The New Sudoku Players' Forum

[coloin]

Well ...... improved search on the horizontal-9plus12s got at least 20 more !
here is 5

Code: Select all

123456789........1...2.......8..1.........4.5.........54....2.....7.8.6..........
123456789........1...2.......8..1.........4.5.........54....2.....7.3.6..........
123456789........1...2.......8..1.........4.5.........54....2.....8.7.6..........
123456789........1...2.......8..1.........4.5.........54....2.....3.7.6..........
123456789........1...2.......8..1.........4.5.........54....2.....8.7.3..........

C

[dobrichev]

Congratulations!

I am confirming the new 5 puzzles 9+12 givens distribution

Minimizing the first row results in 42 puzzles, 20 of size 18 and 22 of size 19. Massive search within 19's + magic patterns?

Hidden Text: Show

Code: Select all

.234.678.........1...2.......8..1.........4.5.........54....2.....7.8.6..........       18
.2345.7.9........1...2.......8..1.........4.5.........54....2.....7.8.6..........       18
.23456.89........1...2.......8..1.........4.5.........54....2.....7.8.6..........       19
1.3.56.89........1...2.......8..1.........4.5.........54....2.....7.8.6..........       18
1.34.6789........1...2.......8..1.........4.5.........54....2.....7.8.6..........       19
1.345.789........1...2.......8..1.........4.5.........54....2.....7.8.6..........       19
12.456.89........1...2.......8..1.........4.5.........54....2.....7.8.6..........       19
12.4567.9........1...2.......8..1.........4.5.........54....2.....7.8.6..........       19
.234.678.........1...2.......8..1.........4.5.........54....2.....7.3.6..........       18
.2345.7.9........1...2.......8..1.........4.5.........54....2.....7.3.6..........       18
.23456.89........1...2.......8..1.........4.5.........54....2.....7.3.6..........       19
1.3.56.89........1...2.......8..1.........4.5.........54....2.....7.3.6..........       18
1.34.6789........1...2.......8..1.........4.5.........54....2.....7.3.6..........       19
1.345.789........1...2.......8..1.........4.5.........54....2.....7.3.6..........       19
12.45.789........1...2.......8..1.........4.5.........54....2.....7.3.6..........       19
12.4567.9........1...2.......8..1.........4.5.........54....2.....7.3.6..........       19
.234.678.........1...2.......8..1.........4.5.........54....2.....8.7.6..........       18
.2345..89........1...2.......8..1.........4.5.........54....2.....8.7.6..........       18
.2345.7.9........1...2.......8..1.........4.5.........54....2.....8.7.6..........       18
1.3.56.89........1...2.......8..1.........4.5.........54....2.....8.7.6..........       18
1.34.6789........1...2.......8..1.........4.5.........54....2.....8.7.6..........       19
1.345..89........1...2.......8..1.........4.5.........54....2.....8.7.6..........       18
12.456.89........1...2.......8..1.........4.5.........54....2.....8.7.6..........       19
12.4567.9........1...2.......8..1.........4.5.........54....2.....8.7.6..........       19
123.567.9........1...2.......8..1.........4.5.........54....2.....8.7.6..........       19
.234.678.........1...2.......8..1.........4.5.........54....2.....3.7.6..........       18
.2345..89........1...2.......8..1.........4.5.........54....2.....3.7.6..........       18
.2345.7.9........1...2.......8..1.........4.5.........54....2.....3.7.6..........       18
1.3.56.89........1...2.......8..1.........4.5.........54....2.....3.7.6..........       18
1.34.6789........1...2.......8..1.........4.5.........54....2.....3.7.6..........       19
1.345..89........1...2.......8..1.........4.5.........54....2.....3.7.6..........       18
12..56789........1...2.......8..1.........4.5.........54....2.....3.7.6..........       19
12.4567.9........1...2.......8..1.........4.5.........54....2.....3.7.6..........       19
.234.678.........1...2.......8..1.........4.5.........54....2.....8.7.3..........       18
.2345..89........1...2.......8..1.........4.5.........54....2.....8.7.3..........       18
.234567.9........1...2.......8..1.........4.5.........54....2.....8.7.3..........       19
1.3.56.89........1...2.......8..1.........4.5.........54....2.....8.7.3..........       18
1.34.6789........1...2.......8..1.........4.5.........54....2.....8.7.3..........       19
1.345..89........1...2.......8..1.........4.5.........54....2.....8.7.3..........       18
12.456.89........1...2.......8..1.........4.5.........54....2.....8.7.3..........       19
12.4567.9........1...2.......8..1.........4.5.........54....2.....8.7.3..........       19
123.567.9........1...2.......8..1.........4.5.........54....2.....8.7.3..........       19

[coloin]

Thanks ..... well it seems you can always remove 2 clues from a row/box of 9.
Usually a few 6plus12s are valid.
suppose that if there isnt a 6plus 12 then my technique wont find them .....
hmmmmm
fwiw - it is always possible to " fix" 2 of the 12 clues ..... but we are not close to an exaustive search just yet !

C.

[Mauricio]

Well ...... improved search on the horizontal-9plus12s got at least 20 more !
here is 5...

In the meantime, I hope this is not one of your 20 more

Code: Select all

123456789400000000000000500600000120050970000000000000079000000000001040000000000

[coloin]

In the meantime, I hope this is not one of your 20 more ...............

My total of horizontal 9plus12s is 94, and my lasts batches didnt give any new ones. Your puzzle is included in my list which might be expected if that is the lot......

the problem appears simple - but its not easy.

how are you doing it btw ?

C

[coloin]

As a by-product
a quick look through a few of the lists i have made reveals these 2 potential minima [and i think they have to be minima]

Code: Select all

+---+---+---+
|123|456|789|
|...|...|..1|
|...|3..|...|
+---+---+---+
|...|.71|...|
|...|...|...|
|..6|...|4..|
+---+---+---+
|518|692|347|
|...|...|6..|
|.7.|...|...|
+---+---+---+  18plus8

Code: Select all

+---+---+---+
|123|456|789|
|..9|...|..1|
|...|...|...|
+---+---+---+
|518|972|463|
|...|..1|...|
|...|...|.5.|
+---+---+---+
|751|689|342|
|4..|...|...|
|...|...|...|
+---+---+---+   27plus5

If this could be proven ....

in any 8 rows there must be at least 12 clues
in any 7 rows there must be at least 8 clues
in any 6 rows there must be at least 5 clues
and also
in any 5 rows there must be at least 3 clues

[to go along with
in any 3 rows [in a band] there must be at least 2 clues
in any 2 rows [in a band] there must be at least 1 clue ]

And to follow on a similar vein - [edited]

Code: Select all

+---+---+---+
|123|456|789|
|.8.|...|..1|
|...|..7|..5|
+---+---+---+
|7..|..1|..4|
|...|...|..8|
|...|.3.|..2|
+---+---+---+
|.5.|.8.|..3|
|...|...|..7|
|4..|...|..6|
+---+---+---+  a 17plus8 was found !!!!  [betters the 17plus9]

This probably the best we can do with a full complement of clues on 2 adjacent edges
So this arrangement of 64 cells must have at least 8 clues
C

[coloin]

Well ...... ongoing fruitless searching has given me a total of 105 horizontal 9plus12s.

The previous puzzle also provides

Code: Select all

+---+---+---+
|612|934|578|
|...|...|.16|
|...|...|..4|
+---+---+---+
|...|...|..1|
|...|..5|2.7|
|14.|...|..3|
+---+---+---+
|...|...|..5|
|...|.4.|..2|
|485|612|739|
+---+---+---+

so these 56 cells would appear to need at least 6 clues. [at least i cant find a 25plus5]

and for completeness i provide this puzzle

Code: Select all

+---+---+---+
|123|456|789|
|8..|...|..6|
|9..|...|..3|
+---+---+---+
|4..|...|.12|
|3..|...|..4|
|5..|..3|..7|
+---+---+---+
|6..|...|..1|
|2..|7..|..5|
|715|239|468|
+---+---+---+

so these 49 cells would appear to need at least 3 clues [one of which needs to be in the middle box]

Absolute proof awaited for all or any !

C

[coloin]

This puzzle [unfortunately] gives us

Code: Select all

+---+---+---+
|398|647|1..|
|572|831|...|
|641|529|...|
+---+---+---+
|123|468|...|
|456|793|...|
|789|152|...|
+---+---+---+
|...|.1.|...|
|...|...|.9.|
|...|...|.58|
+---+---+---+

the confirmation that B36789 needs minimum 5 clues.......
although with the proviso that there are no empty boxes

Code: Select all

+---+---+---+
|398|467|...|
|572|381|...|
|641|259|8..|
+---+---+---+
|123|648|.9.|
|456|973|...|
|789|512|...|
+---+---+---+
|..7|...|1..|
|...|1..|.4.|
|...|...|...|
+---+---+---+

6 clues is the minimum
proved by this maximal no-puzzle pattern

Code: Select all

        P134       
+-----+-----+-----+
|. . .|. . x|. . x|
|. . .|. . x|. . x|
|. . x|. . x|. . x|
+-----+-----+-----+
|. . .|x x x|x x x|
|. . .|x x x|x x x|
|x x x|x x x|x x x|
+-----+-----+-----+
|. . .|x x x|x x x|
|. . .|x x x|x x x|
|x x x|x x x|x x x|
+-----+-----+-----+

and in a similar way

Code: Select all

+---+---+---+
|123|596|.7.|
|456|287|...|
|789|143|..6|
+---+---+---+
|938|451|..7|
|264|378|.5.|
|517|962|.4.|
+---+---+---+
|...|...|...|
|...|...|..9|
|...|..5|...|
+---+---+---+

If there is 2 clues in a band, it would appear that one needs a total of 5 clues in B3 and B6
these 2 impossible patterns confirm that {2 plus 2} or {3 plus 1} or {4 plus 0} clues are impossible

Code: Select all

+-----+-----+-----+   +-----+-----+-----+
|. . .|. . x|x x x|   |. . .|. x x|. x x|
|. . .|. . x|x x x|   |. . .|. x x|. x x|
|. . x|. . x|x x x|   |. . x|. x x|. x x|
+-----+-----+-----+   +-----+-----+-----+
|. . .|x x x|x x x|   |. . .|x x x|x x x|
|. . .|x x x|x x x|   |. . .|x x x|x x x|
|. x .|x x x|x x x|   |. x .|x x x|x x x|
+-----+-----+-----+   +-----+-----+-----+
|. . .|x x x|x x x|   |. . .|x x x|x x x|
|. . .|x x x|x x x|   |. . .|x x x|x x x|
|. . .|x x x|x x x|   |. . .|x x x|x x x|
+-----+-----+-----+   +-----+-----+-----+


and finally ....... this puzzle

Code: Select all

+---+---+---+
|398|647|1..|
|572|831|...|
|641|529|...|
+---+---+---+
|123|.6.|.7.|
|456|...|...|
|789|...|...|
+---+---+---+
|...|.1.|...|
|...|...|.9.|
|...|...|.58|
+---+---+---+

provisionally confirms that a total of 7 clues are required for B356789 [as 6 not found]

Anyway ..............here are the new horizontal 9plus12s i have found - now 105.

Code: Select all

123456789........1.5..8......7..1.......4..5...9...........7..6..........8.....4.
123456789........1....2.........1........9....5....2......6.5..9.....3....4..7...
123456789........1....2.........1........9....5....2......7.5..9.....6....4..3...
123456789........1....7.........1.96........8..5......6....2.........54...8......
123456789........1....7.........1.36........8..5......9....2.........54...8......
123456789........1....2.........1.....5...2....9..8......63.5..8.......7.........
123456789........1..5.3....79...1..........4.8.............7......8.......4....5.
123456789........1..5.3....79...1..........4.8.............7......8.......4....3.
123456789........1..5.3....97...1..........4.8.............7......8.......4....3.
123456789........1..5.3....97...1..........4.8.............7......8.......4....5.
123456789........1..53..........1.....8....3......9...7.....9.6...8.......4......
123456789........1..........6...1..........3...9...54......7..2.......6...53.....
123456789..8.....1..............1......3....854.............52...9..7..........4.
123456789..7.....1....8.......3.1..7.....9....5.......9.1............52..........
123456789.5......1...8.........21..............4....6.4.76.............2..9......
123456789........1...2.....9....1.........5........2......98....7......6.54......
123456789........1.4..2.........1........7....5.....3.7........9...3........4..2.
123456789........1...2..........1.......89....6....4..8.1........4............6.7
123456789........1...2.......9..1.........45..........54....2.....9.7..3.........  # Mauricio
123456789....8...1.9..........2.1........7.....6....5......2..7.........8.5......
123456789........1..5.........8.1.............4....5..98..4........6.31..........
123456789........1..5.........8.1.............4....5..98..4........7.31..........
123456789........1..7.........8.1.............5....6..98..4........6.31..........
123456789........1....2.........1..7..2....5....9.................23..4.97.......
1234567897.......1.........6....1......3...4........3......7..6.842..............
123456789..8.....1....7.......3.1..8.....9...5........9.1............52..........
123456789..8.....1....7.........1......3.9..85........9.1............52..........
123456789........1...8.....9.4..1..................53......4..8.5.......73.......
123456789........1.8.......9....1.......7.32..........7.9.....6....2....5........
123456789........1....3.........1........92..7.5...3........5....6.......9...7...

Fairly difficult to find any more ......

C

[coloin]

Well it took another big effort to get these two

Code: Select all

1234567898.......1....3...........4........3.9....1....45...........98..........6#[several other puzzles within{+5}]
123456789........16............91........5...2.....3....9.......8..3.......2..6..#[no other puzzles within {+5}]

they are within {+7} of each other which is probably not unexpected. The 2nd puzzle is more remote .....

And 4 more

Code: Select all

123456789.....2..1.............31..864..................1.8.......5...2.......6..
123456789..8.....1....2.........1.....7...42........6..6........4............7..8
123456789........1...2.......7.31.........54...........6.5..........7..34........
123456789........1..6.........7.19.....9.......5..........8.65.94................

C

[coloin]

revisiting the box 9plus12s - with only 2 clues in a band

these patterns have been shown to have no puzzles

Code: Select all

        P123       
+-----+-----+-----+
|. . .|. x x|x x x|
|. . .|. x x|x x x|
|. . .|. x x|x x x|
+-----+-----+-----+
|. . .|x x x|x x x|
|. . .|x x x|x x x|
|x x x|x x x|x x x|
+-----+-----+-----+
|. . .|x x x|x x x|
|. . .|x x x|x x x|
|x x x|x x x|x x x|
+-----+-----+-----+

        P110       
+-----+-----+-----+
|. . .|. . x|x x x|
|. . .|. . x|x x x|
|. . x|. . x|x x x|
+-----+-----+-----+
|. . .|x x x|x x x|
|. . .|x x x|x x x|
|. x .|x x x|x x x|
+-----+-----+-----+
|. . .|x x x|x x x|
|. . .|x x x|x x x|
|. . .|x x x|x x x|
+-----+-----+-----+

         P114             
 +-----+-----+-----+     
 |. . .|. x x|. x x|     
 |. . .|. x x|. x x|     
 |. . x|. x x|. x x|     
 +-----+-----+-----+     
 |. . .|x x x|x x x|     
 |. . .|x x x|x x x|     
 |. x .|x x x|x x x|     
 +-----+-----+-----+     
 |. . .|x x x|x x x|     
 |. . .|x x x|x x x|     
 |. . .|x x x|x x x|     
 +-----+-----+-----+

this means that the minimum patterns are

033
132
123

or

033
132
132

which means that a 9plus14 is impossible with patterns with only 2 clues in a band

Code: Select all

+---+---+---+
|2..|...|...|
|...|8..|...|
|...|...|...|
+---+---+---+
|6..|123|.8.|
|..8|456|.9.|
|...|789|.4.|
+---+---+---+
|7..|6..|5..|
|..9|3..|1..|
|..5|...|..2|
+---+---+---+ 9plus15

C

[coloin]

Here are my [not quite] final results of a particularly obscessive search of 9plus12-puzzles !

I would be surprised if there is many more - but possibly there are !!

143 Central Box 9plus12s - EDIT and four more is 147 - EDIT and two more is 149 - EDIT and 3 more is 152

Hidden Text: Show

Code: Select all

............3...7.2....4......123...9..456..2...789....1......8.73............9.6
............5..47.6......3....123...8..456..9...789...........8.7.3.......2.....6
............8...7.6.......4...123...9..456..3...789....1.....8..7...2.......6...5
............8...7.6.......4...123...9..456..3...789....1...2....7.....8.....6...5
..........3.....7.6....4.3....123...9..456......789....1....4...738...........6..
.....5.........1...1....27....123...9..456......789...........9.782.......2.....5
...3..4.........7.6.2........9123..6...456......789............473..........6...5
..8.4..........97.............123......456.1...2789....3......8.7...........6.2.5
2...............7........31...123...8..4562.....789....1........74..1.......6.8..
2...........3..97.6......3....123......4562.....789....13.......7...........6.4..
2.....5......6.........7.3....123..79..456......789....1........73............9.6
2...4..........1.3..4.........123......456......789..1.1......8.73..........9..2.
2...4..........97........3....123...8..456..2...789....1........7...........6.8.5
4.............71..2......6..9.123......456..2...789....1........73...9......4....
4....58........27.............1237..9..456......789....1........72.............95
4....8.........12........7....123...9..456......789...........8.572.......2.....3
5...............7.......13....123...2..456..8...789....1.......47...1.......6...5
5...............7.......13....123...2..456..9...789....1........74..1.......9...5
5...............7.6......31...123...2..4569.....789....1........7..9........6.4..
5...............72..9..8......123...9..4563.....789....1...54............72......
5..............17........3....123...9..456......789....1......8.73........2.6...5
5..............17.....4.8.....123...9..456..3...789....13........7..........6...5
5.............21..7..........6123..9...456......789..........78..3....5...2..1...
5............9..7...1....6..4.123...9..456......789.........9.8......5....26.....
5...........2...7.......6.....123...9..4563.....789........54...7..3.....12......
5...........23..7........3...7123......456......789.....3.....8.71.........6....5
5...........3...7........8....123...9..456..2...789....1......6.739.............5
5...........3...7.......83....123...8..456......789....13.....6.7...........6...5
5...........3..1..6...........123.5.9..456.2....789....1........7.2............65
5...........3..67........3....123......456..2...789....1......8.73..........4...5
5...........3..79........3....123...8..456......789....1......8.73..........4...5
5...........3..87........3....123...8..456......789....13.....6.7...........6...5
5...........9..17...8.......96123......456......789.........3.8.7.2...........6..
5..........7...1........73....123...2..456..8...789....4........73..........6...5
5.........9.8..1..............123......456....6.7893.........2..739............45
5........29..4...........3....123.7....456..8...789....13.......7...........6...5
5........3.6.........8....1...123...9..456.3....789....1......8.....5.....2.....7
5........4..3..97........1....123...9..456..3...789....1........7............4..5
5.......46...........9...3....123...8..456..2...789....1.....9...3....7.....6....
5.......6....3..7...1.9.......123...8..456......7893..........8.73............9..
5.......7......2......1.....9.1236.....456......789....1......8.23...........4..5
5......3.......27.8..9.......7123.4....456......789...6.......8...........2.3....
5......3.......27.8..9.......7123.4....456......789...6.......8....3......2......
5......3.......27.8..9.......7123.6....456......789...6.......8....3......2......
5......7.28..4...........3....123......456..9...789....13.......7...........6...5
5.....2......6.........7.3....123..79..456......789....1........73............9.4
5.....2......6.........7.3....123..79..456......789....1........73............9.6
5.....3.....3..19.6...........123......456.2....789.....1.......73..........6..4.
5.....7.......21..3.4.........123...9..456..3...789....1....8.....5.............5
5.....8......6.........7.3....123..79..456......789....1........73............9.4
5.....8......6.........7.3....123..79..456......789....1........73............9.6
5.....9........17.6.2.........123.....8456..2...789....1....7...............3...5
5....48........17.............1237..9..456......789....17.............69..2......
5....8.........17........4....1237..9..456......789..........58.71.......2.......
5...1...........7...4....3....123......756.....7489.....9.....1.73..........6...5
5...1...........7...9....3....123......456....3.789.4.........1.7...........6.8.5
5...1....9......7........3....123......456....3.789.4...........7......1....6.8.5
5...1....9......7........3....123......456....3.789.4.........1.7...........6.8.5
5...4...........1.......93....123......456....3.789....1......8.73..........6...5
5...4...........7...1....3...7123......456......789.....9.....4.73..........6...5
5...4...........79.......3....123......4568...3.789....13.......7.............4.5
5...4..........13........2....123......456..9...789.1..1........73..........6...5
5...4..........16........3....123...9..456..2...789...........8.13..........9..5.
5...4..........16.2......3....123...92.456......789....1.........3..........9...5
5...4..........17..1.....3....123...2..456......789...........6.73........8.....5
5...4..........97........3....123...2..456..8...789....1........7...........6.8.5
5...6..........17..1.....3....123...2..456......789.....8.....4.73..............5
5...6.......3...7.............123...9..456..2...789....1....6.8.73..............5
5...6.......3...7.............123...9..456..2...789....1....8.6.73..............5
5...6......9....7.............123...9..456..2...789....1..4...8.73...9...........
5...6.2.9..........1.....3....123.7.8..456......789.............73............8.5
5...7..........19........3...9123.6....456......789...7.......8..39.............5
5...9..........7........13....123...9.2456......789..........98.7.3.............5
5...9.....9.....7........3...6123......456......789..4......9.8......5....23.....
5..29...................73....123...8..456......789....1......2.73.............89
5..6...........17.8.....3...4.1237.....456......789.............7..3......9.....5
5..6...........17.8.....3...4.1237.....456......789.......3.....7.........9.....5
5..6...........24.8......3..4.123......456......789.............7.23..1.........5
5..8...........1....9....3....123.9..8.456......789....1....2.8..3..............5
5.2.........6..17.............123...9..456..8...789....1.8.............9.......35
5.2.3...........7...1....9....123.6....456......789.......1...8.76..............5
5.6............1.........3....123.6....456....1.789.....23......7....9.....6....5
5.6............17.2......3....123.....2456..8...789.............7.....1.....6...5
5.6.9....9......7........3...4123......456......789.........9.8......5....23.....
5.8.........6..17.............123...9..456..2...789...........9.7.2...........3.5
5.8.........9..17...........96123......456......789.........3.8.7.2...........6..
5.9.........8...7.2......3....123...9..456......789...........9.7.3.....6.......5
5.9.6....6......7........3...4123......456......789.........6.8......5....23.....
51..........3...7.............123...9..456..1...789...........4.738...........9.5
52..4...................93....123...2..456..8...789.............13........7.6...5
52..4.....9.....7........3....123.....8456......789..2....6...8.73...............
52..4.....9.....7........3....123.....8456......7892............73..........6.4..
53.............1.....6...7....1234..9..456......789....17..........3...........95
53.............1.....6..4.....123......456......789..3.9......8.74..........3...5
53.............1.....6..4.....123......456......789..3.9..3...8.74..............5
53..........2...7........3...7123......456......789.....3.....8.71.........6....5
53..........6..1........4.....123......456......789..3.9......8.71..........3...5
53..........6..1........4.....123......456......789..3.9..3...8.71..............5
54............21.............71236.....456......789..........58..3..1.....2....9.
54............217.............123...9..456..3...789...........4..7........2...9.6
58..............7.......13...7123.4....456......789...........8.73..........6...9
59..........2...7........4....123...9..456..3...789...........9.72............6.5
59..........2...7........8....123...9..456..3...789...........9.72............6.5
6...4..........17..1.....3....123...2..456......789.....8.....6.73..............5
6...4.....1....97.............123...9..456..2...789.....3.....4.7...........6...5
6..51...........7........3....123...9..456..1...789......6.......3..7.....2.....5
68.............1........73...7123......456..8...789.............73........9.6...5
69..............7.......13...7123.4....456......789...........8.73..........6...9
8...............7........31...123...2..4568.....789....1........7..9........6.2.5
8...4.....3....97.............123......456.1...2789...........8.7...........6.2.5
8...9...........7........3...7123.6....456.....1789...........8.73..........1...5
94.............1........73...7123......456..9...789.......6...8.73........2......
.......94.........62..........1237..9..456......789.......6..5...4...2...1....6..
..........1.9..7...26.........123...8..456...6..789....7.5............9........86
.......89.5.......6...........1235..8..456......789.......6..4...9..8....1....7..
.......89.5.......6...........1235..8..456......789.......6..7...9..8....1....4..
...3..1....2........9...5.....1234.....456.2....789...17.8............9.3........
...3..1....8.....7..9.........123......456.8....789..517.............29.3........
...3..1....8.....2..9.........123......456.8....789...17...........4..9.3.....7..
...3..1....8.....5..9.........123......456.8....789...17...........4..9.3.....7..
12.......3.....6.....2..5.....123......456......789.....5....3...49....2........1
69.......7...............48..4123......456......7896....5.3...........2.......9.6
13.....7.7............4.......1234.....4562.....789.....5.......24.............91
17.....9.9............4.......1234.....4562.....789.....5.......24.............71
1....7.8.9............4.......1234.....4562.....789.....5.......24.............71
1....7.8.3............4.......1234.....4562.....789.....5.......24.............71
1....7.8.6............4.......1234.....4562.....789.....5.......24.............71
.......186.......7.4..........123...1..456......7893....8.1.....2....4.........6.
......2...46..8....8.......7..1235.....456......789..........98...2.........7...6
......4..5.2.....6..93........123....3.456......789....1..6.....4..............29
.......85.9..7................1239..8..456......789..........6..35..8....2....7..
.......75.9.8.................1239..7..456......789..........6..35..7....2....8..
.......85.9..4................1239....8456......789..........6..35..8....2....4..
...3..1.56..........9.......5.123......456......789.2..3.5.....8......9......1...
93.......7.....8......1.......1235.....4561.....789..........9..51...........4.6.
1.......2.....4......5.....8..123......456......789.4......87....4....6...5.....1
.....14....2...8..9...........123......4561..6..789....4...........6...9..1....7.
.......65........9..13.......7123......456......7893...........8..2.....59......6
...........1.....7.....5.3....123.9...84562.....789..............2...1.8.3...7...
...........1.....7.....5.3....123.9...84562.....789.........1....2.....873.......
......6.........3..715.......5123......456......7894..6....4....2.....5.........1
................1..9.5..6....4123......456......7895.......2.4..5......168.......
59.......8......2....3...1...4123......4567.....7895.......58....1...............

14........3.............57....123..4..7456.2....789.....6.............8....3....1
1..2.....8...............5....123......456.7.2..789.........1.3..6..7.....4.....2
1.....8...........9....2.....6123.....2456......7891....58.............9.......32
13.......7.....5.......48.....123......4561.....789.....8..............7....7..36

........1..2.....58...37......123......456...4..789.....15.....6.....3........9..
.......81.5............8..7...123....3.456......789.....1.4.......5..4....8...3..

14.5...........6..3.....2.....123......456.....5789...9.6..2...........1........4
1........78....6.....5..4.....123.....3456......789..........8...4....2......8..1
12......53............4.9.....123......4567.....7896....6........9.........3....1

111 Horizontal Line 9plus12s - EDIT and two more is 113 and two more is 115 and two more is 117 and two more is 119
and two more is 121 ............... and one more is 122

Hidden Text: Show

Code: Select all

123456789.......1.....3................1...2..36..............5.....76.348.......
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123456789.......1.....3................1...9..36..............5.....76.328.......
123456789.......1.....3................1...9..36..............5.....76.348.......
123456789.......2.....3................2...9..36..............5.....76.348.......
123456789.......4.....3................2...7..36..............5.....96.328.......
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123456789......1....4........9.....6...178......2......1............3..4.7.......
123456789......1....5.........1........278.....9.....6.....3..5.1........7.......
123456789......3.....2.......5..........786..4.2..............5........4.7...3...
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123456789.......5.4..........5....63............2....8..8.6............4.....12..
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1234567897...........2..5..2.5....................3.7...8..7...........4.....12..
123456789............21..........1.4..6..9...........22.........8...3.7........5.
123456789............21.........86............1.....246.8..3...........1.......5.
123456789........5....1.........8.7..4....1...5.........8..............46.7..2...
123456789.......3....21.........8...6........41......2..8..7...........4.......1.
123456789.......3....21.........8...6........45......2..8..7...........4.......5.
123456789.......3.5...9.........8............49......5..8..7.......1...4.3.......
123456789.......4.....1....7.4......6............8...2...3.7....9......1.....4...
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123456789......5......2........8....69......34..........8..7......6....4..5......
123456789......5......3........8....69......14..........8..7......6....4..5......
123456789.....7.3..6............8.......3...64.......273...................2....1
123456789.....9.........3........5..6....4...49.........8.............14..5.3....
123456789....9..3....2.......1..3..................9.26....7.1..9....5...........
123456789..8..........1.........83...1........5.........4..7.........6.2.......51
1234567896...........2..........41....2.......59......3....7..........1........52
1234567897............8........286...........45.......3.6..7...................58
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123456789....9....4..........9....62...1.............8..8.2...........4.....6.1..
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123456789....8....4..........1....56.......9....2.......5.9.......3..2.4.........
123456789.......1.....3.....5....4..2....9.7...........4....3.5.........8....1...
123456789.......1.....3.....5....4..9....8.7...............23........5..8....1...
123456789.......1.....3.....9....4.......8.2............6...3.......25..8....1...
123456789.......1...4.3........7....8....9.6.......5....7...3.......8........1...
123456789.......1...4.3........7.....8...9.6.......5....7...3.......8........1...
123456789.......1...4.3........7....86.....2.......5....7...3.......8........1...
123456789....1...........6.7.8........6..........4...1...6.7....5...9..2.........
123456789...........4.3......5.1...4.....7.6..................5.8.......76...8...
1234567899......1.....3......5...4.......8.6...7............3........5..8....1...
123456789...1.............3....9.........3...6.....4........62...5.......39.8....
123456879.............3........68.1...4....2...5............3.5.....9...7....2...
123456789..........6..3....7.8........4..........9...3...8.7.1..9............1...
123456789.......1...6.3..........5..9...81..........4...5...3.......9........7...
123456789.......31...........9.81.............5....4....1..8....4....5..........6#mauricio
123456789........1...2.......8..1.........4.5.........54....2.....7.8.6..........
123456789........1...2.......8..1.........4.5.........54....2.....7.3.6..........
123456789........1...2.......8..1.........4.5.........54....2.....8.7.6..........
123456789........1...2.......8..1.........4.5.........54....2.....3.7.6..........
123456789........1...2.......8..1.........4.5.........54....2.....8.7.3..........
123456789........1.5..8......7..1.......4..5...9...........7..6..........8.....4.
123456789........1....2.........1........9....5....2......6.5..9.....3....4..7...
123456789........1....2.........1........9....5....2......7.5..9.....6....4..3...
123456789........1....7.........1.96........8..5......6....2.........54...8......
123456789........1....7.........1.36........8..5......9....2.........54...8......
123456789........1....2.........1.....5...2....9..8......63.5..8.......7.........
123456789........1..5.3....79...1..........4.8.............7......8.......4....5.
123456789........1..5.3....79...1..........4.8.............7......8.......4....3.
123456789........1..5.3....97...1..........4.8.............7......8.......4....3.
123456789........1..5.3....97...1..........4.8.............7......8.......4....5.
123456789........1..53..........1.....8....3......9...7.....9.6...8.......4......
123456789........1..........6...1..........3...9...54......7..2.......6...53.....
123456789..8.....1..............1......3....854.............52...9..7..........4.
123456789..7.....1....8.......3.1..7.....9....5.......9.1............52..........
123456789.5......1...8.........21..............4....6.4.76.............2..9......
123456789........1...2.....9....1.........5........2......98....7......6.54......   
123456789........1.4..2.........1........7....5.....3.7........9...3........4..2.
123456789........1...2..........1.......89....6....4..8.1........4............6.7
123456789........1...2.......9..1.........45..........54....2.....9.7..3.........#mauricio
123456789....8...1.9..........2.1........7.....6....5......2..7.........8.5......
123456789........1..5.........8.1.............4....5..98..4........6.31..........
123456789........1..5.........8.1.............4....5..98..4........7.31..........
123456789........1..7.........8.1.............5....6..98..4........6.31..........
123456789........1....2.........1..7..2....5....9.................23..4.97.......
1234567897.......1.........6....1......3...4........3......7..6.842..............
123456789..8.....1....7.......3.1..8.....9...5........9.1............52..........
123456789..8.....1....7.........1......3.9..85........9.1............52..........
123456789........1...8.....9.4..1..................53......4..8.5.......73.......
123456789........1.8.......9....1.......7.32..........7.9.....6....2....5........
123456789........1....3.........1........92..7.5...3........5....6.......9...7...
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123456789........16............91........5...2.....3....9.......8..3.......2..6..
123456789.....2..1.............31..864..................1.8.......5...2.......6..
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123456789........1.....2....6....2.....89..................74..8.91............6.
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123456789........1..............8..5..7...2....49.....5..............4..89...3...
123456789........1..............8..4..7...2....59.....4..............5..89...3...

123456789..9.....1...............25......1.....6.7.........9...4........25.....4.
123456789.7......1..............1.....5.........7.9..6....8.42........5..1.......

123456789........1............5....36........79.......8.....6.....9........23..4.
123456789........1.....2........8..3.........47..........7...2...8....7...5.9....

123456789........14............956.......3....8.......9.....5.......2.....18.....
123456789........1....9.........1..........5..6.8.24.......3..7.4.......5........

123456789........1.....7................2...8..6....4.....3....5.....6..2..81....

C

[blue]

Here are a few more of these.

Box form (total --> 154):

Code: Select all

.................1.45.3.......123.5..9.456...4..789.......4.9....1.....67........
................14..2.68......1236.....456....4.789.......1....3.6.....99........

Row form (total --> 133):

Code: Select all

123456789.................1.......2...7..1....8....4.....2.......9.....7.3.84....
123456789.................1.......4......7.2...8.19........3...2..8.....4.....5..
123456789.................1.......4....9.2.....8...6.....58...2..97......6.......
123456789.................1......45......9.2...6..........38..7.1........4.5.....
123456789........1.....2................1..6..4....2........5..8.......49...3...7
123456789........1.....2..........2........6...9.1.......37..4...8.......6......5
123456789........1.....7.........4.......2.7.9.8..........3...8...9......7....2..
123456789........1.....7.........4......79.....5....6....3...5..4.......7.......3
123456789........1.....7.........4....5....6.9...7.......3...5..4.......7.......3
123456789........1.....7.........6......2..1...98.........3......6...4...8...1...
123456789........14....2...............7.8.2.5...........1....5.7.8.....6........

[coloin]

That is a great effort ....they are hard to find after all these years !!
I think I searched for these by random generation of an overwhelming amount of 9plus13s with {-1} search -> 8plus13s / 9plus12s

Is that [ somehow] an exhaustive search ? or how ?

I liked the way you opti-morph the puzzles.. keeping the first row/ box 5 as 123/456/789 -> a resultant minimal morph.

[blue]

I think I searched for these by random generation of an overwhelming amount of 9plus13s with {-1} search -> 8plus13s / 9plus12s

Is that [ somehow] an exhaustive search ? or how ?

It wasn't an exhaustive search. I did more or less what you did.
I kept a record of the 9plus13s, and made sure that each one got {-1,+1} and {-2,+1} tested. The 9plus12s got {-1,+1},{-2,+2} and {-1,+2} tested.
I also did a thing where I look for small unavoidable sets in the solution grids that include two or more puzzle clues, and try changing the clues to match the alternate fill for the UA set, to see if that produces a valid puzzle. It doesn't have a large yield.

I did look into an exhaustive search for the "9c box" case, but it was looking like best I could hope for was (~15) ~21 days to complete it, running 8 (physical) cores at 4.5 GHz. (15 days if I throw my other machine at it too).

I liked the way you opti-morph the puzzles.. keeping the first row/ box 5 as 123/456/789 -> a resultant minimal morph.

Thanks

[coloin]

It wasn't an exhaustive search.....

I checked your new row and box puzzles with a {-3+3} ...... Suffice to say there were no new puzzles produced. There were no old ones either - not surprising as my puzzles I think had already been shown to be a closed group at the {-3+3} level.

Given that your new puzzles were found in addition to the ones found by my large scale vicinity search - its highly likely that all puzzles have been found.