Everything about Sudoku that doesn't fit in one of the other sections
Here is a minimal:

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`  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.

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`Steps  Number of puzzles27:    126:    425:    424:    123:   1022:   3321:   6120:  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 . | . . . | +-------+-------+-------+  `
Ocean

Posts: 442
Joined: 29 August 2005

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.
Last edited by vidarino on Wed Mar 29, 2006 8:06 pm, edited 1 time in total.
vidarino

Posts: 295
Joined: 02 January 2006

I could hardly believe it when I discovered this one:

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`. . 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.
Ruud

Posts: 664
Joined: 28 October 2005

Ruud wrote: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
vidarino

Posts: 295
Joined: 02 January 2006

vidarino wrote: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?
ab

Posts: 451
Joined: 06 September 2005

ab wrote: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.
vidarino

Posts: 295
Joined: 02 January 2006

Ocean wrote: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.
ab

Posts: 451
Joined: 06 September 2005

Ruud wrote:28 rounds of pure misery! Symmetrical! Minimal!
Very impressive!
ab wrote: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).
Ocean

Posts: 442
Joined: 29 August 2005

Ruud wrote: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
JPF
2017 Supporter

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Joined: 06 December 2005
Location: Paris, France

JPF wrote: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.)
ravel

Posts: 998
Joined: 21 February 2006

ravel wrote: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 :

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`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)`

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`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 | . 6 720 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
JPF
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Location: Paris, France

### ?? less clues - easier to solve ??

Ocean wrote:... 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

Pat

Posts: 3641
Joined: 18 July 2005

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.
vidarino

Posts: 295
Joined: 02 January 2006

### typo

vidarino wrote:
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
JPF
2017 Supporter

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

Ruud wrote: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):
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`+-------+-------+-------+ | 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):
Code: Select all
`1-stepper: 48 clues2-stepper: 36 clues3-stepper: 28 clues4-stepper: 24 clues5-stepper: 22 clues6-stepper: 22 clues`
Ocean

Posts: 442
Joined: 29 August 2005

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