The New Sudoku Players' Forum

[SteveG48]

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 *-----------*
 |.8.|54.|...|
 |..3|...|...|
 |4..|..1|2..|
 |---+---+---|
 |12.|8..|.93|
 |..8|1.7|5..|
 |97.|...|.81|
 |---+---+---|
 |..7|9..|..6|
 |...|...|1..|
 |...|.25|.4.|
 *-----------*


[Cenoman]

Two steps:

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 +-------------------------+-----------------------+------------------------+
 |  267     8       1269   |  5      4      2369   |  369    1367   79      |
 |  2567    1569    3      |  267    678    2689   |  4689   1567   45789   |
 |  4       569     69     |  367    3678   1      |  2      3567   5789    |
 +-------------------------+-----------------------+------------------------+
 |  1       2       456*   |  8      56     46*    |  7      9      3       |
 |  36      36-4    8      |  1      9      7      |  5      26     24      |
 |  9       7       456    |  2346   356    2346   |  46     8      1       |
 +-------------------------+-----------------------+------------------------+
 |  2358    345*    7      |  9      1      348*   |  38     235    6       |
 |  23568   34569   269-4  |  3467   3678   3468   |  1      2357   25789   |
 |  368     1369    169    |  367    2      5      |  389    4      789     |
 +-------------------------+-----------------------+------------------------+

1. Skyscraper: (4)r4c3 = r4c6 - r7c6 = r7c2 => -4 r5c2, r8c3; lcls, 13 placements

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 +--------------------+-----------------------+-------------------+
 | e67     8     2    |  5      4      36     |  39    1    f79   |
 |  567    1     3    |  2      678    9      |  4     67    58   |
 |  4      59   d69   |  367    3678   1      |  2     367   58   |
 +--------------------+-----------------------+-------------------+
 |  1      2     45   |  8      56     46     |  7     9     3    |
 |  36     36    8    |  1      9      7      |  5     2     4    |
 |  9      7     45   |  34     35     2      |  6     8     1    |
 +--------------------+-----------------------+-------------------+
 |  2      45    7    |  9      1      348    |  38    35    6    |
 |  3568   459  c69   | b3467  b367   b3468   |  1     357   2    |
 |  368    36    1    | a36-7   2      5      |  389   4    g79   |
 +--------------------+-----------------------+-------------------+

2. (6)r9c4 = r8c456 - r8c3 = r3c3 - (6=7)r1c1 - r1c9 = (7)r9c9 => -7 r9c4; ste

[SteveG48]

Nice solution, but wow. We may be looking at a first.

All of the Stumble series are puzzles that I come across in my daily reading- usually the local newspaper. I work all of them with pen and paper- sometimes successfully and sometimes not. (In this case I was successful.) Then, if the puzzle seems to me to be a cut above the typical newspaper puzzle, I may post it. I have no idea when I do whether it has a one-step solution, but this is the first time that we haven't seen one. Anyone?

[Cenoman]

@Steve,
This puzzle is maybe a bit paradoxical. It has not a high SE rating (6.6), in line with the simple two-step solution.
But look at its backdoors: there are 7 with singles (6r1c6 6r2c1 5r2c9 6r3c8 3r7c6 5r8c1 6r8c3), plus 1 with basics (3r3c5); all but one (r7c6) in cells with at least four candidates. No single anti-backdoor at all. So one-step solutions are much unlikely.
My solver found one: an ugly net encompassing 18 krakens ! I didn't feel like drawing such a monster. But if you insist...

[P.O.]

i have the same eliminations as Cenoman and the same observations on antibackdoors
after basics the puzzle has no size 1-AntiBackdoors in singles or singles + intersections, but it has a lot of size 2-AntiBackdoors in singles, i counted 235, but impossible to have together one of these two eliminations with the techniques i use.

basics:

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( n1r7c5   n7r4c7   n9r5c5 )

intersection:
((((5 0) (4 3 4) (4 5 6)) ((5 0) (6 3 4) (4 5 6))))


Code: Select all

267    8      1269   5      4      2369   369    1367   79             
2567   1569   3      267    678    2689   4689   1567   45789           
4      569    69     367    3678   1      2      3567   5789           
1      2      456    8      56     46     7      9      3               
36     346    8      1      9      7      5      26     24             
9      7      456    2346   356    2346   46     8      1               
2358   345    7      9      1      348    38     235    6               
23568  34569  2469   3467   3678   3468   1      2357   25789           
368    1369   169    367    2      5      389    4      789       

r4n4{c3 c6} - r7n4{c6 c2} => r5c2 r8c3 <> 4


basics:

Hidden Text: Show

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( n4r5c9   n6r6c7   n2r5c8   n2r8c9   n2r7c1   n4r2c7   n2r1c3
  n1r9c3   n1r2c2   n1r1c8 )

intersections:
((((9 0) (9 7 9) (3 8 9)) ((9 0) (9 9 9) (7 8 9)))
 (((9 0) (3 2 1) (5 6 9)) ((9 0) (3 3 1) (6 9)))
 (((8 0) (7 7 9) (3 8)) ((8 0) (9 7 9) (3 8 9)))
 (((6 0) (4 5 5) (5 6)) ((6 0) (4 6 5) (4 6)))
 (((5 0) (7 8 9) (3 5)) ((5 0) (8 8 9) (3 5 7))))

PAIR COL: ((5 2 4) (3 6)) ((9 2 7) (3 6)) 
(((3 2 1) (5 6 9)) ((7 2 7) (3 4 5)) ((8 2 7) (3 4 5 6 9)))

PAIR COL: ((1 9 3) (7 9)) ((9 9 9) (7 9)) 
(((2 9 3) (5 7 8 9)) ((3 9 3) (5 7 8)))

( n9r2c6   n2r6c6   n2r2c4 )

intersection:
((((8 0) (7 6 8) (3 4 8)) ((8 0) (8 6 8) (3 4 6 8))))


Code: Select all

67    8     2     5     4     36    39    1     79             
567   1     3     2     678   9     4     67    58             
4     59    69    367   3678  1     2     367   58             
1     2     45    8     56    46    7     9     3             
36    36    8     1     9     7     5     2     4             
9     7     45    34    35    2     6     8     1             
2     45    7     9     1     348   38    35    6             
3568  459   69    3467  367   3468  1     357   2             
368   36    1     367   2     5     389   4     79       

7r9c4 => r19c9 <> 7
 r9c4=7 - r9n6{c4 c12} - c3n6{r8 r3} - r1c1{n6 n7}
=> r9c4 <> 7
ste.


otherwise the puzzle is in 2-template, and is solved with a single combination: (6 7)

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Initialization:
#VT: (2 9 48 4 18 112 12 11 14)
Cells: nil nil nil (16 45) nil nil nil nil nil
SetVC: ( n4r2c7   n4r5c9   n6r6c7   n2r5c8   n2r8c9   n2r7c1
         n2r1c3   n1r9c3   n1r2c2   n1r1c8 )

#VT: (1 2 23 4 6 9 7 5 6)
Cells: nil nil nil nil nil nil nil nil nil
Candidates:nil nil nil (66) (17 21 26 66) (13 22 30 68 69) nil (81) (27 74)

67     8      2      5      4      369    39     1      79             
567    1      3      27     678    2689   4      67     5789           
4      569    69     37     3678   1      2      367    578             
1      2      45     8      56     46     7      9      3               
36     36     8      1      9      7      5      2      4               
9      7      45     234    35     234    6      8      1               
2      345    7      9      1      348    38     35     6               
3568   34569  69     3467   378    348    1      357    2               
368    36     1      367    2      5      389    4      79             


1: (6 7) 16 instances

.....6..77......6...6.7........6.7...6...7....7....6....7.....6...6...7.6..7.....
7....6..........67..6.7........6.7...6...7....7....6....7.....6...6...7.6..7.....
7....6.......7..6...6.....7....6.7...6...7....7....6....7.....6...6...7.6..7.....
7....6......7...6...6....7.....6.7...6...7....7....6....7.....6...67....6.......7
7....6.......7..6...6....7.....6.7...6...7....7....6....7.....66..7........6....7
7....6......7...6...6....7.....6.7...6...7....7....6....7.....66...7.......6....7
.....6..77......6...6.7........6.7..6....7....7....6....7.....6...6...7..6.7.....
7....6..........67..6.7........6.7..6....7....7....6....7.....6...6...7..6.7.....
7....6.......7..6...6.....7....6.7..6....7....7....6....7.....6...6...7..6.7.....
7....6......7...6...6....7.....6.7..6....7....7....6....7.....6...67.....6......7
7....6.......7..6...6....7.....6.7..6....7....7....6....7.....6.6.7........6....7
7....6......7...6...6....7.....6.7..6....7....7....6....7.....6.6..7.......6....7
7....6.......7..6..6.....7.....6.7..6....7....7....6....7.....6..67........6....7
7....6......7...6..6.....7.....6.7..6....7....7....6....7.....6..6.7.......6....7
7....6...6......7.....7..6.....6.7...6...7....7....6....7.....6..67........6....7
7....6...6......7....7...6.....6.7...6...7....7....6....7.....6..6.7.......6....7

.....6..........6...6..........6.....6.............6..........6...6.....6........
.....6..........6...6..........6.....6.............6..........66...........6.....
.....6..........6...6..........6....6..............6..........6...6......6.......
.....6..........6...6..........6....6..............6..........6.6..........6.....
.....6..........6..6...........6....6..............6..........6..6.........6.....
.....6...6...............6.....6.....6.............6..........6..6.........6.....

........77............7..........7.......7....7.........7.............7....7.....
7................7....7..........7.......7....7.........7.............7....7.....
7...............7.....7..........7.......7....7.........7.........7.............7
7...............7....7...........7.......7....7.........7..........7............7
7............7............7......7.......7....7.........7.............7....7.....
7............7...........7.......7.......7....7.........7.........7.............7
7...........7............7.......7.......7....7.........7..........7............7

#VT: (1 2 23 4 6 6 7 5 6)
Cells: nil nil nil nil nil (6 32) nil nil nil
SetVC: ( n6r1c6   n6r4c5   n4r4c6   n7r1c1   n9r1c9   n5r4c3
         n4r6c3   n7r9c9   n3r1c7   n8r7c7   n9r9c7   n3r7c6
         n5r7c8   n8r8c6   n3r8c8   n6r9c4   n2r6c6   n4r7c2
         n7r8c5   n3r9c2   n8r2c5   n9r2c6   n5r2c9   n3r3c5
         n8r3c9   n6r5c2   n3r6c4   n5r6c5   n4r8c4   n8r9c1
         n6r2c1   n7r2c8   n9r3c3   n7r3c4   n6r3c8   n3r5c1
         n5r8c1   n9r8c2   n6r8c3   n2r2c4   n5r3c2 )
7 8 2   5 4 6   3 1 9
6 1 3   2 8 9   4 7 5
4 5 9   7 3 1   2 6 8
1 2 5   8 6 4   7 9 3
3 6 8   1 9 7   5 2 4
9 7 4   3 5 2   6 8 1
2 4 7   9 1 3   8 5 6
5 9 6   4 7 8   1 3 2
8 3 1   6 2 5   9 4 7


[SteveG48]

@Steve,
This puzzle is maybe a bit paradoxical. It has not a high SE rating (6.6), in line with the simple two-step solution.
But look at its backdoors: there are 7 with singles (6r1c6 6r2c1 5r2c9 6r3c8 3r7c6 5r8c1 6r8c3), plus 1 with basics (3r3c5); all but one (r7c6) in cells with at least four candidates. No single anti-backdoor at all. So one-step solutions are much unlikely.
My solver found one: an ugly net encompassing 18 krakens ! I didn't feel like drawing such a monster. But if you insist...

Thanks, Cenoman, but I'll pass .

I agree that it's paradoxical. I had no idea when I posted it.