Sudokus with an original rare shape

Everything about Sudoku that doesn't fit in one of the other sections
TTHsieh wrote:The easiest puzzle of the pattern.
...
9 steps : 111111 - 2222 - 3333333 - 444444 - 55555 - 66666 - 7777777 - 88888888 - 999999999

What does it mean ?

JPF
JPF
2017 Supporter

Posts: 3751
Joined: 06 December 2005
Location: Paris, France

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

Ruud
Ruud

Posts: 664
Joined: 28 October 2005

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 `

JPF
JPF
2017 Supporter

Posts: 3751
Joined: 06 December 2005
Location: Paris, France

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

TTHsieh
TTHsieh

Posts: 1390
Joined: 13 July 2007

sharp

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 . . `

Pat

Posts: 3295
Joined: 18 July 2005

Re: sharp

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
claudiarabia

Posts: 288
Joined: 14 May 2006

re: sharp

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 . `

Pat

Posts: 3295
Joined: 18 July 2005

re: 2-4-1-0-

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 . . `

Pat

Posts: 3295
Joined: 18 July 2005

Re: re: sharp

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

m_b_metcalf
2017 Supporter

Posts: 8095
Joined: 15 May 2006
Location: Berlin

Offset symmetry

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

m_b_metcalf
2017 Supporter

Posts: 8095
Joined: 15 May 2006
Location: Berlin

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

JPF
JPF
2017 Supporter

Posts: 3751
Joined: 06 December 2005
Location: Paris, France

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.

JPF
JPF
2017 Supporter

Posts: 3751
Joined: 06 December 2005
Location: Paris, France

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

m_b_metcalf
2017 Supporter

Posts: 8095
Joined: 15 May 2006
Location: Berlin

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 . . . . . . . . . . . .`

JPF
JPF
2017 Supporter

Posts: 3751
Joined: 06 December 2005
Location: Paris, France

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

m_b_metcalf
2017 Supporter

Posts: 8095
Joined: 15 May 2006
Location: Berlin

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