## More Homework 5

Everything about Sudoku that doesn't fit in one of the other sections

### More Homework 5

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
JPF
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### Re: More Homework 5

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
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### Re: More Homework 5

JPF wrote: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`

m_b_metcalf
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Location: Berlin

### Re: More Homework 5

m_b_metcalf wrote: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
JPF
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### Re: More Homework 5

JPF wrote: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 |+-------+-------+-------+`
blue

Posts: 967
Joined: 11 March 2013

### Re: More Homework 5

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

Posts: 3067
Joined: 10 February 2008

### Re: More Homework 5

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

m_b_metcalf
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Location: Berlin

### Re: More Homework 5

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
JPF
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### Re: More Homework 5

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
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### Re: More Homework 5

JPF wrote:
m_b_metcalf wrote: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
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Location: Berlin

### Re: More Homework 5

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.`

m_b_metcalf
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### Re: More Homework 5

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
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### Re: More Homework 5

JPF wrote: almost...

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

Mike

m_b_metcalf
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### Re: More Homework 5

And with 4r8c5 you get more symmetry..

JPF
JPF
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### Re: More Homework 5

JPF wrote:
And with 4r8c5 you get more symmetry..

JPF

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

m_b_metcalf
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