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

tarek

Posts: 2737
Joined: 05 January 2006

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 | +-------+-------+-------+ `
Ocean

Posts: 442
Joined: 29 August 2005

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
vidarino

Posts: 295
Joined: 02 January 2006

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.
Ruud

Posts: 664
Joined: 28 October 2005

Ruud wrote: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.|...|.342..|...|..6...|47.|...-----------..7|8..|.....8|.5.|3.....|..2|9..-----------...|.93|...4..|...|..865.|...|.93`
ab

Posts: 451
Joined: 06 September 2005

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

tarek

Posts: 2737
Joined: 05 January 2006

vidarino wrote: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.
JPF
JPF
2017 Supporter

Posts: 3754
Joined: 06 December 2005
Location: Paris, France

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 . | . . . | . . 74 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 . 34 steps : 14,12,19,8`

We should try to find really minimal puzzles.

Who's next?

JPF
JPF
2017 Supporter

Posts: 3754
Joined: 06 December 2005
Location: Paris, France

JPF wrote: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.
vidarino

Posts: 295
Joined: 02 January 2006

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

Posts: 442
Joined: 29 August 2005

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 | . . . | . . . | +-------+-------+-------+ `
Ocean

Posts: 442
Joined: 29 August 2005

Ocean wrote: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
2017 Supporter

Posts: 3754
Joined: 06 December 2005
Location: Paris, France

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
2017 Supporter

Posts: 3754
Joined: 06 December 2005
Location: Paris, France

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)`
JPF
2017 Supporter

Posts: 3754
Joined: 06 December 2005
Location: Paris, France

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
Jo88

Posts: 12
Joined: 22 March 2006

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