Low-stepper Puzzles.

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

Postby JPF » Thu Jul 13, 2006 9:07 pm

3-stepper, 25 clues, no symmetry :

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



2-stepper, 28 clues, no symmetry :

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


JPF
JPF
2017 Supporter
 
Posts: 3752
Joined: 06 December 2005
Location: Paris, France

Postby Ocean » Fri Jul 14, 2006 12:43 am

Nice improvements, JPF! Again pushing the limits at the low end!
Ocean
 
Posts: 442
Joined: 29 August 2005

Postby JPF » Fri Jul 14, 2006 5:36 pm

An improvement (1-stepper, 180-degree rotational symmetry)

Code: Select all
Type V , 1 step, 39 clues


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


Some more :

Code: Select all
Type VI, 1 step, 40 clues

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


Code: Select all
Type VII, 1 step, 39 clues

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


JPF
JPF
2017 Supporter
 
Posts: 3752
Joined: 06 December 2005
Location: Paris, France

Postby JPF » Sat Jul 15, 2006 7:29 am

improvements of the night :

Code: Select all
Type VII, 2 steps, 32 clues

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


Code: Select all
Type VI, 2 steps, 31 clues

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


Code: Select all
Type V, 2 steps, 31 clues

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


Code: Select all
Type V, 1 step, 38 clues

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


Code: Select all
Type VI, 1 step, 39 clues

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


Code: Select all

Type VI, 1 step, 38 clues

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



Ocean, Thanks for doing all this clerical work !

JPF
JPF
2017 Supporter
 
Posts: 3752
Joined: 06 December 2005
Location: Paris, France

Postby Ocean » Sun Jul 16, 2006 5:06 am

JPF wrote:improvements of the night :
Twelve improvements in a few days. Impressive series!
Ocean
 
Posts: 442
Joined: 29 August 2005

Postby JPF » Sun Jul 16, 2006 6:14 pm

Ocean wrote:Impressive series!
Thanks Ocean,

One more for the road :
Code: Select all
Type VII, 1 step, 38 clues


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


JPF
JPF
2017 Supporter
 
Posts: 3752
Joined: 06 December 2005
Location: Paris, France

Postby JPF » Mon Jul 17, 2006 3:19 pm

Some last improvements for the 1-steppers.
Now, for every type of symmetries, the minimum number of clues is less or equal to 40.

Code: Select all
Type I, 1 step, 40 clues


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



Code: Select all
Type III, 1 step, 40 clues


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



Code: Select all
Type IV, 1 step, 39 clues


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



Here is an improvement for a 2-stepper :
Code: Select all
Type III, 2 steps, 32 clues


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


As mentioned earlier, the S-minimality of these puzzles has not been tested, as I still don't have a program to do it !
(except for s = 0 and s = 5 ).

I'll work on it.

JPF
JPF
2017 Supporter
 
Posts: 3752
Joined: 06 December 2005
Location: Paris, France

Postby Ocean » Tue Jul 18, 2006 7:49 am

JPF wrote:Some last improvements for the 1-steppers.
Now, for every type of symmetries, the minimum number of clues is less or equal to 40.

Nice improvements again!
JPF wrote:As mentioned earlier, the S-minimality of these puzzles has not been tested, as I still don't have a program to do it !
(except for s = 0 and s = 5 ).

I'll work on it.

This is no problem, as every submitted puzzle is run through gsf's program, which tells whether the puzzle is minimal, s-minimal or not minimal, in addition to counting the steps and verifying the symmetry type. For those categories where we have non-minimal puzzles with fewer clues than the s-minimals both entries are kept in the table of 'lowest known'.

And a general comment:
This thread is also meant to be a collection of puzzles with various symmetries that require 1 to 8 single-steps. New contributions that fit into this category are welcomed! It's not necessary to beat the absolute best every time - as this would be hard for newcomers (and getting harder for every improvement). The point is to beat your personal best in categories where you already submitted puzzles.
Ocean
 
Posts: 442
Joined: 29 August 2005

Postby gsf » Wed Jul 19, 2006 6:46 am

Ocean wrote:
gsf wrote:I just set off two background processes with a new sort that should keep
generated file sizes in the Kb instead of Gb, one for inferior and one for
ulterior (another thread). They are set to reap the entire step range. Will
get back in a week or so.


Looking forward to see the results from these runs.


here is the latest table of the progress for min # clues for each step count
it includes posts to this list and gordon's 17 and 18 collections
Code: Select all
|||||1||2||3||4||5||6||7||8||9|10|11|12|13|14|15|16|17|18|19|20|21|22|23|24|25|26|27|28|29|30|31
||O|35|28|25|23|22|18|18|17|17|17|17|17|17|17|17|17|17|17|17|17|17|17|17|17|17|17|17|18|18|18|18
||I|40|32|28|28|24|24|24|20|24|24|24|24|24|24|25|28|28|28|28|21|21|21|24|24|24|20|24|--|--|--|--
|II|40|32|24|24|21|20|20|20|24|24|24|24|24|24|24|24|24|24|28|24|20|24|--|28|28|--|--|--|--|--|--
III|40|32|28|25|22|22|22|22|24|24|24|24|24|24|24|24|26|24|24|26|24|24|--|24|--|--|--|--|--|--|--
|IV|39|32|26|26|24|20|20|20|24|24|23|23|24|22|24|24|24|24|25|23|19|24|22|24|26|--|--|--|--|--|--
||V|38|31|26|24|20|20|18|18|22|22|21|22|21|22|22|22|22|22|22|22|20|22|19|24|19|23|25|20|--|--|--
|VI|38|31|27|24|23|23|22|20|22|22|22|22|22|22|21|22|22|21|22|22|22|24|23|24|23|24|--|--|--|--|--
VII|38|32|25|23|22|22|18|18|18|18|18|18|18|18|18|18|18|18|18|18|18|18|18|22|21|23|24|23|--|--|--


Ocean wrote:Interesting statistics. Also noticed the jump between 8 and 9, indicating that <=8 has been attacked specifically, while >=9 follows a more uniform statistical pattern. When special collections are investigated, the general statistics is disturbed.
For instance, these two from gfroyle's 17s would lead to new anomalies:

Code: Select all
VII,13,17,M,000000001000000023004005000000100000000040600006000405000076000010000000320008000,gfroyle/Red_Ed
VII,16,17,M,000000001000000023004005000000100000000040600006000405000076000010000000820009000,gfroyle/Red_Ed

How long time would it take to find those two by ordinary search?

my random symmetric minimal generator rarely strays below 22

here are three low steppers from my holiday (the machine worked, I didn't)
Code: Select all
# inferior VII 2 steps 32 clues antidiagonal symmetric minimal

. . 9  4 1 .  . 2 5
. . 8  2 . .  . 7 4
2 4 .  9 . .  . . 3

1 3 7  . . .  . . .
6 . .  . . .  4 5 .
. . .  . . .  1 . 9

. . .  . 3 6  . . .
4 6 .  . 5 .  . . 1
7 2 5  . . 4  . 6 .

# inferior IV 3 steps 26 clues diagonal and antidiagonal symmetric minimal

3 . .  . . 8  6 . .
. 4 .  . 1 5  . . .
. . .  . . 2  9 . 4

. . .  . . .  3 8 5
. 3 .  . . .  . 9 .
8 6 7  . . .  . . .

5 . 6  7 . .  . . .
. . .  2 9 .  . 7 .
. . 8  4 . .  . . 2

# inferior VII 4 steps 23 clues diagonal symmetric minimal

. 1 7  . . .  . . 2
. 9 .  . . 8  . . .
. . 2  6 . 4  . . .

. . .  . 9 .  4 1 .
5 . .  . . 3  . . .
. . .  2 . .  6 . .

8 . .  . . .  3 . 5
. . .  . . .  . 6 8
2 . 1  . 6 .  . . .
gsf
2014 Supporter
 
Posts: 7306
Joined: 21 September 2005
Location: NJ USA

Postby JPF » Wed Jul 19, 2006 1:26 pm

Ocean wrote:And a general comment:
This thread is also meant to be a collection of puzzles with various symmetries that require 1 to 8 single-steps. New contributions that fit into this category are welcomed! It's not necessary to beat the absolute best every time - as this would be hard for newcomers (and getting harder for every improvement). The point is to beat your personal best in categories where you already submitted puzzles.

:idea:I understand your point :
Here are some improvements beating my personal...
... and the absolute best at the same time.

Code: Select all
Type IV, 2 steps, 31 clues


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


Code: Select all
Type VII, 2 steps, 30 clues


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


JPF
JPF
2017 Supporter
 
Posts: 3752
Joined: 06 December 2005
Location: Paris, France

Postby Ocean » Thu Jul 20, 2006 12:20 am

gsf wrote:here are three low steppers from my holiday (the machine worked, I didn't)
Thanks! The four-stepper with 23 clues (Type VII symmetry) is also the lowest number of clues we have for a symmetrical four-stepper! And it's symmetrically minimal.
JPF wrote:I understand your point :
Here are some improvements beating my personal...
... and the absolute best at the same time.
The point was mainly to encourage new potential submitters. But of course I appreciate it every time an absolute best is beaten. The 30-clues two-stepper (type VII symmetry) is also the lowest number of clues we have for a symmetrical two-stepper! Thanks again!
Ocean
 
Posts: 442
Joined: 29 August 2005

Postby JPF » Tue Jul 25, 2006 7:03 am

New improvement .

1 step, 34 clues, no symmetry

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


JPF
JPF
2017 Supporter
 
Posts: 3752
Joined: 06 December 2005
Location: Paris, France

Postby Ocean » Fri Sep 22, 2006 5:35 pm

A new improvement:
Code: Select all
#Type I, 7 steps, 21 clues, Minimal.
 *-----------*
 |...|1.2|...|
 |.1.|...|.3.|
 |..4|.5.|6..|
 |---+---+---|
 |3..|...|..2|
 |..5|.7.|8..|
 |9..|...|..1|
 |---+---+---|
 |..8|.4.|5..|
 |.2.|...|.6.|
 |...|5.8|...|
 *-----------*
Ocean
 
Posts: 442
Joined: 29 August 2005

Postby Ocean » Thu Oct 05, 2006 5:13 pm

#
Code: Select all
# Type IV, 8 steps, 19 clues, Minimal.
 *-----------*
 |...|..1|.2.|
 |.3.|...|..1|
 |..4|.5.|...|
 |---+---+---|
 |...|4..|..6|
 |..7|.8.|4..|
 |2..|..5|...|
 |---+---+---|
 |...|.7.|2..|
 |1..|...|.5.|
 |.6.|3..|...|
 *-----------*

#
Ocean
 
Posts: 442
Joined: 29 August 2005

Postby Ocean » Sat Oct 14, 2006 10:49 pm

Two improvements for puzzles with double diagonal symmetry:
Code: Select all
# Type IV, 7 steps, 19 clues, Minimal.
 *-----------*
 |...|..1|.2.|
 |.3.|...|..4|
 |..4|.5.|...|
 |---+---+---|
 |...|3..|..6|
 |..5|.7.|3..|
 |7..|..2|...|
 |---+---+---|
 |...|.6.|8..|
 |5..|...|.7.|
 |.6.|4..|...|
 *-----------*
#
# Type IV, 6 steps, 19 clues, Minimal.
 *-----------*
 |...|..1|.2.|
 |.3.|...|..4|
 |..1|.5.|...|
 |---+---+---|
 |...|6..|..3|
 |..7|.3.|5..|
 |5..|..2|...|
 |---+---+---|
 |...|.7.|1..|
 |8..|...|.7.|
 |.6.|2..|...|
 *-----------*

The latter is also breaking a record: lowest number of clues for a symmetric 6-stepper.
Ocean
 
Posts: 442
Joined: 29 August 2005

PreviousNext

Return to General