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DB Saturday Puzzle: August 25, 2007

 
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

PostPosted: Sat Aug 25, 2007 11:07 am    Post subject: DB Saturday Puzzle: August 25, 2007 Reply with quote

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

PostPosted: Sat Aug 25, 2007 12:53 pm    Post subject: Reply with quote

I went down the XY chain route after initial reduction.
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Earl



Joined: 30 May 2007
Posts: 677
Location: Victoria, KS

PostPosted: Sat Aug 25, 2007 3:24 pm    Post subject: DB Aug 25 Reply with quote

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

PostPosted: Sat Aug 25, 2007 4:08 pm    Post subject: W-wing meets coloring Reply with quote

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

PostPosted: Sat Aug 25, 2007 4:54 pm    Post subject: Reply with quote

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

PostPosted: Sat Aug 25, 2007 5:09 pm    Post subject: Reply with quote

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

PostPosted: Sat Aug 25, 2007 9:02 pm    Post subject: Reply with quote

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

PostPosted: Sun Aug 26, 2007 7:56 pm    Post subject: Reply with quote

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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