One-clue-boxes patterns

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

Re: One-clue-boxes patterns

Postby eleven » Tue May 15, 2012 7:34 am

coloin wrote:
Code: Select all
but not

110
222
999


Confirmed, no valid puzzles found.
eleven
 
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Re: One-clue-boxes patterns

Postby eleven » Tue May 15, 2012 9:03 am

Code: Select all
0 1 1
2 2 9
9 9 9

seems to be invalid too.
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Re: One-clue-boxes patterns

Postby coloin » Tue May 15, 2012 11:19 pm

well done

I searched through a large number of 19s before this very rare ? 18 emerged
Code: Select all
+---+---+---+
|1..|...|...|
|...|2..|...|
|...|...|...|
+---+---+---+
|3..|.1.|.2.|
|..2|.4.|.5.|
|...|..5|.6.|
+---+---+---+
|7..|3..|4..|
|..5|8..|9..|
|..4|...|..1|
+---+---+---+

110
233
323


However i neednt have bothered as an 18 with vertical symmetry with [only] 2 clues in a band is impossible !!!!!
im sure Serg has noted this

C
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Re: One-clue-boxes patterns

Postby Serg » Wed May 16, 2012 10:22 am

Hi, colleagues!
I am sorry for long silence. I am writing now a program generating all possible patterns for given map (it is not ready yet).
Maybe I missed something but I don't see general idea of the search (sequence of checked maps).

For eleven.
I am under impression of your exhaustive search for map
Code: Select all
1 1 0
2 2 2
9 9 9

Impressive result! How many patterns did you check?

I keep in mind cross-checking of your search for map
Code: Select all
1 1 1
1 1 2
9 9 9

(I am planning to repeat this search in some time.)

Serg
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Re: One-clue-boxes patterns

Postby eleven » Wed May 16, 2012 10:26 pm

Serg wrote:
Code: Select all
1 1 0
2 2 2
9 9 9

Impressive result! How many patterns did you check?

I found 34 n-e placements for the 6 cells in the first 5 boxes. For 16 of them i found valid completions, about 1.5 mio totally. But none gave a valid puzzle with a pair of cells in box6.
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Re: One-clue-boxes patterns

Postby Serg » Thu May 17, 2012 7:41 am

Hi, eleven!
eleven wrote:
Serg wrote:
Code: Select all
1 1 0
2 2 2
9 9 9

Impressive result! How many patterns did you check?

I found 34 n-e placements for the 6 cells in the first 5 boxes. For 16 of them i found valid completions, about 1.5 mio totally. But none gave a valid puzzle with a pair of cells in box6.

Please, describe your method in details.

Serg
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Re: One-clue-boxes patterns

Postby eleven » Thu May 17, 2012 12:42 pm

Serg wrote:Please, describe your method in details.

You should know better, Serg, because its basically your method, and i already described what i did for the other pattern.

As said, i processed each of the 34 n-e patterns for the 6 clues in boxes 1-5, e.g. this one:
Code: Select all
1...........1..............1...1.....1.1.........................................

With the 2 clues in band one there are only 3 n-e valid band completions, [Added:](in fact the 3 are equivalent, but i only used 12 morphs - changing cols in stack 3 and switch stacks 12+row swapping r12/r45), one being
Code: Select all
156897234798234516243165789......................................................


I combined each one with the possible completions of boxes 1,4. Each band gave 2016 valid 4-box completions (including equivalents), one being
Code: Select all
156897234798234516243165789567......982......314.................................

Now these were combined with the possible completions of boxes 4,5. This pattern gave 26 valid 5-box completions, one being
Code: Select all
156897234798234516243165789567983...982641...314752..............................

Totally for this 6 clue pattern i got 180535 valid 5-box completions (don't know, how many are n-e).

In the last step i checked for the 8 possible box 6 fillings: For each of the 36 ways to pick 2 cells from it i looked, if together with the 6 pattern clues in the 5 boxes they would fix all UAs in the 2 bands. None found.

The UA checks are done in the usual way:
Take the first solution of a possible completion, remove all but the pattern clues in the completion's boxes and solve again. If it is unique, all UA's (in these boxes) are fixed by the pattern clues - if not, the completion is invalid for a unique puzzle.
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Re: One-clue-boxes patterns

Postby Serg » Thu May 17, 2012 3:46 pm

Hi, eleven!
Sorry, I don't understand what is "n-e" patterns.

Serg
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Re: One-clue-boxes patterns

Postby eleven » Thu May 17, 2012 4:35 pm

Non equivalent. These patterns cannot be morphed to one another, but all with 1,1,0/2,2 clues in the 5 boxes can be morphed to one of them.
Hidden Text: Show
1...........1...............1..1......1...........1..............................
1...........1...............1..1......1..1.......................................
1...........1...............1..1.....1............1..............................
1...........1...............1..1.....1...........1...............................
1...........1...............1..1.....1...1.......................................
1...........1...............1..1.....1..1........................................
1...........1...............11..........1.........1..............................
1...........1...............11..........1........1...............................
1...........1...............11..........11.......................................
1...........1...............11.1.........1.......................................
1...........1...............11.1........1........................................
1...........1..............1.........1...........11..............................
1...........1..............1.........1..1.........1..............................
1...........1..............1.........1..1........1...............................
1...........1..............1.........1..1.......1................................
1...........1..............1.........1..11.......................................
1...........1..............1...1.....1............1..............................
1...........1..............1...1.....1...........1...............................
1...........1..............1...1.....1..........1................................
1...........1..............1...1.....1...1.......................................
1...........1..............1...1.....1..1........................................
1...........1..............1...1.....1.1.........................................
1...........1..............1...11....1...........................................
1...........1..............1..1......1...........1...............................
1...........1..............1..1......1..1........................................
1...........1..............11...........1.........1..............................
1...........1..............11...........1........1...............................
1...........1..............11...........11.......................................
1...........1..............11..........1.........1...............................
1...........1..............11..........11........................................
1...........1..............11..1.........1.......................................
1...........1..............11..1........1........................................
1...........1..............11..1.......1.........................................
1...........1..............11.1.........1........................................

[Edit:] Ah, now i know, why you ask. I mistakingly eliminated the ones, which have no clues in c23, c56 and r45.
I will process them also, don't expect that they can produce valid puzzles.
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Re: One-clue-boxes patterns

Postby eleven » Thu May 17, 2012 6:21 pm

Done, I now processed also these 16 patterns.
Hidden Text: Show
1...........1...............11.11................................................
1...........1..............1........1............11..............................
1...........1..............1...1....1.............1..............................
1...........1..............1...1....1............1...............................
1...........1..............1...1....1...........1................................
1...........1..............1...1....1....1.......................................
1...........1..............1...1....1...1........................................
1...........1..............1...11...1............................................
1...........1..............1..1.....1............1...............................
1...........1..............1..1.....1...........1................................
1...........1..............1..1.....1...1........................................
1...........1..............1..1.....1..1.........................................
1...........1..............11..........1........1................................
1...........1..............11..11................................................
1...........1..............11.1........1.........................................
1...........1..............11.11.................................................

Nine of them had valid 5-box completions, 197809 totally.
No valid puzzles.
eleven
 
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Postby eleven » Thu May 17, 2012 9:26 pm

OT: Btw this reminded me on a result by Red Ed, which was lost by the forum crash. If you have a puzzle with only 2 clues in a band, like this
Code: Select all
 1 . . | . . . | . . .
 . . . | 2 . . | . . .
 . . . | . . . | . . .

you immediately can place them also here
Code: Select all
 1 . . | . . . | . . .
 . . . | 2 . . | . . .
*2 . . |*1 . . | . . .

This follows from the fact, that there is only one non equivalent valid band completion, which has the givens there too (and no transformation can change that).

It's not a big help for Coloin's puzzle above (which is easy anyway), but we had found some harder ones, which became easy with this trick.
eleven
 
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Re: One-clue-boxes patterns

Postby Serg » Thu May 17, 2012 10:35 pm

Hi, eleven!
Thank you for clarification of your method. I need some time to ponder it.
Congratulations! You are so fast in coding! (It took me typically several weeks to code a searching program and cross-check results for given map.)

Serg
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Re: One-clue-boxes patterns

Postby coloin » Thu May 17, 2012 11:23 pm

I didnt know that one ...... thanks

coloin wrote:
Code: Select all
110       011
199  or   199
999       999
doesnt come up with a valid puzzle...............


it would probably take you a couple of seconds to confirm these patterns are devoid of a valid puzzle !!

one clue in box 4 would seem to never be enough, strange ......

C
coloin
 
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Joined: 05 May 2005

Re: One-clue-boxes patterns

Postby eleven » Mon May 21, 2012 10:17 am

coloin wrote:
Code: Select all
110       011
199  or   199
999       999
doesnt come up with a valid puzzle...............

Yes, i did not find a valid 4-box completion for them.
Also this is invalid:
Code: Select all
011
299
999

Then 2 clues in a band would need at least 2 clues in all other boxes and 3 clues in the other boxes of the stack with the empty box.
eleven
 
Posts: 1534
Joined: 10 February 2008

Re: One-clue-boxes patterns

Postby Serg » Wed May 23, 2012 9:26 pm

Hi, eleven!
I wrote at last program generating all essentially different patterns without pairs of empty rows (columns) in a band (stack) for given map.
It turns out that map
Code: Select all
1 1 1
1 1 2
9 9 9

has 288 e-d non-empty patterns (i.e. patterns without pairs of empty rows (columns) in a band (stack)).

I am writing now universal program doing exhaustive search for all valid puzzles belonging to given map.

Serg
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