The New Sudoku Players' Forum

[JPF]

What is the total minimum number of clues in B2,B6,B7,B8 required to get a minimal valid puzzle?

Code: Select all

+-------+-------+-------+
| . . . | . . . | . . . |
| . 1 . | . . . | . . . |
| . . . | . . . | . . 1 |
+-------+-------+-------+
| 1 . . | . . . | . . . |
| . . . | . 1 . | . . . |
| . . . | . . . | . . . |
+-------+-------+-------+
| . . . | . . . | . . . |
| . . . | . . . | . 1 . |
| . . . | . . . | . . . |
+-------+-------+-------+


JPF

[m_b_metcalf]

What is the total minimum number of clues in B2,B6,B7,B8 required to get a minimal valid puzzle?

2?

Code: Select all

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

[JPF]

Hi Mike,

Sorry if my question was not clear.
Boxes B1,B3,B4,B5,B9 must have only one clue equal to 1.
The other boxes B2,B6,B7,B8 must be filled in order to have a valid and minimal puzzle.

JPF

[coloin]

Tough one
Was really difficult to get this grid

Code: Select all

+---+---+---+
|...|47.|...|
|.1.|685|...|
|...|239|..1|
+---+---+---+
|1..|...|237|
|...|.1.|896|
|...|...|.54|
+---+---+---+
|95.|728|...|
|382|546|.1.|
|746|.93|...|
+---+---+---+


which gave this minimal puzzle

Code: Select all

+---+---+---+
|...|4..|...|
|.1.|.85|...|
|...|.39|..1|
+---+---+---+
|1..|...|237|
|...|.1.|8..|
|...|...|.54|
+---+---+---+
|.5.|7.8|...|
|382|...|.1.|
|..6|.9.|...|
+---+---+---+   24C  [5C plus 19C]

[JPF]

That's a good start!

JPF

[m_b_metcalf]

Same comments:

Code: Select all

 . . . . 3 5 . . .
 . 1 . 7 . . . . .
 . . . . . 4 . . 1
 1 . . . . . 6 7 3
 . . . . 1 . . 2 4
 . . . . . . . . 8
 . 2 . . . 9 . . .
 8 7 . 6 . 2 . 1 .   
 3 . 4 . 8 . . . .   24 clues, minimal

[JPF]

Code: Select all

+---+---+---+
|...|..2|...|
|.1.|73.|...|
|...|698|..1|
+---+---+---+
|1..|...|372|
|...|.1.|.4.|
|...|...|.5.|
+---+---+---+
|..7|54.|...|
|29.|...|.1.|
|6..|.8.|...|
+---+---+---+   23C  [5C plus 18C]


JPF

[m_b_metcalf]

Here's another:

Code: Select all

 . . . 5 . . . . .
 . 1 . . 6 . . . .
 . . . 2 7 . . . 1
 1 . . . . . 7 . .
 . . . . 1 . 6 3 5
 . . . . . . . 2 9
 . 6 2 . . 3 . . .
 7 3 4 . . 2 . 1 .
 . . . . . 9 . . .  23C

Mike

[JPF]

slight improvement:

Code: Select all

+---+---+---+
|...|...|...|
|.1.|..2|...|
|...|345|..1|
+---+---+---+
|1..|...|3.2|
|...|.1.|674|
|...|...|.8.|
+---+---+---+
|.63|97.|...|
|..4|.8.|.1.|
|2..|...|...|
+---+---+---+   22C (5C plus 17C)


JPF

[coloin]

Code: Select all

+---+---+---+
|...|.2.|...|
|.1.|345|...|
|...|.6.|..1|
+---+---+---+
|1..|...|.5.|
|...|.1.|342|
|...|...|.6.|
+---+---+---+
|...|..7|...|
|835|...|.1.|
|.64|2..|...|
+---+---+---+   yes another 22 [5plus17]


Wouldnt bet on finding a 21 .... although presumably there are many valid "full B2B6B7B8 grids"

[JPF]

Wouldnt bet on finding a 21...

Well,...

Code: Select all

+---+---+---+
|...|..5|...|
|.1.|...|...|
|...|623|..1|
+---+---+---+
|1..|...|5..|
|...|.1.|897|
|...|...|.4.|
+---+---+---+
|...|54.|...|
|6.9|...|.1.|
|2.5|.8.|...|
+---+---+---+   21C (5C plus 16C)


JPF

[coloin]

Very good .... I cant match the search process... removing clues from a full grid is not efficient !
whereas specific clue removal and insertion is ... [in B2678]

For the record here is an 18C with all different clues in the B13459, so the pattern is possible !!

Code: Select all

+---+---+---+
|...|...|...|
|.1.|..7|...|
|...|38.|..2|
+---+---+---+
|3..|...|.9.|
|...|.4.|...|
|...|...|713|
+---+---+---+
|...|63.|...|
|.71|...|.5.|
|.5.|.2.|...|
+---+---+---+  18C


[m_b_metcalf]

Very good .... I cant match the search process... removing clues from a full grid is not efficient !

My method was to generate large numbers of solutions to the five-clue puzzle, remove from each the other clues from B13459, and retain those puzzles that had only one solution (about 1 in 6000). The last step was then to repeatedly remove clues at random from the full boxes in the usual top-down way. Didn't get to 21C, though

Mike

[JPF]

I'm away from home and can only use a poor performance laptop.
I found 12 21C:

Code: Select all

.....7....1..........6.9..11.....9.6....1.432..........8..4....63.58..1.5.9......
.....7....1..........6.9..11.....9.6....1.432..........8..4....63.58..1..29......
.....5....1..........6.9..11.....5......1.432.......8.78..4....6..58..1..29......
.....5....1..........6.9..11.....5......1.432.......8.78..3....6..58..1..29......
.....5....1..........672..11.....5......1.843.......9....54....6.9....1.57..8....
.....5....1..........672..11.....5......1.843.......9....54....6.9....1.52..8....
.....2....1..........657..11.....2......1.893.......4....24....6.9....1.5.2.8....
.....2....1..........657..11.....2......1.893.......4....24....6.9....1.7.2.8....
...2......1..........674..11.......2....1.689.......3.....35...79..8..1.2.4......
...2......1..........674..11.......4....1.689.......3.....35...79..8..1.2.4......
.....2....1..........657..11.....2......1.839.......4...2.4....7.3....1.6..28....
.....2....1..........657..11.....2......1.839.......4...2.4....7.3....1.5..28....


and about 2000 22C.
I guess there is no 20C.

Now here is the last part of the assignment:
same question (lowest number of clues for a valid puzzle) with this template:

Code: Select all

+-------+-------+-------+
| . . . | . . . | . . . |
| . 1 . | . . . | . . . |
| . . . | 1 . . | . . . |
+-------+-------+-------+
| 1 . . | . . . | . . . |
| . . . | . . . | . 1 . |
| . . . | . . . | . . . |
+-------+-------+-------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-------+-------+-------+


and this one:

Code: Select all

+-------+-------+-------+
| . . . | . . . | . . . |
| . 1 . | . . . | . . . |
| . . . | 1 . . | . . . |
+-------+-------+-------+
| 1 . . | . . . | . . . |
| . . . | . 1 . | . . . |
| . . . | . . . | . . . |
+-------+-------+-------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-------+-------+-------+


JPF

[coloin]

A

Code: Select all

+---+---+---+
|...|...|..3|
|.1.|...|45.|
|...|1..|.89|
+---+---+---+
|1..|27.|...|
|...|836|.1.|
|...|..4|...|
+---+---+---+
|2..|5..|.7.|
|37.|.2.|...|
|84.|..9|...|
+---+---+---+  24C


B

Code: Select all

+---+---+---+
|...|...|..9|
|.1.|...|4..|
|...|1..|8.3|
+---+---+---+
|1..|...|6..|
|...|71.|98.|
|...|...|24.|
+---+---+---+
|92.|.6.|...|
|.45|.92|...|
|3..|..4|...|
+---+---+---+   23 clues .... but cant get rid of the interlopping clue !