One-clue-boxes patterns

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Re: One-clue-boxes patterns

Postby eleven » Sun May 06, 2012 7:17 pm

Now i have searched through all possible 6-box-completions for puzzles with 1 given in the first 5 boxes. There was none, which had a pair in the 6th box, which together with the 5 cells could fix all UAs in the first two bands.

So, if i made no mistake, this pattern is invalid:
Code: Select all
1 1 1
1 1 2
9 9 9
eleven
 
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Re: One-clue-boxes patterns

Postby Serg » Sun May 06, 2012 9:31 pm

Hi, eleven!
eleven wrote:So, if i made no mistake, this pattern is invalid:
Code: Select all
1 1 1
1 1 2
9 9 9

Very interesting result! So, we could filter out new portion of symmetric 18-clue puzzles. How many patterns did you process?
2 clues in B6 box seems to me maximal, because you have already published valid puzzle having 3 clues in B6 box.

Serg
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Re: One-clue-boxes patterns

Postby eleven » Mon May 07, 2012 8:11 am

Hi Serg,

this list shows, how much completions for the 5 boxes i processed (pattern/count).
Code: Select all
1..1...........1...........1..1..................................................      798
1..1...........1...........1...1.................................................     2520
1..1...........1...........1...........1.........................................      546
1..1...........1...........1............1........................................    17506
1..1...........1............1..1.................................................    27402
1..1...........1............1...........1........................................    24723
1...........1...........1..1..1..................................................      870
1...........1...........1..1...1.................................................    21362
1...........1...........1..1...........1.........................................     2764
1...........1...........1..1............1........................................    16906
1...........1...........1...1..1.................................................    22796
1...........1...........1...1...........1........................................    46237
1...........1..1...........1..1..................................................     1236
1...........1..1...........1...1.................................................    61728
1...........1..1...........1...........1.........................................    25271
1...........1..1...........1............1........................................    36033
1...........1..1............1.1..................................................    11828
1...........1..1............1..1.................................................    42158
1...........1..1............1..........1.........................................    46777
1...........1..1............1...........1........................................   221151
                                                                            total   630612


Note that these sets are not e-d. I have used the column/stack and band 1 automorphisms of the 5 clue pattern only. Especially i did not use row 56 swappaing (if available), but i did use column 89 swapping.
Then each of these completions leaves 8 possible fillings for box 6 (only). So i simply tested all the 36 ways to take 2 cells in box 6 and checked the UA's in bands 12.

It would be nice, when you could validate this result. With all the case distinctions and consecutive steps (band 1, then 4,5,6 boxes) there is a big potential for bugs. I had made some checks (and also found bugs), but not enough to be sure, that all is correct.
[Edit:] corrected the sum
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Re: One-clue-boxes patterns

Postby coloin » Tue May 08, 2012 9:33 am

Thanks for spotting the 3 that i missed.......

I suppose the assumption that these patterns are invalid
Code: Select all
101     111     011
191     091     191
999     999     999

is based on the fact that my generator drew a blank after half an hour with them. i made a lot of puzzle and didnt find a single superfluos clue in the 5 boxes ..................
i did find the
Code: Select all
102
190
999
though

Well done eleven on that. I had hoped it could be proved.
More B12345 solvable with 5 one-in-box clues than i thought, im not sure how you did it so easily !!
i had noted that there could have been some B12345 combinations with several different 5 one-in-box completions.

so , if verified, there is no puzzle with 3,4,27 [11] clues in 3 bands [edit eg with 111,112,344]

with 2 clues in the first band only [cant be 2 in a box] only one band out of the 416 has this property
Code: Select all
 
110
223
999

Code: Select all
+---+---+---+
|1..|...|...|
|...|2..|...|
|...|...|...|
+---+---+---+
|.2.|.3.|.4.|
|..5|.1.|.7.|
|...|...|..6|
+---+---+---+
|492|381|765|
|357|649|821|
|681|725|439|
+---+---+---+

we might be able to go one better than this valid combination - but somehow its not that easy.
Maybe a
Code: Select all
110
129
999
is possible.....
C
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Re: One-clue-boxes patterns

Postby eleven » Wed May 09, 2012 4:34 pm

coloin wrote:
Code: Select all
101     111     011
191     091     191
999     999     999

If my 1-in-5-boxes sets (which should be supersets for the 5-box completions of these patterns) are complete, only the second of them has unique puzzles:
Code: Select all
 +-------+-------+-------+
 | 1 . . | . . . | . . . |
 | . . . | 2 . . | 3 . . |
 | . . . | . . . | . . . |
 +-------+-------+-------+
 | . . . | 3 . . | 2 7 5 |
 | . . . | . . . | 4 8 1 |
 | . . . | . . . | 6 3 9 |
 +-------+-------+-------+
 | 7 4 6 | 5 3 9 | 8 1 2 |
 | 8 1 3 | 7 4 2 | 5 9 6 |
 | 9 5 2 | 6 8 1 | 7 4 3 |
 +-------+-------+-------+
1...........2..3..............6..275......481......639746381592812569743953742816
1...........2..3.................283....4.619......547489312765523764891671895432
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Re: One-clue-boxes patterns

Postby coloin » Sun May 13, 2012 3:05 pm

eleven that is a rare one

with only 2 clues in the first band this seems to preclude a puzzle with a one-clue-box in any of the other boxes
even
Code: Select all
110       011
199  or   199
999       999
doesnt come up with a valid puzzle

so the best might well be
Code: Select all
110
223
999

but not

110
222
999

C
Last edited by coloin on Tue May 15, 2012 2:58 pm, edited 1 time in total.
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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.
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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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