The New Sudoku Players' Forum

[Pat]

while every "ulterior" puzzle requires box-to-line exclusion
in the sense that it cannot be solved by "hidden singles" alone,

the above example has an extra property --
it requires box-to-line exclusion
in the sense that it cannot be solved by "singles" + subsets.

[Pat]

filtered ~2M generated symmetric puzzles from last March --

[ 30 clues ]

Code: Select all

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



an absolute marvel

bonus:
cannot be solved by "singles" + subsets

[Pat]

Sudoku Explainer rating = 1.7


[ 21 clues ]

Code: Select all

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



bonus:
cannot be solved by "singles" + subsets

[Pat]

[ 65 clues ]

Code: Select all

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



seems a high number of clues -- has this been exceeded ?
( for a puzzle requiring box-to-line exclusion )

bonus:
cannot be solved by "singles" + subsets

[Pat]

[ 26 clues ]

Code: Select all

2..4....3.....2.6.5..8...4.4...3.5....52.86....8.5...2.3...1..7.1.5.....8....7..1



Code: Select all

 2 . . | 4 . . | . . 3
 . . . | . . 2 | . 6 .
 5 . . | 8 . . | . 4 .
-------+-------+------
 4 . . | . 3 . | 5 . .
 . . 5 | 2 . 8 | 6 . .
 . . 8 | . 5 . | . . 2
-------+-------+------
 . 3 . | . . 1 | . . 7
 . 1 . | 5 . . | . . .
 8 . . | . . 7 | . . 1



bonus:
cannot be solved by "singles" + subsets

[Pat]

[ 20 clues ]

Code: Select all

1.......2...3.4.....2...5...3..5..6....1.7....6..8..4...3...2.....6.8...5.......1



Code: Select all

 1 . . | . . . | . . 2
 . . . | 3 . 4 | . . .
 . . 2 | . . . | 5 . .
-------+-------+------
 . 3 . | . 5 . | . 6 .
 . . . | 1 . 7 | . . .
 . 6 . | . 8 . | . 4 .
-------+-------+------
 . . 3 | . . . | 2 . .
 . . . | 6 . 8 | . . .
 5 . . | . . . | . . 1



bonus:
cannot be solved by "singles" + subsets

[Pat]

44 cells given

8269.43.11...63.4.435..1..69.1.2....5423...1.7.3.15..22.4.381.531.....2.65.1427..

Code: Select all


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



[Pat]

7...8...2..1....3..4....7......538..8..42.......1....7..52..3...1.....8.2....7..6

[ play ]

23 cells given
(layout 214 of the Patterns Game)

Code: Select all


 7 . . | . 8 . | . . 2
 . . 1 | . . . | . 3 .
 . 4 . | . . . | 7 . .
-------+-------+------
 . . . | . 5 3 | 8 . .
 8 . . | 4 2 . | . . .
 . . . | 1 . . | . . 7
-------+-------+------
 . . 5 | 2 . . | 3 . .
 . 1 . | . . . | . 8 .
 2 . . | . . 7 | . . 6



bonus:
cannot be solved by "singles" + subsets

[Marty R.]

cannot be solved by "singles" + subsets

I think I solved it with those two plus Locked Candidates.

[Pat]

If you wish to simulate a human solver,
then chained pointing pairs should count as only one step:

Code: Select all

-----|-----|* | *
* X X|. . .|X | X
* X X|. . .|X | X
-----+-----+-----
| X X|. . .|X | *
| * *|-----|--|--
| X X|. . .|X | *
-----+-----+-----
| . .|. . .|. | .
| . .|. . .|. | .
| . .|. . .|. A .



A computer would first exclude A from r1c123,
then in step 2 exclude A from r456c1,
in step 3 exclude A from r5c79,
in step 4 exclude A from r1c9
solving r1c7=A.

If you are a human solver
that don't use pencilmarks
(or memorize the previous pointing pairs in any other way)
then the only way you can use the 2nd, 3rd and 4th pointing pair
is by immediately following up the first one.
That's how slicing and dicing works,
you don't stop as long as new lines are exposed.

got a bit carried away?
the 3rd move solves the A for c7
(4th move not needed)

anyway my puzzle provides a real example of a triple move

7...81..2.21.74638.48..27151..7538..87.42.153...1.8..7.852..371.17..528.2..8175.6
[ play ]

[Pat]

.75...2..31.9.....6.9.....1.9.7....5.....43......1..8.2...4.8.......8.2...15....9

[ play ]

24 cells given
(layout 212 of the Patterns Game)

Code: Select all


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



[7b53]

Code: Select all

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

fun puzzle, what will be the key move...