Sudokus with an original rare shape

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

Postby JPF » Sun Dec 16, 2007 1:02 am

TTHsieh wrote:The easiest puzzle of the pattern.
...
9 steps : 111111 - 2222 - 3333333 - 444444 - 55555 - 66666 - 7777777 - 88888888 - 999999999

What does it mean ?

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Postby Ruud » Sun Dec 16, 2007 2:11 am

JPF wrote:What does it mean ?

Steps are counted by collecting all the possible moves (placements in case of singles) at each successive state of the grid. No move may depend on another move in that same step.

The number of steps is an indicator of the narrowness of the solving path. More steps are needed as the solving path narrows.

References:

Low-stepper puzzles
Inferior puzzles
Ulterior puzzles

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Postby JPF » Sun Dec 16, 2007 2:29 am

With the definition of these threads, there are only 6 steps :

Code: Select all
1:  r1c1=2      r2c3=6      r2c7=5      r3c8=6      r4c5=2      r4c9=5     
    r6c1=1      r6c7=3      r7c8=1      r8c7=2      r9c2=2      r9c6=1      r9c9=6     
 
2:  r1c4=1      r1c8=7      r3c3=1      r4c3=4      r5c5=1      r6c5=9     
    r7c1=4      r7c4=3      r9c3=3
     
3:  r1c9=3      r2c5=3      r3c2=3      r3c7=4      r5c4=8      r5c6=3     
    r7c3=5      r8c5=7      r8c9=4
     
4:  r4c6=7      r5c2=9      r5c8=4      r6c6=4      r7c2=7      r8c3=8     
   
5:  r1c3=9      r1c7=8      r2c4=7      r3c1=7      r4c4=6      r4c8=9     
    r6c4=5      r6c8=8      r8c6=5      r9c1=9      r9c7=7
     
6:  r2c1=8      r2c6=9      r3c6=8      r3c9=9      r4c2=8      r6c2=6     
    r7c7=9      r7c9=8      r8c4=9


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Postby TTHsieh » Sun Dec 16, 2007 2:41 am

According to the digits order, The solving path is :
  • digit 1 : r6c1 - r7c8 - r9c6 - r1c4 - r3c3 - r5c5
  • digit 2 : r1c1 - r4c5 - r9c2 - r8c7
  • digit 3 : r6c7 - r7c4 - r5c6 - r2c5 - r9c3 - r3c2 - r1c9
  • digit 4 : r4c3 - r6c6 - r5c8 - r7c1 - r8c9 - r3c7
  • digit 5 : r2c7 - r4c9 - r6c4 - r8c6 - r7c3
  • digit 6 : r2c3 - r4c4 - r6c2 - r9c9 - r3c8
  • digit 7 : r4c6 - r2c4 - r3c1 - r7c2 - r8c5 - r9c7 - r1c8
  • digit 8 : r5c4 - r4c2 - r6c8 - r8c3 - r2c1 - r3c6 - r1c7 - r7c9
  • digit 9 : r1c3 - r2c6 - r3c9 - r5c2 - r6c5 - r4c8 - r9c1 - r8c4 - r7c7
Any move is box hidden single. So the solving path is (without pencilmark):
111111 - 2222 - 3333333 - 444444 - 55555 - 66666 - 7777777 - 88888888 - 999999999

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sharp

Postby Pat » Mon Feb 04, 2008 3:23 pm

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

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Re: sharp

Postby claudiarabia » Sun Feb 10, 2008 2:56 pm

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



I like these diagonal stripes. I reduced the 4 clues in the center from 4 to one:

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

And here another 21clue-sudoku:
Code: Select all
2 . . . 3 . . . 7
. 6 . . . 5 . . .
. . . 8 . . 4 . .
. . 9 . . . . 6 .
7 . . . 4 . . . 3
. 5 . . . . 2 . .
. . 1 . . 2 . . .
. . . 6 . . . 5 .
4 . . . 7 . . . 8
SE 7.3

If you change the middle clue from 4 to 1 you can boost the ER-Rating to 9.0
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re: sharp

Postby Pat » Wed Feb 20, 2008 12:33 pm

claudiarabia wrote:I like these diagonal stripes

here's a similar pattern which won't suit "the patterns game"
as they insist on minimal puzzles --

28 clues

fully-symmetrical

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

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re: 2-4-1-0-

Postby Pat » Wed Feb 20, 2008 1:32 pm

claudiarabia wrote:I like these diagonal stripes. I reduced the 4 clues in the center from 4 to one:
      [ 21 clues ]
Code: Select all
 . . 8 . . . 3 . .
 . . . 9 . 7 . . .
 2 . . . 6 . . . 4
 . 7 . . . . . 1 .
 . . 6 . 2 . 9 . .
 . 9 . . . . . 5 .
 3 . . . 1 . . . 2
 . . . 5 . 8 . . .
 . . 4 . . . 6 . .




beautiful!

and you can even drop the central clue --
ab (2006.Apr.19) wrote:
      [ 20 clues ]

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

      [ -- shift row 3 up to top, shift row 7 down to bottom; likewise with columns -- giving claudiarabia's pattern -- ]
Code: Select all
 . . 6 . . . 5 . .
 . . . 7 . 2 . . .
 2 . . . 4 . . . 6
 . 4 . . . . . 9 .
 . . 1 . . . 3 . .
 . 3 . . . . . 7 .
 4 . . . 2 . . . 1
 . . . 5 . 3 . . .
 . . 8 . . . 9 . .


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Re: re: sharp

Postby m_b_metcalf » Wed Feb 20, 2008 2:53 pm

Pat wrote:here's a similar pattern which won't suit "the patterns game"
as they insist on minimal puzzles --

28 clues

fully-symmetrical

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



Code: Select all
 .  6 .  .  .  .  .  7 .
 9 .  8 .  .  .  2 .  6
 .  7 .  9 .  8 .  1 .
 .  .  3 .  1 .  6 .  .
 .  .  .  8 .  4 .  .  .
 .  .  1 .  9 .  4 .  .
 .  8 .  2 .  3 .  6 .
 2 .  5 .  .  .  7 .  3
 .  1 .  .  .  .  .  2 .   Minimal, SE 2.3

They're few and far between, but do exist.

Regards,

Mike Metcalf
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Offset symmetry

Postby m_b_metcalf » Wed Feb 20, 2008 4:54 pm

We usually define symmetry with respect to the 9 x 9 grid and sometimes within that a 7 x 7 subset. The cell r5c5 is always the centre. There are, of course, patterns which have a symmetry within an offset 8 x 8 grid, such as
Code: Select all
 . 3 . . 6 1 8 . .
 . . . . . . . 2 .
 9 . . . . . . 4 .
 4 . . 5 9 . . . .
 . . . 8 3 . . 6 .
 2 . . . . . . 7 .
 7 . . . . . . . .
 . 5 4 1 . . 3 . .
 . . . . . . . . .  Minimal, 20 givens, SE 2.3

which has this restricted 180 degree rotational symmetry with no central cell, and
Code: Select all
 2 1 5 . . 4 8 6 .
 3 . . . . . . 1 .
 6 . . . . . . 5 .
 . . . 6 1 . . . .
 . . . 3 9 . . . .
 7 . . . . . . 2 .
 1 . . . . . . 8 .
 4 6 8 . . 5 3 7 .
 . . . . . . . . . Minimal, 24 givens, SE 5.6

with 90 degree symmetry.

Just for fun.

Regards,

Mike Metcalf
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Postby JPF » Thu Feb 21, 2008 12:08 am

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

minimal, ER=8.9

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Postby JPF » Thu Feb 21, 2008 12:35 am

m_b_metcalf wrote:We usually define symmetry with respect to the 9 x 9 grid and sometimes within that a 7 x 7 subset. The cell r5c5 is always the centre. There are, of course, patterns which have a symmetry within an offset 8 x 8 grid, such as...

There are similar ideas here and here.

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Postby m_b_metcalf » Thu Feb 21, 2008 9:46 pm

JPF wrote:
m_b_metcalf wrote:We usually define symmetry with respect to the 9 x 9 grid and sometimes within that a 7 x 7 subset. The cell r5c5 is always the centre. There are, of course, patterns which have a symmetry within an offset 8 x 8 grid, such as...

There are similar ideas here and here.

Thanks for reminding me. Here's another.
Code: Select all
 1 . . 4 3 . . 9 .
 . . . 9 5 . . . .
 . 6 . . . . 2 . .
 . . . . . . . . .
 8 . . . . . . 4 .
 2 3 . . . . 7 1 .
 . 1 . 7 9 . 6 . .
 4 . . 3 8 . . 5 .
 . . . . . . . . .  Minimal, SE 7.2, small pearl, 22 givens

Regards,

Mike Metcalf
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Postby JPF » Fri Feb 22, 2008 12:24 am

20 clues, minimal :
Code: Select all
 . 1 2 . . 3 4 . .
 5 . . . . . . 6 .
 7 . . . . . . 8 .
 . . . 3 8 . . . .
 . . . 2 5 . . . .
 6 . . . . . . 1 .
 1 . . . . . . 5 .
 . 9 3 . . 7 2 . .
 . . . . . . . . .


24 clues, minimal :
Code: Select all
 . . 1 2 3 4 . . .
 . 5 . . . . 6 . .
 7 . . . . . . 1 .
 2 . . 1 7 . . 6 .
 6 . . 5 8 . . 9 .
 1 . . . . . . 3 .
 . 2 . . . . 5 . .
 . . 8 3 1 2 . . .
 . . . . . . . . .

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Postby m_b_metcalf » Fri Feb 22, 2008 4:00 am

Code: Select all
 7 . . 1 . . 9 . .
 . 8 . . 4 . . 6 .
 . . 1 . . 3 . . .
 9 . . . . . 1 . .
 . 2 . . 6 . . 5 .
 . . 8 . . . . . .
 3 . . 9 . . . . .
 . 4 . . 5 . . 8 .
 . . . . . . . . .   SE 8.4, minimal, 19 clues.

Code: Select all
 8 . . 5 . . 3 . .
 . 7 . . 4 . . 6 .
 . . 1 . . 9 . . .
 3 . . 1 . . 5 . .
 . 9 . . . . . 7 .
 . . 2 . . . . . .
 5 . . 3 . . 8 . .
 . 4 . . 6 . . 9 .
 . . . . . . . . . SE 9.2/9.2 Pearl, minimal, 20 clues

Code: Select all
   
 1 . . 2 . . 3 . .
 . 9 . . 6 . . 5 .
 . . 2 . . 8 . . .
 3 . . 4 . . 2 . .
 . 6 . . . . . 7 .
 . . 5 . . . . . .
 8 . . 3 . . 4 . .
 . 7 . . 9 . . 6 .
 . . . . . . . . . SE 9.3, minimal, 20 clues

Regards,

Mike Metcalf
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