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6/20-6/22 competition puzzles

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storm_norm

Joined: 18 Oct 2007
Posts: 1741

Posted: Sun Jun 22, 2008 5:31 am Post subject: 6/20-6/22 competition puzzles

6/20

Code:

7 6 .|. . .|. 2 .
. . .|. . .|. . 8
1 . 5|. 2 7|. . .
-----+-----+-----
. . 6|. . 4|8 . .
. 4 .|8 . 1|. 5 .
. . 3|7 . .|9 . .
-----+-----+-----
. . .|1 . .|2 . 4
6 . .|. . .|. . .
. 9 .|. 5 .|. 1 6

6/22

Code:

. 4 6|. 7 .|9 . .
. . .|. . 1|. . .
2 5 .|9 . .|. . .
-----+-----+-----
6 . .|8 . .|3 . 4
. 7 .|6 . 3|. 2 .
8 . 3|. . 2|. . 5
-----+-----+-----
. . .|. . 6|. 8 3
. . .|5 . .|. . .
. . 5|. 8 .|7 4 .

enjoy, and good luck.

Asellus

Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA

Posted: Mon Jun 23, 2008 12:48 am Post subject:

"6/20" was a very interesting puzzle. After a Skyscraper, I was here:

Code:

+-----------------+-----------------+--------------+
| 7 6 49 | 3459 148 3589 | 1345 2 359 |
| 2349 23 249 | 6 14 59 | 145 7 8 |
| 1 8 5 | 349 2 7 | 34 6 39 |
+-----------------+-----------------+--------------+
| 25 17 6 | 25 9 4 | 8 3 17 |
| 29 4 279 | 8 3 1 | 6 5 27 |
| 8 125 3 | 7 6 25 | 9 4 12 |
+-----------------+-----------------+--------------+
| 35 35 78 | 1 78 6 | 2 9 4 |
| 6 27 1 | 2349 47 239 | 357 8 35 |
| 24 9 2478 | 23 5 238 | 37 1 6 |
+-----------------+-----------------+--------------+

I noted a potential 249-29-24 DP in R259C13, with its various internal conjugate links, plus the 49 bivalue at r1c3. There are two cases:
Case A: r1c3 is <9>, or it is <4>. r1c3=4 => a potential 29UR in r25c13 with diagonal 29 bivalues and conjugate <9>s in r5 => r2c1<>9 => r2c3=9. Either way, r5c3<>9.
Case B: r1c3 is <4>, or it is <9>. r1c3=9 => a potential 24UR in r29c13 with diagonal 24 bivalues and conjugate <4>s in r9 => r2c1<>4 => r2c3=4. Either way, r9c3<>4.
And, Cases A and B together => r2c3<>2.
So, there are three eliminations due to this DP/bivalue complex.

That led me here for another interesting step:

Code:

+--------------+-----------------+--------------+
| 7 6 49 | 3459 148 3589 | 1345 2 359 |
| 23 23 49 | 6 14 59 | 145 7 8 |
| 1 8 5 | 349 2 7 | 34 6 39 |
+--------------+-----------------+--------------+
| 25 17 6 | 25 9 4 | 8 3 17 |
| 9 4 27 | 8 3 1 | 6 5 27 |
| 8 125 3 | 7 6 25 | 9 4 12 |
+--------------+-----------------+--------------+
| 35 35 78 | 1 78 6 | 2 9 4 |
| 6 27 1 | 2349 47 239 | 357 8 35 |
| 4 9 278 | 23 5 238 | 37 1 6 |
+--------------+-----------------+--------------+

r2c1 and r9c4 form a W-Wing on <3> via r4. And...
r2c2 and r9c4 form a W-Wing on <3> via b7.
These two pincer strong links joined by the <3> weak link in r2 mean that r9c4=3. This is a tiny AIC loop with a strong link discontinuity. However, if you prefer a less technical way to see it: Either or both of r2c1 and r9c4 must be <3>; either or both of r2c2 and r9c4 must be <3>; one of r2c1 or r2c2 cannot be <3>; therefor r9c4 must be <3>.

This leads to a BUG+1.

storm_norm

Joined: 18 Oct 2007
Posts: 1741

Posted: Mon Jun 23, 2008 4:44 am Post subject:

that 6/20 was definitely the hardest daily diabolical I have seen.

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