The New Sudoku Players' Forum

[Ocean]

Here is a minimal:

Code: Select all

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

Some statistics:

Among the 29 on the list, there are 9 minimals: #1,3,4,9,16,20,26,27,28.
Also 89 of Ruud's 294 are minimals.

Code: Select all

Steps  Number of puzzles
27:    1
26:    4
25:    4
24:    1
23:   10
22:   33
21:   61
20:  208

Code: Select all

[Edit: Same  puzzle. Slightly more pleasant pattern.]
+-------+-------+-------+
| . . . | . 2 9 | . . 7 |
| . . . | 8 . 4 | . 6 5 |
| . . . | 1 . . | 2 8 9 |
+-------+-------+-------+
| . . 1 | . . . | . . 3 |
| . 9 . | . . . | . 2 . |
| 5 . . | . . . | 7 . . |
+-------+-------+-------+
| 9 3 7 | . . 1 | . . . |
| 4 1 . | 9 . 2 | . . . |
| 2 . . | 3 4 . | . . . |
+-------+-------+-------+ 

[vidarino]

Here's a fully minimal 22-stepper:

(Edit: correct puzzle this time... )

Code: Select all

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

By the way, have anyone tried to solve any of these many-steppers manually yet? They are surprisingly hard.

[Ruud]

I could hardly believe it when I discovered this one:

Code: Select all

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

28 rounds of pure misery! Symmetrical! Minimal!

And I know they are extremely tough to solve manually. My solver rates them much higher than normal.

Ruud.

[vidarino]

28 rounds of pure misery! Symmetrical! Minimal!

Wow, that's amazing!

Very tight path, all the way to the end; 2,1,2,1,1,2,2,1,1,2,2,2,1,1,2,1,3,3,1,4,4,1,2,2,5,3,5,3

[ab]

Here's a fully minimal 23-stepper:

Code: Select all

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

Correct me if I'm wrong vidarino, but I think this puzzle needs a hidden pair to solve it. Did you post the wrong one by any chance?

[vidarino]

Correct me if I'm wrong vidarino, but I think this puzzle needs a hidden pair to solve it. Did you post the wrong one by any chance?

Oops, quite correct, it was the wrong puzzle. But I also got the wrong stats, so in reality it was only a 22-stepper. Minimal and symmetric, though. Original post edited. Thanks for pointing out my mistake.

[ab]

Here is a minimal:

This obsession with minimals is misguided. I was playing around with a 15 step puzzle earlier today and found that I could remove a clue or 2 (I can't remember the details) and found to my surprise that it became a 9 or 10 step puzzle. I've been searching for the puzzle again, but seem to have mislaid it. I'm sure someone else can corroborate my anecdote with another example.

[Ocean]

28 rounds of pure misery! Symmetrical! Minimal!

Very impressive!

This obsession with minimals is misguided. I was playing around with a 15 step puzzle earlier today and found that I could remove a clue or 2 (I can't remember the details) and found to my surprise that it became a 9 or 10 step puzzle. I've been searching for the puzzle again, but seem to have mislaid it. I'm sure someone else can corroborate my anecdote with another example.

... I also remember puzzles that needed a swordfish or jellyfish - but after removing some clues, the puzzle was solved easily with only 'singles'! (maybe we should start a thread, similar to this one, for preserving such puzzles... it's a pity they were lost).

[JPF]

28 rounds of pure misery! Symmetrical! Minimal!

Congratulations Ruud !
it's going to be hard to defeat.

We'll try anyway...

On the minimal question, I'm ready to discuss (maybe in a different thread) the strange question :
Can a valid puzzle (A) be "less difficult" to solve than a valid puzzle (B), when (A) is included in (B)

JPF

[ravel]

Can a valid puzzle (A) be "less difficult" to solve than a valid puzzle (B), when (A) is included in (B)

You mean, if a puzzle can become harder by adding a (redundant) clue? I had thought, it must be impossible, but if it can be solved with Vidar's uniqueness trick, maybe, because adding a clue would not allow to use the trick. (Similarly in this thread there are samples, where a technique only can be used when special clues are not given.)

[JPF]

You mean, if a puzzle can become harder by adding a (redundant) clue? I had thought, it must be impossible, but if it can be solved with Vidar's uniqueness trick, maybe, because adding a clue would not allow to use the trick. (Similarly in this thread there are samples, where a technique only can be used when special clues are not given.)

Yes, thanks ; It's exactly what I wanted to say, but now, it's in english...

Some more, very far from Ruud's impressive 28 record :

Code: Select all

21 steps

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

21 steps : (5,2,1,2,3,2,1,3,1,3,1,2,3,1,1,2,5,5,4,4,4)


Code: Select all

20 steps

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


20 steps : (5,3,3,3,1,1,2,2,1,2,2,5,3,5,2,2,4,4,4,1)



Code: Select all

20 steps

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


20 steps : (5,2,1,2,1,1,2,1,1,2,2,2,5,2,2,2,6,9,5,1)


There are not minimal, but who cares ?

JPF

[Pat]

... I also remember puzzles that needed a swordfish or jellyfish - but after removing some clues, the puzzle was solved easily with only 'singles'!

hi Ocean,

you seem to be stating this seriously
- surely you must be joking?

going in the other direction:
take a puzzle which can be solved by "singles",
add some clues and the "singles" are lost and the puzzle needs "fish"

so you're pulling my leg?
am i the only one who took you seriously?

~ Pat

[vidarino]

Regarding puzzles that become harder as you add clues; I assumed that in the process of adding clues you will also change some of the existing ones, making an overall harder puzzle (which only looks similar to the original).

Just adding clues to a singles-only puzzle can not make it harder in any way.

[JPF]

Just adding clues to a singles-only puzzle can not make it harder in any way.

I agree and I don't see why it shouldn't be true for all the puzzles.

JPF

[Ocean]

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.
...

And a 22-Clue 5-Stepper:
...
Who's next?

Ruud.

This one apparently fills a gap, a two-stepper (36 clues, minimal with respect to its full symmetry):

Code: Select all

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

Then the current status for puzzles with some symmetry is (minimum known number of clues for each category):

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1-stepper: 48 clues
2-stepper: 36 clues
3-stepper: 28 clues
4-stepper: 24 clues
5-stepper: 22 clues
6-stepper: 22 clues