The New Sudoku Players' Forum

[JPF]

Congratulations to blue for his homeworks 3 and 4!

Here is a puzzle:

Code: Select all

+-------+-------+-------+
| 1 . . | . . . | x x x |
| . 2 . | . x . | x x x |
| . . 3 | . . . | x x x |
+-------+-------+-------+
| . . . | 1 . . | . . . |
| . x . | . 2 . | . x . |
| . . . | . . 3 | . . . |
+-------+-------+-------+
| x x x | . . . | 1 . . |
| x x x | . x . | . 2 . |
| x x x | . . . | . . 3 |
+-------+-------+-------+


Rules :
The puzzles must be minimal
B1B5B9 must stay as they are.
one clue has to be in the center of each box B2B4B6B8
Boxes B3B7 are free.


Question A : what is the lowest number of clues?
Question B : what is the greatest number of clues?
Question C : any puzzles with symmetry of their pattern?
Question D : any puzzles with symmetry of their pattern and digits?

example questions A/B:

Code: Select all

+-------+-------+-------+
| 1 . . | . . . | 2 6 5 |
| . 2 . | . 6 . | . . 7 |
| . . 3 | . . . | 9 4 . |
+-------+-------+-------+
| . . . | 1 . . | . . . |
| . 4 . | . 2 . | . 9 . |
| . . . | . . 3 | . . . |
+-------+-------+-------+
| . . 5 | . . . | 1 . . |
| 4 6 1 | . 7 . | . 2 . |
| 9 7 . | . . . | . . 3 |
+-------+-------+-------+   25C


JPF

[m_b_metcalf]

A:

Code: Select all

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


C:

Code: Select all

 1 . . . . . 2 6 .
 . 2 . . 6 . . 1 7
 . . 3 . . . . . 8
 . . . 1 . . . . .
 . 4 . . 2 . . 9 .
 . . . . . 3 . . .
 2 . . . . . 1 . .
 4 6 . . 7 . . 2 .
 . 7 8 . . . . . 3  23C, crossword symmetry

Mike

[m_b_metcalf]

Question D : any puzzles with symmetry of their pattern and digits?

Could you please clarify D? In the following, the diagonal values are only partially symmetric, but I don't anyway see how "B1B5B9 must stay as they are." is consistent with symmetry

Code: Select all

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

[JPF]

Could you please clarify D? In the following, the diagonal values are only partially symmetric, but I don't anyway see how "B1B5B9 must stay as they are." is consistent with symmetry

Could be something like that (diagonal symmetry):

Code: Select all

+-------+-------+-------+
| 1 . . | . . . | a c . |
| . 2 . | . 8 . | b d f |
| . . 3 | . . . | . e g |
+-------+-------+-------+
| . . . | 1 . . | . . . |
| . 8 . | . 2 . | . 9 . |
| . . . | . . 3 | . . . |
+-------+-------+-------+
| a b . | . . . | 1 . . |
| c d e | . 9 . | . 2 . |
| . f g | . . . | . . 3 |
+-------+-------+-------+


JPF

[blue]

Question D : any puzzles with symmetry of their pattern and digits?

Yes.

Code: Select all

+-------+-------+-------+
| 1 . . | . . . | . 4 . |
| . 2 . | . 8 . | 6 . 7 |
| . . 3 | . . . | . 9 . |
+-------+-------+-------+
| . . . | 1 . . | . . . |
| . 8 . | . 2 . | . 5 . |
| . . . | . . 3 | . . . |
+-------+-------+-------+
| . . 6 | . . . | 1 . . |
| . . 9 | . 5 . | . 2 . |
| 4 7 2 | . . . | . . 3 |
+-------+-------+-------+   22C

The automorphism is: reflect across the diagonal, swap bands 1&3 and stacks 1&3, and remap symbols (46)(58)(79).

This morph shows the symmetry as a "diagonal reflection" symmetry.

Code: Select all

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

[eleven]

Nice one to solve, too. For that a digit symmetry on the other diagonal can be simply seen after c79->97, r79->97.

[m_b_metcalf]

A

Code: Select all

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


B

Code: Select all

 1 . . . . . 8 3 4
 . 2 . . 7 . 5 . 1
 . . 3 . . . . 6 7
 . . . 1 . . . . .
 . 6 . . 2 . . 4 .
 . . . . . 3 . . .
 8 7 6 . . . 1 . .
 3 . 4 . 8 . . 2 .
 . 1 2 . . . . . 3  27C

Mike

[JPF]

A

Code: Select all

+-------+-------+-------+
| 1 . . | . . . | 4 . . |
| . 2 . | . 7 . | . 6 9 |
| . . 3 | . . . | 8 . . |
+-------+-------+-------+
| . . . | 1 . . | . . . |
| . 9 . | . 2 . | . 5 . |
| . . . | . . 3 | . . . |
+-------+-------+-------+
| . . 4 | . . . | 1 . . |
| . 6 . | . 5 . | . 2 . |
| . . . | . . . | . . 3 |
+-------+-------+-------+   19C


JPF

[m_b_metcalf]

A+C:

Code: Select all

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

B+C:

Code: Select all

 1 . . . . . 8 3 .
 . 2 . . 7 . 5 . 1
 . . 3 . . . 2 6 7
 . . . 1 . . . . .
 . 6 . . 2 . . 4 .
 . . . . . 3 . . .
 8 7 6 . . . 1 . .
 3 . 4 . 8 . . 2 .
 . 1 2 . . . . . 3   27C, diagonal and anti-diagonal symmetry

[m_b_metcalf]

Could you please clarify D? In the following, the diagonal values are only partially symmetric, but I don't anyway see how "B1B5B9 must stay as they are." is consistent with symmetry

Could be something like that (diagonal symmetry):

Code: Select all

+-------+-------+-------+
| 1 . . | . . . | a c . |
| . 2 . | . 8 . | b d f |
| . . 3 | . . . | . e g |
+-------+-------+-------+
| . . . | 1 . . | . . . |
| . 8 . | . 2 . | . 9 . |
| . . . | . . 3 | . . . |
+-------+-------+-------+
| a b . | . . . | 1 . . |
| c d e | . 9 . | . 2 . |
| . f g | . . . | . . 3 |
+-------+-------+-------+


My best effort so far:

Code: Select all

 1 . . . . . 2 3 .
 . 2 . . 3 . 4 . 6
 . . 3 . . . 5 7 8
 . . . 1 . . . . .
 . 3 . . 2 . . 9 .
 . . . . . 3 . . .
 2 4 . . . . 1 . .
 3 . 7 . 9 . . 2 .
 5 6 8 . . . . . 3  126 solutions

[m_b_metcalf]

D:

Code: Select all

 1 . . . . . 2 3 .
 . 2 . . 3 . 4 . 6
 . . 3 . . . 5 7 8
 . . . 1 . . . . .
 . 7 . . 2 . . 4 .
 . . . . . 3 . . .
 2 4 . . . . 1 . .
 3 . 7 . 6 . . 2 .
 5 6 8 . . . . . 3      4 solutions, 2 non-overlapping UA6s.

[JPF]

D

Code: Select all

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


JPF

[m_b_metcalf]

almost...

Yes. And with 4r8c5 you get more symmetry, but 6 solutions.

Mike

[JPF]

And with 4r8c5 you get more symmetry..

JPF

[m_b_metcalf]

And with 4r8c5 you get more symmetry..

JPF

10-5 = 5; 10-4 = 6.