The New Sudoku Players' Forum

[JPF]

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

What does it mean ?

JPF

[Ruud]

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

[JPF]

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

[TTHsieh]

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

[Pat]

24 clues

fully-symmetrical

pure X-wing

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 . .



[claudiarabia]

24 clues

fully-symmetrical

pure X-wing

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

[Pat]

I like these diagonal stripes

glad you liked it!
plenty more ( at all levels of difficulty ) in "the patterns game"

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]

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 --

[ 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 . .



[m_b_metcalf]

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]

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

[JPF]

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]

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

[m_b_metcalf]

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

[JPF]

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

[m_b_metcalf]

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