The New Sudoku Players' Forum

[Serg]

Hi, coloin!

probably all the possible

Code: Select all

111
191
999

have puzzles ?

Maybe it would be possible to generate all the possible

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111
1-1

B12346 combinations which are solveable with 5 [one in each box] clues - are there really that many ?

During my search I was really interested in principle question - do the map examined have valid puzzles at all? So, I've done not exhaustive, but partial search for valid puzzles having the map

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1 1 1
1 1 9
9 9 9


It turned out that some patterns had valid puzzles even during partial search. It was sufficient to say that this map has valid puzzles. But I agree, it makes sense to study every pattern having this map to determine - does it have any valid puzzles? If there are some patterns which have no valid puzzles, it would be useful for further filtering out invalid symmetric 18-clue patterns (at least). I'll do such search in the coming days.

If there are not to much which case we could easily resolve the next level

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111
121
999

We know the map

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1 1 1
1 1 9
9 9 9


has valid puzzles, but the map

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1 1 1
1 1 1
9 9 9


has no valid puzzles. If we will increase number of clues in B6 box (2,3, ... 7 clues), we'll found "boundary" map having no valid puzzles with maximal number of clues in B6 box. More clues will be in B6 box for boundary map, more useful will be such "exclusive" map. Even intermediate results - knowing patterns not having valid puzzles in the case when its map have valid puzzles (other patterns of this map have valid puzzles) - will be useful for invalid patterns exclusion.
Maybe I'll do it in the coming days.

Serg

[coloin]

Well it seems all the potential patterns with 5 one-clue-boxes

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111
191
999

have puzzles

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1...........2...........3...4.816.5....925......734...972361584615478293483592716
1...........2...........3...4.538......129.5....674...951843726734962581286751439
1...........2...........3..4..981.5....753......642...839426715724315896516879243
1...........2...........3..4..8375.....529......461...394186752652743891871952436
1...........2...........3..4..613......428.5....579...936742185715836942842195736

1.....2.....3...............4.281......673.5....594...275846139483159672619732485
1.....2.....3...............4.276.5....483......159...678942135431865972259731684
1.....2.....3..............4..123......649.5....587...629815743713964825845732169
1.....2.....3..............4..751......6245.....893...514936782239187654687542193
1.....2.....3..............4..821.5....574......963...734652189518497623269138475
1.....2.....3..............4..8625.....439......517...543726189689143725721958643
                                                                                 
1..2...........3............4.7935.....642......581...865179432291436857437825961
1..2...........3............4.386.5....791......542...857134962231967845964825731
1..2...........3............4.589......127.5....634...462853719785916423931742685
1..2...........3...........4..6785.....359......124...834795612279461853651832794
1..2...........3...........4..182.5....549......376...684915723531427968279863541
1..2...........3...........4..123......467.5....859...615932784948571263732684591


this is the reciprical complete B12346 in the first puzzle.

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134657829598243671726189345347...952861...437259...168...........................


will just try to find a "few" more....

edit - added the ones i forgot !
C

[coloin]

this all implies that there arnt puzzles with

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101     111     011
191     091     191
999     999     999

C

[eleven]

I would take about 15 minutes per all stages because there are 20 valid B1+B2+B3+B4+B5 one-clue-box configurations only.

I dont understand that. Could you post the 20 please and explain more ?

[Serg]

Hi, eleven!

I would take about 15 minutes per all stages because there are 20 valid B1+B2+B3+B4+B5 one-clue-box configurations only.

I dont understand that. Could you post the 20 please and explain more ?

This is wrong statement. I'll edit that post.

Serg

[coloin]

I would take about 15 minutes per all stages because there are 20 valid B1+B2+B3+B4+B5 one-clue-box configurations only.

if it helps there are the 17 above along with these 6 multisol invalids [two empty rows in a band]

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1..3..2.....................4.281......673.5....594...275846139483159672619732485
1..3..2.....................4.276.5....483......159...678942135431865972259731684
1..3..2....................4..123......649.5....587...629815743713964825845732169
1..3..2....................4..751......6245.....893...514936782239187654687542193
1..3..2....................4..821.5....574......963...734652189518497623269138475
1..3..2....................4..8625.....439......517...543726189689143725721958643  [all multisol.]

if i have havent missed 3 others somewhere.....
C

[eleven]

There are thousands unique. From the 3 best populated 5 box sets i did not find any with 2 clues in the 6th box, but some with 3:

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

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1..2...........3...........3.....1.7....6..9..........219784563543126879786395241
1..2...........3...........5.......1....6.9.........7.295876413461593287873124695
1..2...........3...........2......91....7.5...........456182739872963154931457826
1..2...........3...........2......91....7.8...........432167589876953124951482736
1..2...........3...........5.......1....6.9.........8.495723618761548293823196475
1..2...........3...........7.....8.1....6...........7.297845163543196287861723594
1..2...........3...........9......24....7.5...........276983451459167832831452796
1..2...........3...........9......24....7.8...........276953481459182736831467592
1..2...........3...........9......42....7.8...........259167438381452796674938521
1..2...........3...........8......24....7.9...........298157436354862719671439582
1..2...........3...........8......24....6.7...........483159672529876431716432985
1..2...........3...........8......24....6.9...........423179685586432791719856432
1..2...........3...........9......42....7.6...........439187526651432789872965413
1..2...........3...........9......42....7.5...........479185623651432789832967415

I dont have time now to try all with 2, but it could be done in a day (more time for adopting the code than for cpu).

[Serg]

Hi, colleagues!
I've done exhaustive search for all patterns having map

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1 1 1
1 1 9
9 9 9


If am not mistaken there exist 20 essentially different such patterns. It turns out that each pattern has valid puzzles. Here are examples:

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        P1                      P2                      P3                      P4

1 . . 5 . . . . .       1 . . 5 . . . . .       1 . . 5 . . . . .       1 . . 5 . . . . .
. . . . . . 3 . .       . . . . . . 3 . .       . . . . . . 7 . .       . . . . . . 7 . .
. . . . . . . . .       . . . . . . . . .       . . . . . . . . .       . . . . . . . . .
2 . . 6 . . 1 5 9       2 . . . 3 . 6 9 1       . 4 . . 3 . 1 5 9       2 . . . . . 1 6 9
. . . . . . 4 8 6       . . . . . . 5 2 8       . . . . . . 2 6 4       . . . 6 . . 5 8 2
. . . . . . 7 2 3       . . . . . . 7 3 4       . . . . . . 3 7 8       . . . . . . 3 7 4
6 1 2 8 5 4 9 3 7       5 1 2 7 6 9 8 4 3       6 1 4 2 5 3 9 8 7       6 1 2 9 3 4 8 5 7
8 3 4 9 7 6 5 1 2       6 3 8 1 2 4 9 7 5       8 3 2 6 9 7 4 1 5       8 7 4 1 6 5 9 2 3
9 7 5 1 2 3 8 6 4       9 4 7 8 5 3 1 6 2       9 7 5 8 1 4 6 2 3       9 3 5 2 8 7 4 1 6

        P5                      P6                      P7                      P8

1 . . 5 . . . . .       1 . . 5 . . . . .       1 . . . . . . . .       1 . . . . . . . .
. . . . . . 7 . .       . . . . . . 3 . .       . . . 3 . . 7 . .       . . . 7 . . 8 . .
. . . . . . . . .       . . . . . . . . .       . . . . . . . . .       . . . . . . . . .
2 . . . . . 1 5 9       . 4 . . . . 5 3 7       2 . . 5 . . 3 9 4       2 . . . 4 . 9 1 6
. . . . 4 . 3 2 7       . . . . 8 . 2 4 9       . . . . . . 6 5 8       . . . . . . 3 8 4
. . . . . . 4 8 6       . . . . . . 1 8 6       . . . . . . 2 1 7       . . . . . . 2 5 7
6 1 2 9 5 3 8 7 4       6 1 2 8 3 5 7 9 4       6 3 2 8 1 4 9 7 5       3 1 5 6 8 4 7 9 2
8 3 5 1 7 4 9 6 2       8 7 4 1 2 9 6 5 3       8 7 1 9 5 2 4 6 3       6 7 2 5 1 9 4 3 8
9 7 4 6 2 8 5 1 3       9 3 5 4 6 7 8 1 2       9 4 5 7 6 3 8 2 1       9 4 8 2 3 7 5 6 1

        P9                      P10                     P11                     P12

1 . . . . . . . .       1 . . . . . . . .       1 . . . . . . . .       1 . . . . . . . .
. . . 7 . . 8 . .       . . . 2 . . 8 . .       . . . 7 . . 8 . .       . . . 8 . . 2 . .
. . . . . . . . .       . . . . . . . . .       . . . . . . . . .       . . . . . . . . .
. 6 . 4 . . 3 9 1       . 3 . . 1 . 9 4 8       2 . . . . . 4 5 9       2 . . . . . 5 9 8
. . . . . . 2 8 4       . . . . . . 2 3 7       . . . 9 . . 3 7 8       . . . . 5 . 7 1 6
. . . . . . 5 7 6       . . . . . . 1 6 5       . . . . . . 2 6 1       . . . . . . 3 4 2
3 1 2 6 7 4 9 5 8       3 1 2 8 4 5 7 9 6       3 1 2 4 9 6 7 8 5       3 1 2 5 4 8 9 6 7
6 4 5 8 9 2 7 1 3       6 4 8 9 3 7 5 1 2       6 4 5 8 1 7 9 2 3       6 4 5 7 3 9 8 2 1
9 7 8 3 1 5 4 6 2       9 7 5 1 6 2 3 8 4       9 7 8 3 5 2 6 1 4       9 7 8 2 1 6 4 3 5

        P13                     P14                     P15                     P16

1 . . . . . . . .       1 . . . . . . . .       1 . . . . . . . .       1 . . . . . . . .
. . . 8 . . 7 . .       . . . 8 . . 2 . .       . . . 3 . . . . .       . . . 9 . . . . .
. . . . . . . . .       . . . . . . . . .       . . . . . . 4 . .       . . . . . . 4 . .
. 3 . . . . 4 9 1       . 3 . . . . 4 1 6       2 . . 7 . . 3 9 1       2 . . . 5 . 6 8 9
. . . 2 . . 3 7 8       . . . . 2 . 7 9 8       . . . . . . 2 4 8       . . . . . . 1 3 4
. . . . . . 2 5 6       . . . . . . 3 5 2       . . . . . . 6 7 5       . . . . . . 2 5 7
3 1 2 5 4 8 9 6 7       3 1 2 5 8 6 9 7 4       3 1 2 9 6 7 8 5 4       3 1 2 8 9 5 7 4 6
6 7 5 9 2 1 8 3 4       6 4 5 7 9 1 8 2 3       6 7 5 1 8 4 9 3 2       6 4 5 3 1 7 8 9 2
9 4 8 7 3 6 5 1 2       9 7 8 2 4 3 5 6 1       9 4 8 2 3 5 7 1 6       9 7 8 6 2 4 5 1 3

        P17                     P18                     P19                     P20

1 . . . . . . . .       1 . . . . . . . .       1 . . . . . . . .       1 . . . . . . . .
. . . 8 . . . . .       . . . 8 . . . . .       . . . 9 . . . . .       . . . 9 . . . . .
. . . . . . 6 . .       . . . . . . 3 . .       . . . . . . 4 . .       . . . . . . 5 . .
. 3 . . 6 . 4 9 1       2 . . . . . 1 5 6       2 . . . . . 6 8 7       . 3 . . . . 6 1 8
. . . . . . 3 7 8       . . . 7 . . 4 9 8       . . . . 4 . 1 3 9       . . . . 4 . 3 5 7
. . . . . . 2 6 5       . . . . . . 2 3 7       . . . . . . 2 4 5       . . . . . . 2 9 4
3 1 2 9 7 4 5 8 6       3 1 2 6 5 8 9 7 4       3 1 2 7 9 5 8 6 4       3 1 2 6 7 4 9 8 5
6 4 8 1 3 5 9 2 7       6 4 8 3 7 9 5 1 2       6 4 5 2 1 8 7 9 3       6 4 8 1 9 5 7 2 3
9 7 5 2 8 6 1 4 3       9 7 5 4 2 1 6 8 3       9 7 8 6 3 4 5 1 2       9 7 5 8 3 2 4 6 1


The same in linear form:

Code: Select all

1..5...........3...........2..6..159......486......723612854937834976512975123864
1..5...........3...........2...3.691......528......734512769843638124975947853162
1..5...........7............4..3.159......264......378614253987832697415975814623
1..5...........7...........2.....169...6..582......374612934857874165923935287416
1..5...........7...........2.....159....4.327......486612953874835174962974628513
1..5...........3............4....537....8.249......186612835794874129653935467812
1...........3..7...........2..5..394......658......217632814975871952463945763821
1...........7..8...........2...4.916......384......257315684792672519438948237561
1...........7..8............6.4..391......284......576312674958645892713978315462
1...........2..8............3..1.948......237......165312845796648937512975162384
1...........7..8...........2.....459...9..378......261312496785645817923978352614
1...........8..2...........2.....598....5.716......342312548967645739821978216435
1...........8..7............3....491...2..378......256312548967675921834948736512
1...........8..2............3....416....2.798......352312586974645791823978243561
1...........3...........4..2..7..391......248......675312967854675184932948235716
1...........9...........4..2...5.689......134......257312895746645317892978624513
1...........8...........6...3..6.491......378......265312974586648135927975286143
1...........8...........3..2.....156...7..498......237312658974648379512975421683
1...........9...........4..2.....687....4.139......245312795864645218793978634512
1...........9...........5...3....618....4.357......294312674985648195723975832461


You can see that patterns P11, P12, P18 are new for coloin's list.

The next my goal - to check, do the patterns having map

Code: Select all

1 1 1
1 1 7
9 9 9


have valid puzzles? But I need a program determining all e-d patterns for given map. These patterns hardly can be found manually because they are several hundred. So, I can do it in some time.

Serg

[Serg]

Hi, coloin!

this all implies that there arnt puzzles with

Code: Select all

101     111     011
191     091     191
999     999     999

Why have you decided that all these 3 maps have no valid puzzles?

Serg

[eleven]

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:

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1 1 1
1 1 2
9 9 9

[Serg]

Hi, eleven!

So, if i made no mistake, this pattern is invalid:

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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

[eleven]

Hi Serg,

this list shows, how much completions for the 5 boxes i processed (pattern/count).

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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

[coloin]

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

[eleven]

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

[coloin]

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