The New Sudoku Players' Forum

[JPF]

What is the lowest number of clues of a valid and minimal puzzle included in this pattern?

Code: Select all

+-------+-------+-------+
| . . . | . . . | . . . |
| . x x | x x x | x x . |
| . x x | x x x | x x . |
+-------+-------+-------+
| . x x | . . . | x x . |
| . x x | . . . | x x . |
| . x x | . . . | x x . |
+-------+-------+-------+
| . x x | x x x | x x . |
| . x x | x x x | x x . |
| . . . | . . . | . . . |
+-------+-------+-------+


Here is an example:

Code: Select all

+---+---+---+
|...|...|...|
|...|4.9|.7.|
|.87|316|...|
+---+---+---+
|.39|...|72.|
|..8|...|31.|
|.15|...|89.|
+---+---+---+
|..1|763|98.|
|..3|1.8|56.|
|...|...|...|
+---+---+---+  30C


JPF

[coloin]

Code: Select all

+---+---+---+
|...|...|...|
|..2|34.|...|
|.36|.8.|59.|
+---+---+---+
|.58|...|7..|
|.7.|...|93.|
|...|...|84.|
+---+---+---+
|..3|598|.1.|
|.94|.31|2..|
|...|...|...|
+---+---+---+     26C


[JPF]

slowly...

Code: Select all

+---+---+---+
|...|...|...|
|...|123|4..|
|.56|7..|8..|
+---+---+---+
|.73|...|58.|
|...|...|73.|
|...|...|...|
+---+---+---+
|.28|.9.|36.|
|.6.|41.|.9.|
|...|...|...|
+---+---+---+   23C


JPF

[coloin]

Code: Select all

+---+---+---+
|...|...|...|
|..2|34.|.7.|
|.36|1.2|5..|
+---+---+---+
|.58|...|...|
|.7.|...|93.|
|...|...|.4.|
+---+---+---+
|.2.|.79|.8.|
|..4|.6.|1..|
|...|...|...|
+---+---+---+ 22C


[m_b_metcalf]

Code: Select all

 . . . . . . . . .
 . . . 3 4 . . 7 .
 . 3 6 1 . 2 5 . .
 . 7 8 . . . . . .
 . 5 . . . . 3 2 .
 . . . . . . . 4 .
 . 2 . . 7 9 . 8 .
 . . 4 . 6 . 1 . .
 . . . . . . . . .   21C

Mike

[m_b_metcalf]

Code: Select all

 . . . . . . . . .
 . . 1 2 . . . 7 .
 . . 9 1 . 8 4 . .
 . 7 8 . . . . . .
 . 5 . . . . 9 2 .
 . . . . . . . 3 .
 . 2 . . 7 4 . 5 .
 . . 4 . 8 . 1 . .
 . . . . . . . . .  20C

Mike

[JPF]

Code: Select all

+---+---+---+
|...|...|...|
|...|1.2|3..|
|.4.|..5|.6.|
+---+---+---+
|.52|...|1..|
|...|...|73.|
|...|...|...|
+---+---+---+
|.13|.8.|2..|
|.8.|.64|.5.|
|...|...|...|
+---+---+---+   19C


JPF

[JPF]

Code: Select all

+---+---+---+
|...|...|...|
|...|1..|2..|
|.3.|..4|.5.|
+---+---+---+
|..2|...|6..|
|.4.|...|.7.|
|..8|...|1..|
+---+---+---+
|..1|2..|8..|
|.5.|.37|.4.|
|...|...|...|
+---+---+---+    18C


Does anyone want to check that there is no 17C ?

JPF

[Hajime]

So: Scan the 49158 17C db for an empty Box en 2 empty rows and 2 empty columns that doe not intersect that box.
And the 2 rows/columns must be in different bands/stacks. Right?

[m_b_metcalf]

Does anyone want to check that there is no 17C ?

My attempt came up with none. Here's a near miss:

Code: Select all

 . . . . . . . . .
 . 5 . . 2 3 . . .
 . . . . 8 . 1 . .
 . 2 . . . . . 5 .
 . . 7 9 . . . . .
 . . 6 1 . . . . .
 . 3 . . 5 . . 2 .
 . . 1 4 . . 6 . .
 . . . . . . . . .  17C, B5 not empty

There are none with only one clue in B5.

[JPF]

Right, there are no 17C-puzzles with 1 empty box + 2 empty rows + 2 empty columns.

Keeping the Minlex form:
There are 20 puzzles with 1 empty box + 2 empty rows + 1 empty column (up to a 90°-rotation)
Here is an example:

Code: Select all

+---+---+---+
|...|...|...|
|...|...|.12|
|...|.34|...|
+---+---+---+
|...|...|...|
|...|..5|4.6|
|.12|7..|...|
+---+---+---+
|...|.4.|8..|
|..6|2..|...|
|.95|...|3..|
+---+---+---+


There are 2 puzzles with 3 empty rows + 2 empty columns (up to a 90°-rotation)

Code: Select all

+---+---+---+   +---+---+---+
|...|...|...|   |...|...|...|
|...|..1|..2|   |...|..1|..2|
|..3|...|.4.|   |..3|...|.4.|
+---+---+---+   +---+---+---+
|...|...|...|   |...|...|...|
|...|34.|.5.|   |..4|.5.|.3.|
|.1.|.6.|..7|   |.6.|..2|..1|
+---+---+---+   +---+---+---+
|...|...|...|   |...|.3.|.5.|
|..4|..5|.3.|   |.1.|...|.76|
|.7.|8.2|..1|   |.2.|..8|...|
+---+---+---+   +---+---+---+


JPF

[coloin]

Well done on finding that 18 ...

Not sure how many clues we can remove from this next pattern challenge !

Code: Select all

+---+---+---+
|...|...|...|
|...|...|..2|
|.23|156|98.|
+---+---+---+
|.84|239|17.|
|.79|581|32.|
|.31|647|85.|
+---+---+---+
|.52|378|46.|
|7..|...|...|
|...|...|...|
+---+---+---+  37C


Code: Select all

+---+---+---+
|...|...|...|
|...|...|..2|
|.23|156|98.|
+---+---+---+
|.8.|23.|17.|
|.79|5..|3..|
|...|64.|.5.|
+---+---+---+
|.52|3.8|4..|
|7..|...|...|
|...|...|...|
+---+---+---+  26C


[m_b_metcalf]

Code: Select all

 . . . . . . . . .
 . . . . . . . . 2
 . . 3 1 5 6 . 8 .
 . . 4 . . 9 1 . .
 . . 9 . 8 . . 2 .
 . 3 . 6 . 7 8 5 .
 . 5 2 3 . . 4 . .
 7 . . . . . . . .
 . . . . . . . . .   22C, straight off

[m_b_metcalf]

Code: Select all

 . . . . . . . . .
 . . . . . . . . 7
 . . 7 1 2 8 . 9 .
 . . 6 . . 9 3 . .
 . . 9 . 8 . . 4 .
 . . . 7 . 4 5 8 .
 . 5 2 3 . . 1 . .
 4 . . . . . . . .
 . . . . . . . . .    21C

No more time.

[JPF]

Code: Select all

+---+---+---+
|...|...|...|
|...|...|..1|
|.2.|3.4|.5.|
+---+---+---+
|.6.|.1.|7..|
|.8.|..5|64.|
|..5|.79|.2.|
+---+---+---+
|..7|.91|...|
|4..|...|...|
|...|...|...|
+---+---+---+   20C


JPF