The New Sudoku Players' Forum

[denis_berthier]

.
As I was tweaking some pattern, I fell upon the following "why not" 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 !
+-------+-------+-------+

X.......X.X.....X...X...X.....X.X.......X.......X.......X.XXXXX.X......XX.......X
20 givens

After 45 minutes of running gsf's generator, I couldn't find a minimal puzzle; after 2 more hours, I couldn't find a non-minimal (single-solution) one either.

It may just be that I'm not patient enough: minimal puzzles with 20 clues are very rare. Indeed, 0.0044% for a top-down generator and close to 0% in unbiased statistics. Of course, this doesn't say much about any particular pattern.

Does anyone see any a priori reason why this pattern could not have minimal puzzles (or any single-solution puzzle at all)?
If not, can you find one?

[eleven]

I wonder, if a unique puzzle with the pattern of the first 2 bands is possible, even if all cells of the third band are givens.
Maybe Serg or JPF know more.

[eleven]

... ok, there are some, e.g.

Code: Select all

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

Still unlikely for me, that your pattern has unique puzzles.
btw this has a rating of ER 9.0.

[denis_berthier]

I think you're partly right about the first two bands.
I also could generate unique puzzles with your pattern, including another 9.0 one (which makes an unusually high frequency for 9.0):
1.......9.7.....2...8...7.....2.8.......1.......4.....584962371913847265627153984 # 90327 FNTHYG C37/M1.40.1

But it gets harder to generate anything if you add the conditions on first stack to those on the two bands:

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 !
     +-------+-------+-------+
33 givens

I let gsf's program run for 2 hrs on this and I got no (unique) puzzle.
So, it seems the Y pattern is responsible of some obstruction to uniqueness.

[JPF]

So, it seems the Y pattern is responsible of some obstruction to uniqueness.

no problemo:

Code: Select all

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


JPF

[denis_berthier]

After letting gsf's software run longer, I found one unique puzzle with my pattern:
7.......6.4.....8...2...3.....5.4.......6.......7.......4352618.8.6417296..978543 # 191 FNBTH C31; SER = 3.0

It's farther to the "why not" than JPF's:

So, it seems the Y pattern is responsible of some obstruction to uniqueness.

no problemo:

Code: Select all

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


JPF

SER = 2.0
Good. We're coming closer to the "why not" pattern. Is that minimal?
[Edit]: no. It can be reduced to:

Code: Select all

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


[/Edit]

[JPF]

After a quick review, here is a 21 clue puzzle:

Code: Select all

 1 . . | . . . | . . 2
 . 3 . | . . . | . 4 .
 . . 5 | . . . | 3 . .
-------+-------+-------
 . . . | 5 . 3 | . . .
 . . . | . 6 . | . . .
 . . . | 7 . . | . . .
-------+-------+-------
 . . 8 | . 9 4 | . 5 1
 . 4 . | . 8 . | . . 6
 6 . . | . 1 . | . . 9    ED=6.6/1.2/1.2


JPF

[denis_berthier]

After a quick review, here is a 21 clue puzzle:

Code: Select all

 1 . . | . . . | . . 2
 . 3 . | . . . | . 4 .
 . . 5 | . . . | 3 . .
-------+-------+-------
 . . . | 5 . 3 | . . .
 . . . | . 6 . | . . .
 . . . | 7 . . | . . .
-------+-------+-------
 . . 8 | . 9 4 | . 5 1
 . 4 . | . 8 . | . . 6
 6 . . | . 1 . | . . 9    ED=6.6/1.2/1.2


JPF

Great. And it's also a good example for 1-step solutions.

[ghfick]

Both 9.0 puzzles have a 3x3 MSLS that essentially solve the puzzles. One does not see a 3x3 MSLS that often !

[eleven]

Thanks for the hint (now i found it).
The problem with MSLS and Exocet for manual solvers is, that one has to be very eager to solve a puzzle to check for them manually. Different to the (original) SK-loop, which you would find in a minute, if there is one.