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A long slog, but not too hard

 
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
PostPosted: Sat Dec 05, 2015 11:54 pm    Post subject: A long slog, but not too hard Reply with quote
Here is an interesting puzzle:

Code:
 . . 1 2 . . . 3 .
 3 . . . 4 . . . 5
 . 6 . . . . 7 . .
 8 . . 3 . 9 . . .
 . 2 . . 8 . . 7 .
 . . . 1 . 7 . . 9
 . . 6 . . . . 5 .
 4 . . . 1 . . . 8
 . 8 . . . 5 9 . .


Found at http://forum.enjoysudoku.com/post248271.html#p248271

Hey, it's Sunday, you have time!

Keith
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
PostPosted: Sun Dec 06, 2015 2:53 am    Post subject: Reply with quote
Code:

+------------+------------+--------------+
| 59  59 1   | 2   7  68  | 468  3   46  |
| 3   7  8   | 69  4  1   | 26   269 5   |
| 2   6  4   | 589 35 38  | 7    89  1   |
+------------+------------+--------------+
| 8   1  7   | 3   56 9   | 56   4   2   |
| 569 2  359 | 456 8  46  | 1    7   36  |
| 56  4  35  | 1   2  7   | 3568 68  9   |
+------------+------------+--------------+
| 1   3  6   | 48  9  248 | 24   5   7   |
| 4   59 59  | 7   1  236 | 236  26  8   |
| 7   8  2   | 46  36 5   | 9    1   346 |
+------------+------------+--------------+

Play this puzzle online at the Daily Sudoku site

Two steps (I didn't pursue a one-stepper)

1) UR (26)r28c78
SL 2 in r2=> -6r2c78=6r2c4
Thus 3r8c7=6r2c4-(6=8)r1c6-(8=3)r3c6=> -3r8c6

2) XY-Wing (24-6), pivot r7c7=> -6r1c9
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
PostPosted: Sun Dec 06, 2015 6:11 am    Post subject: Reply with quote
Marty,

The basics, I thought, were interesting.

In your posted grid, look at C123. There is a uniqueness pattern on 59, which makes a pseudocell 36 in R5C13, which makes a pair with 36 in R5C9, which solves the puzzle.

Quite nice.

Keith
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JC Van Hay



Joined: 13 Jun 2010
Posts: 494
Location: Charleroi, Belgium
PostPosted: Sun Dec 06, 2015 10:38 am    Post subject: Reply with quote
Enjoyable puzzle Wink

1. First solution
    a. NT(468)R1, NT(236)R8; 22 Singles
    b. N>1-Fish : only possible for the digit 6

      Analysis of the 6s :
        r4c5=6 + r2c4=6 -> 1 solution
        |
        r4c5=6 + r9c4=6 -> 2 solutions
        |
        r9c5=6 -> 1 solution

        The 4 solutions for the digit 6 exclude 6r5c4 and 6r6c7.
      Interpretations :
        Starfish(R12489) -> r5c4≠6, r6c7≠6
        or
        Swordfish(C569) : r4c5=r9c8-r8c6,r9c9=XWing(r15c69) -> r5c4≠6
        Broken Wing[r29c4,r91c9,r1c6] or r1c7 or r6c9 or r9c5-r4c5=r5c7 -> r6c7≠6

    c. XYWing(456)r59c4,r4c5-(6=3)r9c5; singles to a unique solution.
2. Another solution :
    NT(468)R1, NT(236)R8; 22 Singles
    XYWing(246)r27c7,r1c9-4r1c7,r9c9
    Skyscraper(6C59)-6r5c4,r4c7; singles to a unique solution
3. A one-stepper (?) :

Code:
+--------------+--------------------+------------------+
| 59   59  1   | 2      7     8-6   | 468   3    (46)  |
| 3    7   8   | 9(6)   4     1     | 26    269  5     |
| 2    6   4   | 589    35    38    | 7     89   1     |
+--------------+--------------------+------------------+
| 8    1   7   | 3      56    9     | 56    4    2     |
| 569  2   359 | 45(6)  8     46    | 1     7    3(6)  |
| 56   4   35  | 1      2     7     | 3568  68   9     |
+--------------+--------------------+------------------+
| 1    3   6   | 48     9     248   | 24    5    7     |
| 4    59  59  | 7      1     23(6) | 236   26   8     |
| 7    8   2   | (46)   3(6)  5     | 9     1    3(46) |
+--------------+--------------------+------------------+
    r1c6=6 -> r1c9=r9c4=4, r5c4=r9c5=6, 6C9={}; r1c6=8 and singles to a unique solution.

    "Eureka notation" : Triple Kraken 6C49B8 -> (6)[r2c4==r1c9==r8c6]-6r1c6
      Wing[6r2c4=*(6-4)r9c4=4r9c9-(4=6)r1c9]=*6r5c4-6r9c4,6r5c9=*EmptyRectangle(6)[r8c6=*r9c5-r9c9=*r1c9]

4. Deadly patterns can now be used to find the unique solution :
    Marty's solution :
      UR(26)r28c78=*[3r8c7=*9r2c8-(9=83)r3c86]-3r8c6; 17 Singles
      Skyscraper(6C49) -> r1c6=8; stte
    Keith's solution :
      UL(59)r1c12,r5c13,r8c23=5r5c4; 17 singles
      Skyscraper(6C49) -> r1c6=8; stte
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