-------+-------+
| . . . | . 1 . | 7 . . |
| . . . | . . . | . 8 . |
| . . . | 6 7 9 | 1 . 3 |
+-------+-------+-------+ |
The original discussion:
http://www.dailysudoku.com/sudoku/forums/viewtopic.php?p=38501
Keith |
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dongrave
Joined: 06 Mar 2014
Posts: 568
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| Posted: Sun Mar 04, 2018 3:40 pm Post subject: |
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Hi Keith, I'm game! Here's the grid after basics (I think).
| Code: |
+-----------+---------+-------+
| 69 1 689 | 2 3 68 | 4 7 5 |
| 2 3 4 | 1 5 7 | 6 9 8 |
| 5 7 68 | 9 68 4 | 2 3 1 |
+-----------+---------+-------+
| 379 5 379 | 4 69 36 | 8 1 2 |
| 8 6 13 | 7 2 13 | 5 4 9 |
| 19 4 2 | 5 89 18 | 3 6 7 |
+-----------+---------+-------+
| 36 9 36 | 8 1 2 | 7 5 4 |
| 17 2 17 | 3 4 5 | 9 8 6 |
| 4 8 5 | 6 7 9 | 1 2 3 |
+-----------+---------+-------+
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I didn't bother spending too much time looking for basic wings this time. (I took my own word from a few years ago that they didn't exist.)
Also, a few years ago I mentioned that I found a chain simply by assuming a wrong value and then arriving at a contradiction. I still use the same method to find chains but since then Marty and Clement and Dan and Bat explained forcing chains with pincers on both ends and I immediately preferred them over other types of chains or contradictions.
A few years ago my solution was as follows: If r1c1=9, then r1c3<>9 so it's 6,8 and since there's a naked 68 pair in c3, r7c3<>6 so it's 3 so r5c3=1 so r6c1=9 contradiction. To represent this as a chain with pincers on both ends I would simply change the starting point to begin with with 'If r1c3<>9 ... and end with then r6c1=9 so r1c1<>9.
Since then I also began to think about 'best solutions' and when I'd see someone post a shorter chain than mine, I immediately thought that since it was shorter, it must be better! And the simpler the better too. So instead of using my original chain with naked pairs, I looked for a 'better' solution and found the following. (btw, I also learned Eureka notation in the last 3 years - thanks to Marty.)
(6=3)r7c3-(3=1)r5c3-(1=9)r6c1-(9=6)r1c1 => r7c1<>6.
Thanks, Don. |
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immpy
Joined: 06 May 2017
Posts: 571
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| Posted: Thu Dec 20, 2018 3:49 am Post subject: |
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Very late to the game on this puzzle, just noticed it tonight. Loved your comments dongrave, but this wing-dinger found something, albeit not quite a basic wing of the X, XY, XYZ types, not initially, anyway.
First step...W-Wing: 9/6 in r1c1,r4c5 connected by 6 in r3c35=>r4c1<>9.
I love wings! And I like to eat them too...Buffalo Style; the hotter the better.
cheers...immp |
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immpy
Joined: 06 May 2017
Posts: 571
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| Posted: Thu Dec 20, 2018 3:59 am Post subject: |
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Second step is a more basic XY-Wing.
XY-Wing: -137 in r48c1,r5c3=>r6c1,r8c3<>1.
Had to post this as a separate comment. The first one got jammed together. |
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