Minimum number of clues with 3 empty boxes?

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Minimum number of clues with 3 empty boxes?

Postby ixsetf » Thu Oct 30, 2014 7:36 pm

It is possible to generate a sudoku puzzle with three empty boxes when the boxes are arranged in a diagonal. However there are no examples of puzzles with three empty boxes in the list of 17s. This raises the question, what is the minimum number of possible clues?
Last edited by ixsetf on Fri Oct 31, 2014 3:20 am, edited 2 times in total.
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Re: Minimum number of clues with 3 empty boxes?

Postby blue » Thu Oct 30, 2014 10:01 pm

Here's one with 18 clues.

Code: Select all
. . . . 4 9 . . .
. . . . . 3 4 . .
. . . . . . 1 8 .
. . . . . . . 5 9
3 . . . . . . . 8
2 4 . . . . . . .
. 5 9 . . . . . .
. . 8 6 . . . . .
. . . 1 3 . . . .
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Re: Minimum number of clues with 3 empty boxes?

Postby Serg » Thu Oct 30, 2014 10:40 pm

Hi, blue!
blue wrote:Here's one with 18 clues.

Code: Select all
. . . . 4 9 . . .
. . . . . 3 4 . .
. . . . . . 1 8 .
. . . . . . . 5 9
3 . . . . . . . 8
2 4 . . . . . . .
. 5 9 . . . . . .
. . 8 6 . . . . .
. . . 1 3 . . . .

Nice puzzle! This is double-diagonal symmetric 18-clue puzzle (did you search through its full list posted by Afmob?).

Here is my example of 24-clue puzzle, having 3 empty diagonally placed boxes.
Code: Select all
1 9 5 7 8 . . . .
2 . . 4 . . . . .
4 . 7 . . . . . .
6 1 . . . . . . .
8 . . . . . . . 7
. . . . . . . 4 8
. . . . . . 2 . 5
. . . . . 9 . . 1
. . . . 1 3 8 9 6
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Re: Minimum number of clues with 3 empty boxes?

Postby JPF » Thu Oct 30, 2014 11:26 pm

Yes,
good old days!

a new one :
Code: Select all
 6 9 5 1 . . . . .
 2 . . 7 . . . . .
 1 . . 2 . . . . .
 9 2 8 . . . . . .
 . . . . . . . . .
 . . . . . . 7 3 9
 . . . . . 5 . . 4
 . . . . . 8 . . 3
 . . . . . 9 1 2 6

JPF
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Re: Minimum number of clues with 3 empty boxes?

Postby blue » Fri Oct 31, 2014 1:47 am

Nice shapes, Serg and JPF !

Serg wrote:This is double-diagonal symmetric 18-clue puzzle (did you search through its full list posted by Afmob?).

No, generated it on the fly. I remembered the shape, but not from where.

Here's another one with 18 clues.

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