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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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 Posted: Sat Aug 25, 2007 11:07 am Post subject: DB Saturday Puzzle: August 25, 2007 |
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| Code: | Puzzle: DB082507 ******
+-------+-------+-------+
| . . . | . 9 . | . 6 . |
| . 8 . | 5 3 . | 7 . 9 |
| . 1 9 | . . 2 | 5 . . |
+-------+-------+-------+
| 1 2 . | . . . | 3 . . |
| . . . | 8 . 3 | . . . |
| . . 6 | . . . | . 8 4 |
+-------+-------+-------+
| . . 3 | 6 . . | 2 7 . |
| 7 . 1 | . 2 4 | . 9 . |
| . 9 . | . 8 . | . . . |
+-------+-------+-------+ |
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Mogulmeister
Joined: 03 May 2007
Posts: 1151
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| Posted: Sat Aug 25, 2007 12:53 pm Post subject: |
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| I went down the XY chain route after initial reduction. |
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Earl
Joined: 30 May 2007
Posts: 677
Location: Victoria, KS
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| Posted: Sat Aug 25, 2007 3:24 pm Post subject: DB Aug 25 |
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I also used an xy chain (which I dislike doing) to eliminate <3> from R3C1. Anyone find a neater path?
Earl |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sat Aug 25, 2007 4:08 pm Post subject: W-wing meets coloring |
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I'm still working on it. Here is where you get with basic moves:
| Code: | +-------------+--------------+-------------+
| 235 357 257 | 14 9 8 | 14 6 23 |
| 246 8 24 | 5 3 16 | 7 12 9 |
| 36@ 1 9 | 47 67& 2 | 5 34# 8 |
+-------------+--------------+-------------+
| 1 2 8 | 9 4 67 | 3 5 67 |
| 459 57 457 | 8 167* 3 | 169 12 267%|
| 39 37 6 | 2 17 5 | 19 8 4 |
+-------------+--------------+-------------+
| 8 4 3 | 6 5 9 | 2 7 1 |
| 7 6 1 | 3 2 4 | 8 9 5 |
| 25 9 25 | 17 8 17 | 46 34# 36@ |
+-------------+--------------+-------------+ |
Note the W-wing: Two cells <36> @, with a strong link on <3> # in C8. So, one of the cells <36> @ must be <6>.
The four cells @##@ are also a coloring chain on <3>. One of the cells <36> # must be <3>, so they are a remote pair! (Which doesn't help.)
However, if R3C1 is <6>, then coloring via &* says R5C5 * is also <6>. R5C9 % cannot be <6> because one of R5C5 and R9C9 is <6>.
I think this is pretty cool. It says, in effect, that you can regard the two W-wing cells as being a strong link in a simple coloring chain!
Keith |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sat Aug 25, 2007 4:54 pm Post subject: |
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Done it!
So, we are here:
| Code: | +-------------+-------------+-------------+
| 235 357 257 | 14& 9 8 | 14* 6 23 |
| 246 8 24 | 5 3 16 | 7 12 9 |
| 36 1 9 | 47# 67# 2 | 5 34 8 |
+-------------+-------------+-------------+
| 1 2 8 | 9 4 67 | 3 5 67 |
| 459 57 457 | 8 167 3 | 169 12 27 |
| 39 37 6 | 2 17@ 5 | 19% 8 4 |
+-------------+-------------+-------------+
| 8 4 3 | 6 5 9 | 2 7 1 |
| 7 6 1 | 3 2 4 | 8 9 5 |
| 25 9 25 | 17@ 8 17 | 46 34 36 |
+-------------+-------------+-------------+ |
Note the W-wing on <17> @ with the strong link on <7> #. One of the cells @ is <1>.
Coloring on <1> @&* from R9C4 to R1C7. One of R1C7 and R6C5 are <1>. R6C7 % cannot be <1>, it must be <9>, and the puzzle is solved!
I am the first to concede these are chains, but this is a systematic way to find them.
Keith |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sat Aug 25, 2007 5:09 pm Post subject: |
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I couldn't find any W-Wings, but I don't know if my grid was the same as any of the above.
I used two XY-Chains after an unhelpful X-Wing. The first was very convoluted and didn't meet the strict definition of the technique. It may not have been needed, but I found it before the second one, which was an XY-Chain by definition. |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Sat Aug 25, 2007 9:02 pm Post subject: |
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Keith,
I find it interesting to consider how your two implications look using Medusa coloring.
But first, a technical point just to make certain the logic is clear: in W-Wing logic, the relationship is "at least one" (which is the same as "one or both"), not "either/or". Based solely on the W-Wing logic, in the 36 case, one or both cells must be <6>, and in the 17 case, one or both must be <1>. This doesn't affect the implications since an "at least one" relationship functions the same as "either/or" for implication chaining strong links. (As it happens, the relationships in these examples are "either/or"; but that is not due to their being W-Wings.)
In the first case of the <6> elimination, only <3> and <6> are involved in the coloring:
| Code: | +--------------+-------------+---------------+
| 235 357 257 | 14 9 8 | 14 6 23 |
| 246 8 24 | 5 3 16 | 7 12 9 |
| 3g6r 1 9 | 47 6g7 2 | 5 3r4 8 |
+--------------+-------------+---------------+
| 1 2 8 | 9 4 67 | 3 5 67 |
| 459 57 457 | 8 #16r7 3 | 169 12 2-67 |
| 39 37 6 | 2 17 5 | 19 8 4 |
+--------------+-------------+---------------+
| 8 4 3 | 6 5 9 | 2 7 1 |
| 7 6 1 | 3 2 4 | 8 9 5 |
| 25 9 25 | 17 8 17 | 46 3g4 #3r6g |
+--------------+-------------+---------------+ |
The <6> at R5C9 is eliminated by a Medusa "Trap", marked #; it can "see" both a red <6> and a green <6>. [Note: This <6> can also be eliminated by an XY Chain.]
The second case is more interesting. The coloring involves <1>, <4> and <7>:
| Code: | +-------------+----------------+--------------+
| 235 357 257 | 14r 9 8 |#1r4g 6 23 |
| 246 8 24 | 5 3 16 | 7 1g2 9 |
| 36 1 9 | 4g7r 67 2 | 5 34r 8 |
+-------------+----------------+--------------+
| 1 2 8 | 9 4 67 | 3 5 67r |
| 459 57 457 | 8 1r67 3 | 169 12 27 |
| 39 37 6 | 2 1g7r 5 |#1r9 8 4 |
+-------------+----------------+--------------+
| 8 4 3 | 6 5 9 | 2 7 1 |
| 7 6 1 | 3 2 4 | 8 9 5 |
| 25 9 25 | 1r7g 8 1g7r | 4r6 34g 36 |
+-------------+----------------+--------------+ |
In this case, we encounter a Medusa "Wrap" since we find two red <1>s in C7, which is impossible. So, all of the red values are eliminated (not just the <1> in R6C7) and all of the green values are placed.
Since the puzzle succumbs to more common methods (for me, two XY Chains), resorting to these other approaches isn't necessary. Still, I believe it is interesting to see how they work. |
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Mogulmeister
Joined: 03 May 2007
Posts: 1151
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| Posted: Sun Aug 26, 2007 7:56 pm Post subject: |
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I think I only used one XY chain to resolve the puzzle.
Pincers at r1c4 and r6c7 removing the 1 at r1c7. |
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