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One from Ruud

 
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
PostPosted: Fri Jun 16, 2006 10:03 pm    Post subject: One from Ruud Reply with quote
Here is the Nightmare Sudoku from Sunday June 11, during Ruud's Unique Rectangle week:
Code:

Puzzle: DSN061106
+-------+-------+-------+
| . 3 . | . 8 . | . . . |
| . . . | . 2 5 | 6 . . |
| 5 . . | 6 . . | . 1 . |
+-------+-------+-------+
| . . 8 | . . . | . 9 . |
| 4 . . | . . . | . 6 3 |
| 3 . 9 | . . . | 4 . . |
+-------+-------+-------+
| . . . | 8 . 7 | . . . |
| . 5 . | . . . | . . 4 |
| 2 . . | 5 6 . | 7 . . |
+-------+-------+-------+

Some interesting stuff! Solve it, if you can. If you use a computer solver, I'd be interested to hear what it does with the Unique Rectangle reductions.


The basic methods get us here:
Code:

+----------------+----------------+----------------+
| 679  3    467  | 179  8    149  | 259  2457 2579 |
| 8    1479 147  | 3    2    5    | 6    47   79   |
| 5    479  2    | 6    479  49   | 3    1    8    |
+----------------+----------------+----------------+
| 17   2    8    | 4    3    6    | 15   9    157  |
| 4    17   5    | 179  179  2    | 8    6    3    |
| 3    6    9    | 17   5    8    | 4    27   127  |
+----------------+----------------+----------------+
| 19   149  3    | 8    14   7    | 25   25   6    |
| 67   5    67   | 2    19   3    | 19   8    4    |
| 2    8    14   | 5    6    149  | 7    3    19   |
+----------------+----------------+----------------+

Note: I did not say we get here easily. This is a tough puzzle, well up to Ruud's usual standards.

There are two Unique Rectangles:

R18C13 on <67>. This is a Type 4 UR. The only occurrences of <6> in R1 (or B1) are on the corners of the rectangle. Therefore, neither of R1C13 is <7>.

R17C78 on <25>. This is a Type 3 UR. The "extra" values <479> in R1C78 form a reduced set with R2C89. So, R1C9 cannot be <79>.

This is where my solver (Sudoku Susser) stops. But, there is more. The second UR is:
Code:

259  2457
---------
25   25


There is a strong link on <2> in the left column, C7. The only possible values of <2> in C7 are the corners of the UR, so, R1C8 cannot be 5(!). (If R7C7 is <2>, R7C8 is <5> and R1C8 is not <5>. If R7C7 is <5>, R1C7 and R7C8 are both <2>, and to avoid the deadly solution, R1C8 cannot be <5>.)

Similarly, there is a strong link on <5> in C8. R1C7 cannot be <2> (!!).

This solves R7C78, and the result is:
Code:

+----------------+----------------+----------------+
| 69   3    46   | 179  8    149  | 59   247  25   |
| 8    1479 147  | 3    2    5    | 6    47   79   |
| 5    479  2    | 6    479  49   | 3    1    8    |
+----------------+----------------+----------------+
| 17   2    8    | 4    3    6    | 15   9    157  |
| 4    17   5    | 179  179  2    | 8    6    3    |
| 3    6    9    | 17   5    8    | 4    27   127  |
+----------------+----------------+----------------+
| 19   149  3    | 8    14   7    | 2    5    6    |
| 67   5    67   | 2    19   3    | 19   8    4    |
| 2    8    14   | 5    6    149  | 7    3    19   |
+----------------+----------------+----------------+

The rest of the puzzle is not exactly smooth sailing.

However, I wanted to point out these last two reductions which I am finding to be very common (as UR reductions go).

Best wishes,
Keith

PS: If you have no idea what this is all about, take a look at:

http://www.sudoku.com/forums/viewtopic.php?p=29105#29105
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dejsmith



Joined: 23 Oct 2005
Posts: 42
PostPosted: Sun Jun 18, 2006 12:04 am    Post subject: Reply with quote
Keith

The tack I took with the UR on 67 in R18C13 was to assume that R1C3=4 & got a contradiction. Therefore R1C1 had to be 9 & that solved the whole puzzle. Did I just make errors "correctly"? I was surprised I finished this in less than an hour when most Nightmares take me 2 hours.

Dave
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
PostPosted: Sun Jun 18, 2006 3:42 am    Post subject: Reply with quote
This is what I used over and above the basic stuff:

A block interaction on "6", the Type 4 rectangle on "67" and a Finned X-Wing on "7." As far as the "25" rectangle, the "reduced set" concept is still difficult for me to follow. I couldn't see anything from strong links or coloring, but there seemed to be potential with a chain based in r2c8.

The "4" led to a contradiction and solving the cell for "7" broke the puzzle open.
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