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DB Saturday Puzzle - August 19, 2006

 
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keith



Joined: 19 Sep 2005
Posts: 3179
Location: near Detroit, Michigan, USA

PostPosted: Sat Aug 19, 2006 9:08 am    Post subject: DB Saturday Puzzle - August 19, 2006 Reply with quote

After finding a Unique Rectangle I am stuck for the moment.

Keith
Code:
Puzzle: DB081906  ******
+-------+-------+-------+
| . . . | . . . | 3 7 . |
| . . . | 8 . 5 | 9 4 . |
| . . . | 2 . 7 | 8 . 5 |
+-------+-------+-------+
| 4 . 9 | . . . | . 5 . |
| . 5 . | . 8 . | . 3 . |
| . 7 . | . . . | 2 . 4 |
+-------+-------+-------+
| 2 . 5 | 3 . 4 | . . . |
| . 4 3 | 9 . 8 | . . . |
| . 1 6 | . . . | . . . |
+-------+-------+-------+
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ravel



Joined: 21 Apr 2006
Posts: 536

PostPosted: Sat Aug 19, 2006 1:28 pm    Post subject: Reply with quote

Code:
 *-----------------------------------------------------------*
 | 5     89    48    | 16    49   A16    | 3     7     2     |
 | 16    2     7     | 8     3     5     | 9     4     16    |
 | 39    36    14    | 2     49    7     | 8     16    5     |
 |-------------------+-------------------+-------------------|
 | 4     36    9     | 7     2     136   | 16    5     8     |
 | 16    5     2     | 4     8    A1-69  | 167   3     79    |
 |B38    7    B18    |B16    5    A39    | 2     169   4     |
 |-------------------+-------------------+-------------------|
 | 2     89    5     | 3     16    4     | 167   1689  79    |
 | 7     4     3     | 9     16    8     | 5     2     16    |
 | 89    1     6     | 5     7     2     | 4     89    3     |
 *-----------------------------------------------------------*
With 3 strong links the 6 in r5c6 can be eliminated (r5c1-r2c1,r2c9-r3c8,r6c8-r6c4).
And there is an ALS, where the 3 is locked to r6c6 in A (1369) and to r6c1 in B (1368), when r4c6=6. But as always i first found a chain and then constructed the ALS.
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Marty R.



Joined: 12 Feb 2006
Posts: 5165
Location: Rochester, NY, USA

PostPosted: Sat Aug 19, 2006 3:15 pm    Post subject: Reply with quote

Quote:
And there is an ALS,


What's that stand for, other than the dreaded disease?
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TKiel



Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI

PostPosted: Sat Aug 19, 2006 3:20 pm    Post subject: Reply with quote

Almost Locked Set. Not sure what the definition is.

Nice little puzzle, as usual. I tried like heck to make an XY-chain with all the (1,6) pairs but never could get a result. Finally realized it almost had to be an XY-wing, which took a while to find as there were many possibilities.
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Marty R.



Joined: 12 Feb 2006
Posts: 5165
Location: Rochester, NY, USA

PostPosted: Sat Aug 19, 2006 5:17 pm    Post subject: Reply with quote

I also wanted to use the remote pairs technique with 16, but couldn't. I also couldn't find any X-Wings, XY-Wings, strong links, etc., so I had to rely on the old standby, the chain.
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ravel



Joined: 21 Apr 2006
Posts: 536

PostPosted: Sat Aug 19, 2006 9:41 pm    Post subject: Reply with quote

Hi Marty,

here is the original ALS link, but i am sure, you dont need it Smile
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David Bryant



Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado

PostPosted: Sat Aug 19, 2006 11:58 pm    Post subject: Finding the chain of remote pairs Reply with quote

Marty R wrote:
I also wanted to use the remote pairs technique with 16, but couldn't.

Here's how I used the "double-implication chain" technique to extend the chain of remote pairs far enough to crack this puzzle.
Code:
*-----------------------------------------------------------*
 | 5     89    48    | 16    49    16    | 3     7     2     |
 | 16+   2     7     | 8     3     5     | 9     4     16-   |
 | 39    36    14    | 2     49    7     | 8     16+   5     |
 |-------------------+-------------------+-------------------|
 | 4     36    9     | 7     2     136   | 16    5     8     |
 | 16-   5     2     | 4     8     169   | 167   3     79    |
 | 38    7     18    | 16    5     39    | 2     169   4     |
 |-------------------+-------------------+-------------------|
 | 2     89    5     | 3     16+   4     | 167   1689* 79    |
 | 7     4     3     | 9     16-   8     | 5     2     16+   |
 | 89    1     6     | 5     7     2     | 4     89    3     |
 *-----------------------------------------------------------*

As indicated by the +/- signs above, there's already an extensive network of {1, 6} pairs spreading throughout the puzzle. Our "target" cell -- the one needed to make useful inferences from the pattern -- is r7c8, marked with an asterisk above.

We start the double-implication chain in r2c1.

A. r2c1 = 1 ==> r5c1 = 6 ==> r6c3 = 1 ==> r6c4 = 6 ==> r6c8 = 9 ==> r9c8 = 8 ==> {1, 6} at r7c8.

B1. r2c1 = 6 ==> r5c1 = 1 ==> r4c2 = 6 ==> r4c7 = 1
B2. r2c1 = 6 ==> r2c9 = 1 ==> r3c8 = 6
B3 (r4c7 = 1 & r3c8 = 6) ==> r6c8 = 9 ==> r9c8 = 8 ==> {1, 6} at r7c8.

So the double-implication chain reveals that neither "8" nor "9" can appear at r7c8, leaving the grid looking like this.
Code:
*-----------------------------------------------------------*
 | 5     89    48    | 16    49    16    | 3     7     2     |
 | 16+   2     7     | 8     3     5     | 9     4     16-   |
 | 39    36    14    | 2     49    7     | 8     16+   5     |
 |-------------------+-------------------+-------------------|
 | 4     36    9     | 7     2     136   | 16    5     8     |
 | 16-   5     2     | 4     8     169   | 167   3     79    |
 | 38    7     18    | 16    5     39    | 2     169   4     |
 |-------------------+-------------------+-------------------|
 | 2     89    5     | 3     16+   4     | 167   16-   79    |
 | 7     4     3     | 9     16-   8     | 5     2     16+   |
 | 89    1     6     | 5     7     2     | 4     89    3     |
 *-----------------------------------------------------------*

Now we see that r7c7 = 7, and that r6c8 = 9, after which we can extend the {1, 6} network a bit farther, and the entire puzzle falls to pieces. dcb
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keith



Joined: 19 Sep 2005
Posts: 3179
Location: near Detroit, Michigan, USA

PostPosted: Sun Aug 20, 2006 10:40 am    Post subject: Another (neat) solution Reply with quote

Here's what I did. After the usaul basic moves, and a Type 1 UR to remove <16> in R6C6:

Code:
+----------------+----------------+----------------+
| 5    89   48   | 16   49   16   | 3    7    2    |
| 16   2    7    | 8    3    5    | 9    4    16   |
| 39   36B  14   | 2    49   7    | 8    16b  5    |
+----------------+----------------+----------------+
| 4    36b  9    | 7    2    136  | 16   5    8    |
| 16B  5    2    | 4    8    169c | 167  3    79   |
| 38   7    18   | 16a  5    39   | 2    169A 4    |
+----------------+----------------+----------------+
| 2    89   5    | 3    16   4    | 167  1689 79   |
| 7    4    3    | 9    16   8    | 5    2    16   |
| 89   1    6    | 5    7    2    | 4    89   3    |
+----------------+----------------+----------------+

Ravel also found this. I applied the logic of a fork or skyscraper:
If a is <6>, c is not <6>.
If a is not <6>, A is <6>, b is not <6>, B is <6>, and c is not <6>.
So, remove <6> from R5C6.

Now, a short chain:
R6C4 = <1> results in R5C6 = <9> and R6C6 = <3>.
R6C4 = <1> results in R5C3 = <8> and R6C1 = <3>.
So, R6C4 = <6>, which after some more basic moves brings us here:
Code:
+----------------+----------------+----------------+
| 5    89   48   | 1    49   6    | 3    7    2    |
| 16   2    7    | 8    3    5    | 9    4    16   |
| 39   36   14   | 2    49   7    | 8    16   5    |
+----------------+----------------+----------------+
| 4    36   9    | 7    2    13   | 16   5    8    |
| 16   5    2    | 4    8    19   | 167  3    79   |
| 38   7    18   | 6    5    39   | 2    19   4    |
+----------------+----------------+----------------+
| 2    89   5    | 3    16   4    | 17   1689 79   |
| 7    4    3    | 9    16   8    | 5    2    16   |
| 89   1    6    | 5    7    2    | 4    89   3    |
+----------------+----------------+----------------+


There is an X-wing on <1> in R36(C38) which takes out <1> in R7C8.

There is an XY-wing on <361> in R45 which takes out <1> in R5C6.
There is an XY-wing on <391> in R6C6 which takes out <1> in R4C7.

Either of these XY-wings solves the puzzle.

Keith
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