The New Sudoku Players' Forum

[tarek]

What........

It is good that you provided the diagram to illustrate my my misconception.....

I now understand what you men by merging them together.......

so back to the solver for some fixes...

[Edit: I have now fixed the problem]

This is a 28-clue 4-stepper Empty centre boxe, rotational & diagonal reflective symmetry ( a 6 in the centre would turn it to a 3 stepper, but that will not please vidar )

Code: Select all

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

Tarek

[Ocean]

Three 22-steppers.

Code: Select all

 Ocean #3 (22 steps)
+-------+-------+-------+
| . . . | . 5 . | 2 4 1 |
| . . . | 9 . . | 6 . . |
| . . . | . 7 1 | . . . |
+-------+-------+-------+
| 9 7 . | . . . | 3 6 . |
| 2 . . | . . . | . . 9 |
| . 1 6 | . . . | . 2 8 |
+-------+-------+-------+
| . . . | 7 1 . | . . . |
| . . 4 | . . 3 | . . . |
| 5 9 7 | . 2 . | . . . |
+-------+-------+-------+


 Ocean #4 (22 steps)
+-------+-------+-------+
| 7 . . | 3 . 8 | . 5 . |
| . 9 . | . . . | . 2 . |
| . . . | 5 . 9 | . . . |
+-------+-------+-------+
| 5 . . | . 6 . | 4 . 7 |
| . . . | 4 . 1 | . . . |
| 3 . 4 | . 7 . | . . 6 |
+-------+-------+-------+
| . . . | 7 . 4 | . . . |
| . 3 . | . . . | . 9 . |
| . 5 . | 2 . 6 | . . 8 |
+-------+-------+-------+


 Ocean #5 (22 steps)
+-------+-------+-------+
| 7 . . | . 2 . | . . . |
| . . . | 6 . . | 5 . 4 |
| . . . | 7 . . | 2 . . |
+-------+-------+-------+
| . . . | 1 . 7 | 9 . . |
| 9 . . | . . . | . . 3 |
| . . 6 | 4 . 2 | . . . |
+-------+-------+-------+
| . . 5 | . . 6 | . . . |
| 8 . 4 | . . 5 | . . . |
| . . . | . 7 . | . . 8 |
+-------+-------+-------+

[vidarino]

A few more 3-steppers, one of which is particularly nice to look at:

Code: Select all

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

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

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


And in the other end of the inferiority scale, two 26-steppers:

Code: Select all

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

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


Vidar

[Ruud]

Heh, this thread has taken a U-turn into another interesting direction.

Here is a 4-Stepper with only 24 clues. And yes, it is minimal symmetric.

Code: Select all

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

And a 22-Clue 5-Stepper:

Code: Select all

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

Who's next?

Ruud.

[ab]

Heh, this thread has taken a U-turn into another interesting direction.


Ruud.

Yeah just when I'm beginning to find my feet with 20 step puzzles:

Code: Select all

96.|...|.34
2..|...|..6
...|47.|...
-----------
..7|8..|...
..8|.5.|3..
...|..2|9..
-----------
...|.93|...
4..|...|..8
65.|...|.93


[tarek]

2 puzzles 28 clues & require only 3 steps:

Code: Select all

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

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

This is a 20-stepper (3,5,1,1,1,1,2,1,1,2,2,2,1,2,5,6,6,8,4,1)

Code: Select all

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

Tarek

[JPF]

A few more 3-steppers, one of which is particularly nice to look at:
.......

Vidarino,
I’m a bit confused…
After the U-turn, do the puzzles have to be minimal and how ?

This one is not :

Code: Select all

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


You can remove r3c8 and r7c2 and get this one :

Code: Select all

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


which is still nice, but :

6 steps : 13,7,11,8,8,7 ; more minimal , but not minimal .

The following one is only 8 steps : 12,9,7,4,5,8,6,5, after removing r1c7,r9c3 & r3c7,r7c3 which is non minimal...


Same thing for the third one : you can remove r1c9,r9c1 & r3c6,r7c4 but it does’nt qualify for the game.
Thanx for your comments.
JPF

[JPF]

Here are 4-steppers “minimal symmetric” but not minimal.

Code: Select all

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


4 steps : 10,15,17,11


Code: Select all

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


4 steps : 13,20,15,6


Code: Select all

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

4 steps : 14,12,19,8


We should try to find really minimal puzzles.

Who's next?

JPF

[vidarino]

Vidarino,
I’m a bit confused…
After the U-turn, do the puzzles have to be minimal and how ?

This one is not :
...

Sorry, I guess I should have been a bit clearer. All the puzzles in question are all-axis (vertically, horizontally and diagonally) symmetric, and minimal as such. But if you "demote" them to 180 degree symmetry, they aren't minimal anymore, quite true.

[Ocean]

Two candidates:

Code: Select all

  Ocean #6 (25 steps)
+-------+-------+-------+
| . . 1 | 2 3 4 | . . . |
| . 5 . | 1 . . | . . . |
| 2 6 . | . . . | . . . |
+-------+-------+-------+
| 7 8 . | . . . | . 2 . |
| . . 9 | 8 . 7 | 3 . . |
| . 2 . | . . . | . 7 5 |
+-------+-------+-------+
| . . . | . . . | . 5 3 |
| . . . | . . 3 | . 8 . |
| . . . | 9 8 5 | 4 . . |
+-------+-------+-------+


  Ocean #7 (23 steps)
+-------+-------+-------+
| . . . | 3 . . | 2 . . |
| . . . | 8 . 7 | . . 4 |
| . . . | . 9 . | 6 . 5 |
+-------+-------+-------+
| 9 3 . | . . . | 8 . . |
| . 7 6 | . . . | 5 4 . |
| . . 4 | . . . | . 3 2 |
+-------+-------+-------+
| 2 . 5 | . 7 . | . . . |
| 1 . . | 4 . 5 | . . . |
| . . 3 | . . 9 | . . . |
+-------+-------+-------+

[Ocean]

These two are both symmetric and minimal sudokus in the ordinary sense (if any clue is removed the sudoku is invalid).

Code: Select all

(Minimal 21-stepper)
+-------+-------+-------+
| 9 . . | . . . | 5 4 2 |
| 2 1 . | . . . | 9 . . |
| . . 4 | . . . | . . 8 |
+-------+-------+-------+
| . . . | 8 4 1 | . . . |
| . . . | . 2 . | . . . |
| . . . | 3 7 6 | . . . |
+-------+-------+-------+
| 4 . . | . . . | 8 . . |
| . . 7 | . . . | . 1 3 |
| 6 2 8 | . . . | . . 7 |
+-------+-------+-------+

(Minimal 20-stepper)
+-------+-------+-------+
| . . . | . . . | 1 . . |
| 4 . . | . . 8 | 7 3 . |
| 2 . 5 | 9 . . | . . . |
+-------+-------+-------+
| 5 . . | . . . | . 6 . |
| . 8 . | . . . | . 2 . |
| . 4 . | . . . | . . 5 |
+-------+-------+-------+
| . . . | . . 7 | 2 . 3 |
| . 5 6 | 4 . . | . . 1 |
| . . 3 | . . . | . . . |
+-------+-------+-------+

[JPF]

These two are both symmetric and minimal sudokus in the ordinary sense (if any clue is removed the sudoku is invalid).

Nice !
one more :

Code: Select all

 (Minimal 20-stepper)


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


JPF

[JPF]

I'd like to make an observation.

It seems to be impossible to find a puzzle starting with singles only, until n cells are known and stopping after, for 70 < n < 81.
Does anybody have an explanation for that ?
or is it not true ?

JPF

[JPF]

For the road :

Code: Select all

 21-stepper


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


21 steps : (3,1,1,1,1,2,3,1,2,1,4,1,1,2,2,4,7,5,7,5,1)
180°- symmetric minimal ; not abs. minimal



and

Code: Select all

4 steps - 27 clues


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


4 steps : (12,16,15,11)


[Jo88]

Nice puzzle Tarek Like it !

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

Solves nicely in http://kinabaloo.com/relax/sudoku.html

Jo