The New Sudoku Players' Forum

[JPF]

n=3

I havn't explored the minimality of the n=3 puzzles

I got more than 1000 minimal puzzles.
I stopped the search.
Here is an example:

Code: Select all

+---+---+---+
|123|...|...|
|4.5|...|...|
|678|...|...|
+---+---+---+
|...|857|..3|
|...|9.3|...|
|7..|216|...|
+---+---+---+
|...|...|156|
|...|...|4.7|
|...|5..|392|
+---+---+---+  SE=7.2


Finding minimal puzzles when 4<=n<=8 seems not too difficult.
Of course, Mauricio's lemma helps to place the clues.
Here is one (out of 4000+) for n=8 having main diagonal and anti-diagonal symmetries which btw implies 180° rotational symmetry

Code: Select all

+---+---+---+
|123|4..|..5|
|4.6|...|...|
|578|...|4..|
+---+---+---+
|2..|594|...|
|...|1.2|...|
|...|678|..2|
+---+---+---+
|..4|...|253|
|...|...|1.7|
|7..|..5|864|
+---+---+---+  SE=9.0


I will have a look at n=9+; it seems more challenging!

JPF

[coloin]

Code: Select all

+---+---+---+
|123|...|...|
|4.5|...|...|
|678|...|...|
+---+---+---+
|...|857|..3|
|...|9.3|...|
|7..|216|...|
+---+---+---+
|...|...|156|
|...|...|4.7|
|...|5..|392|
+---+---+---+  SE=7.2

Indeed you only need one ... i hadnt thought that there could be ...

Code: Select all

+---+---+---+
|123|4..|..5|
|4.6|...|...|
|578|...|4..|
+---+---+---+
|2..|594|...|
|...|1.2|...|
|...|678|..2|
+---+---+---+
|..4|...|253|
|...|...|1.7|
|7..|..5|864|
+---+---+---+  SE=9.0


and the highest rating for good measure ! It seems that some of these puzzles have neat solving properties

[m_b_metcalf]

I will have a look at n=9+; it seems more challenging!

It was:

Code: Select all

 2 8 3 7 . . . . 6
 5 . 7 . . . . . .
 9 1 6 3 . . 8 . .
 1 . . 5 3 8 . . .
 . . . 1 . 9 . . .
 . . . 2 6 7 . . 9
 . . 2 . . . 6 9 1
 . . . . . . 3 . 5
 6 . . . . 3 7 2 8   ED=7.2/1.0/1.0, n = 9



[JPF]

well done Mike!

I give up: my approach is not very effective for puzzles with a large number of clues.
I also have another homework to do...

JPF

[m_b_metcalf]

well done Mike!

Well, thanks too for your seed pattern!

M

[Serg]

Hi, Marek!

Code: Select all

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

This pattern is not minimal.

Good point! (I spent some time to understand your proof.) What is WLOG and PC?

Serg

[marek stefanik]

Hi Serg,

WLOG means 'without loss of generality' (if a is given in c6 instead, you can just swap the two columns).
PC means 'pointing candidates'.

Marek

[marek stefanik]

I think there maybe a limitation of 3 on the rows/columns as well

Sadly that's not the case, I found a minimal subpuzzle (3352 solutions) with that pattern:
1236.87.44.5......678.........837......9.5......216.........165......4.7......923
(I haven't checked if it can produce minimal puzzles, though)

Marek

[m_b_metcalf]

.... but I do know that there is some way to go with n

So, how far is there still to go?

[coloin]

n=12

[m_b_metcalf]

n=12

Gasp! I give up. This puzzle has 12 extra clues, all of which are minimal, but those in B1B5B9 are not

Code: Select all

 8 3 9 . . 2 . . .
 4 . 5 . . . 9 . .
 2 6 7 . . . . . .
 7 8 . 3 6 9 . . .
 . . 3 2 . 4 . . .
 . . 2 7 8 5 . 3 .
 . . . . . . 3 9 8
 9 . 8 5 . . 2 . 6
 . 2 . 9 . . 1 7 5    ED=4.2/1.0/1.0

No. of givens =  36

[coloin]

Am on vacation ( and my files are at home ) and quietly trying to repeat the exercise ….
Generating the n=10 is not a problem … eventually a n=11 is produced …
I am persevering to get a n=12 …. Knowing that it is possible is reassuring…. and a good question might be whether I will find the same puzzle ….

[coloin]

Code: Select all

+-----+-----+-----+
|1 2 3|. . 5|4 . 6|
|4 . 5|. . .|. . .|
|6 7 8|. . 2|. . 5|
+-----+-----+-----+
|. . .|5 2 9|6 . 4|
|. . .|7 . 6|. . .|
|2 . .|1 3 4|. . .|
+-----+-----+-----+
|7 . .|. . .|2 6 1|
|. . .|. . .|5 . 7|
|5 . .|2 . 7|8 4 3|
+-----+-----+-----+      n=12     36 clues minimal

Finally one was found ..... not sure how all the UA fit in ....

[m_b_metcalf]

Code: Select all

    n=12     36 clues minimal

Finally one was found ..... not sure how all the UA fit in ....

Brilliant! And here's a list of the UA4s:

Code: Select all

1=H r1 c1 r2 c2
2=V
  1  2  1  3  4
  1  1  1  2  7
  1  1  3  2  6
  1  2  3  3  9
  1  1  4  2  9
  1  2  6  3  8
  1  4  1  6  5
  1  5  1  6  9
  1  4  3  6  7
  1  4  6  6  9
  1  8  1  9  7
  1  7  2  9  9
  2  2  1  5  2
  2  3  2  4  3
  2  1  7  4  9


Mike

[m_b_metcalf]

And I think your puzzle has a cousin:

Code: Select all

 1 2 3 . . 4 5 . 6
 5 . 4 . . . . . .
 6 7 8 . . 2 . . 4
 . . . 3 1 9 6 . 5
 . . . 7 . 6 . . .
 3 . . 4 2 5 . . .
 7 . . . . . 2 6 1
 . . . . . . 4 . 7      n=12, all minimal
 4 . . 2 . 7 8 5 3      ED=1.5/1.0/1.0