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DB Saturday Puzzle - June 3, 2006

 
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keith



Joined: 19 Sep 2005
Posts: 3184
Location: near Detroit, Michigan, USA

PostPosted: Sat Jun 03, 2006 3:21 pm    Post subject: DB Saturday Puzzle - June 3, 2006 Reply with quote

More difficult than usual:

Code:

Puzzle: DB060306  ******
+-------+-------+-------+
| 1 9 . | . . 4 | . . 8 |
| . . . | . . . | . . . |
| . 5 . | . 1 . | 2 9 . |
+-------+-------+-------+
| . 6 9 | . . 1 | 4 . . |
| . 8 . | 4 . 3 | . 7 . |
| . . 3 | 9 . . | 8 6 . |
+-------+-------+-------+
| . 4 2 | . 9 . | . 1 . |
| . . . | . . . | . . . |
| 6 . . | 3 . . | . 5 4 |
+-------+-------+-------+


Keith
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Marty R.



Joined: 12 Feb 2006
Posts: 5178
Location: Rochester, NY, USA

PostPosted: Sat Jun 03, 2006 4:55 pm    Post subject: Reply with quote

This was a fun puzzle. It started off generously, with numerous cells able to be solved early. Then things came to a halt and it was some time before I spotted an XY-Wing. After the eliminations therefrom, remote pairs solved a cell. After more eliminations, remote pairs using the same two numbers solved another cell, and that broke open the puzzle.

For me, XY-Wings and remote pairs are more talked about than actually used, so the opportunity to solve a puzzle using both techniques was indeed a treat.

Two thumbs up for DB and two thumbs down for the Pistons. Exclamation
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keith



Joined: 19 Sep 2005
Posts: 3184
Location: near Detroit, Michigan, USA

PostPosted: Sat Jun 03, 2006 9:04 pm    Post subject: I agree! Reply with quote

Marty R. wrote:
This was a fun puzzle .... Two thumbs up for DB and two thumbs down for the Pistons. Exclamation


Marty,

I agree, this is exactly the kind of puzzle I like to solve. I got to this interesting point:

Code:

+----------------+----------------+----------------+
| 1    9    67   | 2    57   4    | 567  3    8    |
| 78   2    678  | 567  3    9    | 1567 4    15   |
| 3    5    4    | 678  1    678  | 2    9    67   |
+----------------+----------------+----------------+
| 57   6    9    | 578  578  1    | 4    2    3    |
| 2    8    15a  | 4    6    3    | 15   7    9    |
| 4    17b  3    | 9    257  257  | 8    6    15   |
+----------------+----------------+----------------+
| 578  4    2    | 5678 9    5678 | 3    1    67   |
| 9    3    57c  | 1    4    567  | 67   8    2    |
| 6    17d  178e | 3    278  278  | 9    5    4    |
+----------------+----------------+----------------+

There is an XY-wing on <7> in "a,b,c", so "d" cannot be <7>. But, wait!

There is an XY-wing on <1> in "c,a,d", so "b,e" cannot be <1>.

Note that either of these wings destroys the other one! If you take the reductions from both wings, you eventually get to this neat pattern:
Code:

+-------------+-------------+-------------+
| 1   9   67  | 2   5   4   | 67  3   8   |
| 78  2   678 | 67  3   9   | 1   4   5   |
| 3   5   4   | 678 1   78  | 2   9   67  |
+-------------+-------------+-------------+
| 5   6   9   | 78  78  1   | 4   2   3   |
| 2   8   1   | 4   6   3   | 5   7   9   |
| 4   7   3   | 9   2   5   | 8   6   1   |
+-------------+-------------+-------------+
| 78  4   2   | 5   9   678 | 3   1   67  |
| 9   3   5   | 1   4   67  | 67  8   2   |
| 6   1   78  | 3   78  2   | 9   5   4   |
+-------------+-------------+-------------+

which can be solved with one remote pair. Neato!

It seems to me that Miami, in spite of having a superstar in Shaq, now have more of the "get it done" work ethic the Pistons used to have. Too bad.

Keith
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Marty R.



Joined: 12 Feb 2006
Posts: 5178
Location: Rochester, NY, USA

PostPosted: Sat Jun 03, 2006 11:30 pm    Post subject: Reply with quote

Keith, I can't re-create my position at any given point, but I'm pretty sure it was the c-a-d XY-Wing that I used to set r6c2=7. Then I used the 67 remote pairs twice to finish it off. In both cases, those pairs set cells = 8.
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keith



Joined: 19 Sep 2005
Posts: 3184
Location: near Detroit, Michigan, USA

PostPosted: Sun Jun 04, 2006 1:32 am    Post subject: Confessions Reply with quote

Marty,

Yes, I solved it via 1 XY-wing as you did. But, if a puzzle seems interesting, I go back and examine it with Sudokuku Susser. It was the Susser that pointed out (to me) the overlapping XY-wings.

Keith


Last edited by keith on Sun Jun 04, 2006 1:19 pm; edited 1 time in total
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TKiel



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

PostPosted: Sun Jun 04, 2006 1:04 pm    Post subject: Reply with quote

MartyR wrote:
remote pairs are more talked about than actually used


I agree with you on that Marty, yet this puzzle, as shown in the grid posted by Keith, has two sets of remote pairs, either of which can be used to solve the puzzle.

Thanks for posting these puzzles Keith. The techniques/patterns used to solve them generally seem to be right up my alley and usually it's not just a single move that finally solves the puzzle.
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