9plus12 game

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Re: 9plus12 game

Postby m_b_metcalf » Thu Dec 09, 2010 8:39 am

There's still room for improvement:

Code: Select all
 . 1 . 2 . . 3 4 5
 3 . . . 5 . . 6 .
 . . . . . . . . .
 1 6 . 5 2 7 4 8 .
 . 2 . 6 8 9 1 . .
 8 . . 3 4 1 6 . .   38 (9plus29)
 . . . 8 3 . . 7 .
 2 . . 7 . 5 8 1 .
 7 8 . . 1 2 . 3 .   ED=7.1/1.2/1.2

 . 1 . 2 3 . 4 5 .
 . 3 . 1 . 4 . 2 6
 . . . . . . . . .
 3 7 . 4 2 1 8 6 .
 8 . . 3 7 5 2 . .
 . . . 6 9 8 . 7 .   38 (9plus29)
 . . . 7 4 . 5 8 .
 7 8 . . . . 6 4 2
 . 5 . . . 2 . . 7   ED=8.5/7.8/7.6

 1 . . 2 3 . 4 . .
 2 . 3 4 . . . . .
 . 5 . . 6 1 . . .
 5 1 . 3 2 6 7 4 .
 . . 2 5 7 8 . . .
 7 . . 1 9 4 5 . .   39 (9plus30)
 3 7 . 6 4 2 . 8 5
 8 2 . 7 . . 6 . 4
 . . . . . . . 7 .   ED=7.3/7.3/2.6

 . 1 . 2 3 . 4 5 .
 3 4 2 . 5 . 1 . .
 . . . . . . . . .
 6 3 . 5 7 2 8 4 .
 . . . 6 8 9 . . .
 . 2 8 1 4 3 6 . 5   40 (9plus31)   !!!!!
 2 . 3 8 6 . 5 . .
 . 8 4 3 . . . . 6
 1 6 . . 2 . . 8 .   ED=7.8/1.2/1.2

Code: Select all
120340500500100003000050040600524370000678000750913406210760034070400602060030710  40               
120340500000500030500010004600254370000678000750193406210760043060400710070030602  40               
100230405002500036030040720360185240000329000201764053610450070700010564000000000  40               
010230450342050100000000000620573840000689000038142605203860500084300006160020080  40               
120340050500020413000000000610273840000689000802514036200860304008400061060030580  40               
012034500050001004000050030060325470075418306000967000007003602006040710021076043  40               


Regards,

Mike Mtcalf
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Re: 9plus12 game

Postby coloin » Thu Oct 27, 2011 9:55 pm

After a while i have now got 110 9plus12s

Code: Select all
...........8.9..3.......16....123......456.1...2789.........2.916.......4........
...........8.9.3.54......6....123......456.1...2789............16.............8.2
...........853..........16....123......456.....2789..........2316.......4.......5
..........69.........5..14.58.123......456......789.........2.64..3...........8..
..........69.........5..71....123....8.456..3...789..........267..3.............8
..........89.........5....44..123....3.456......7892...........1..6....7..2...8..
..........98.........5....44..123....3.456......7892...........1..6....7..2...8..
.........8......2....9..74....123......456...6..789..5..42.............6.3......8
.........8.2.........3..14....123......456...6..789..5.1.5.............6.......98
.........8.2.........9..14....123......456...6..789..5.1.5.............6.......38
.......1.8...........3..57..4.123......456...6..789....1.2...........6........9.8
.......2.8...........3..14..4.123......456...6..789....1.5.............6.......98
.......4..98.........5..1..5..123.7....456......789.........2.91..3...........8..
.......5.8...........3..24....123.....7456...6..789.....35.............6......9.8
.......94.5.......6...........1235..9..456......789.......6..7...4.9.....3....2..
.......97.5.......6...........1235..9..456......789.......6..4...7.9.....3....2..
......1........4.5..6..8...75.123......456......789....1.5............6........98
......1.....6..7..2.9.........123......456..2...789...41.5.............96.......8
......1.....8..7..2.9.........123......456..2...789...47...............95....2..6
......1.....8..7..2.9.........123......456..2...789...47............2..95.......6
......1...56.9.2...8.......9..1236.....456......789..........8........5.1....2...
......1..35..........6....7...1234...9.456......789.......3...........591.7......
......1.2.5........89.........1234...9.456......789..........9........561..2.....
......1.3.5........8..6....7..1236.....4563.....789...3............4..5.1........
......12..5.....3..8.9.....7..123.4....456......789...2............3.....6......8
......12.8........5.6.........123.7....456...6..789....1.2.............6......9.8
......2...5...8..3.8.......7..1236.....456......789..........98..7....5.2........
......21..5.....3..8.9.....7..123.4....456......789............2...3..........6.8
......21..5.....3..8.9.....7..123.4....456......789...2............3.....6......8
......27..5.....3..8.9.....7..123......456......789............4..23..1.........8
......27..5.....3..8.9.....7..123.4....456......789............2...3.....6......8
......27..5.....3..8.9.....7..123.4....456......789...2............3.....6......8
......27..5.....3..8.9.....7..123.4....456......789...3............3.....6......8
......27..5.....3..8.9.....7..123.6....456......789...2............3.....6......8
......41..5.....3..8.9........123.4....456......789...3........4..2...........3.8
......41..5.....3..8.9........123.4....456......789...3........4..23............8
......41..5.....3..8.9.....7..123.4....456......789............4...3......6.....8
......41..5.....3..8.9.....7..123.4....456......789...4............3......6.....8
......7.3.5..9..........1..7..1234.....456......789....9.....8........5.1....7...
.....21............54......7..1236.....456......789...3....1..........582......9.
.....41..8.......5..9.........123.4....456...5..789....1........47....9.........8
...2..1..8.6......5.....3.....123......456...6..789....1.3.............69.......8
...3.....5........68......5...1237.....456......789.......6..98..7........3....6.
...3....2.5........9.......7..1234.....456......789...3..2...........65.1......9.
...3..1....8.....92.6.........1234.....456......789...71..............9........86
...3..1...5.....8..........7..1234.....456......789.....7....9........583.1......
...3..1...54.......9......57..123......456......789..........9........561..2.....
...3..1..25...8....8.......7..1234.....456......789..........98.......5.1........
...3..1..5.8........9.........123......456.8....789....1.2......4.....9........68
...3..1..8.....7..2.9.........12357....456......789....1.5............9.........8
...3..1..8.9...3..5.........4.123......456......789....1..............9.....9..54
...3..1..8.9...3..5.........4.123......456......789....1..............94....9..5.
...3..1.2.7........59.........1234...9.456......789..........9........561........
...3..1.4..........85......7..1234.....456......789...................561..2...9.
...3..1.4.5........8.......7..1234.....456......789..........9........561..2.....
...3..1.7..8.......5.......7..123......456.9....789.............96....8....2..4..
...3..12.8...............4..4.123......456...6..789....1.5.............6.......98
...3..15.8........7.....4.....123......456......789..2..........1....5...5..7...8
...3..17..........8.....5.....123......456...6..789..2.1.5.............6.9......8
...3..17.......5..8...........123......456...6..789..2.1.5.............6.9......8
...3..17.......5..8...........123......456...6..789..2.1.5.......9.....6........8
...3..17..5........8.......7..1234.....456......789..........98........64..2.....
...3..2............56....9.7..1235.....456......789...3.......8.......6.1..2.....
...3..2....5.......89.........1234.....456......789...3............9.65.7......9.
...3..2....5.......89.........1236.....456....4.789...3............9..5.7.......9
...3..2...5..............8.7..1234.....456......789....8.....9.......65.1..8.....
...3..2...5........89.........1237.....456......789...3......9.....9.65.7........
...3..2...5...7....89......4..1237.....456......789...3............9..5.......1..
...3..2...5.6......8.......7..1236.....456......789...3......98.......5.1........
...3..2...59.................4123......4567.....789...........9.6......517.2.....
...3..2...59........8.........1237.....456......789...3............9.6.81.......9
...3..2...59........8.........1237.....456......789...3............9.6.84.......9
...3..2.7..8...1...5.......7..123......456.9....789.............96....5....2.....
...3..4...59.................4123......4567.....789...........9.6......517.2.....
...3..4...59........8.........1237.....456......789...3............9.6.81.......9
...3..7...5........82..5...7..1234.....456......789...........8.......564........
...3..7.1.5.6......8.......7..1234.....456......789..........98.......5.4........
...6..1........7..2.9.........123......456..2...789...47.5.............96.......8
...6..1....5.......89.........123..4...456.9....789...6.....2.........5.4...9....
...6..1....5.......89.........123..4...456.9....789...6.....2.........5.7...9....
...6..1....5.......89.........123..4...456.9....789...6.....3.........5.4...9....
...6..1....5.......89.........123..4...456.9....789...6.....3.........5.7...9....
...6..1....8......2.9......7..1234.....456......789....1.5............9........68
...6..1...5.....8............71234.....456......789...1......9........583.4......
...6..1...52..8....8.......7..1234.....456......789..........98.......5.1........
...6..1..35...............7...123....9.456.3....789.......3..2..........167......
...6..2....5.......89.........123..4...456.9....789...6.....1.........5.4...9....
...6..2....5.......89.........123..4...456.9....789...6.....1.........5.7...9....
...6..2....5.......89.........1234.....456......789...6............9..537......9.
...6..3....2.......85.........1234.....456....5.789...6.3.............58.......9.
...6..3....5.......89.........1234.....456......789...6............9..527......9.
...8..1........7..2.9.........123......456..2...789...41...............95....2..6
...8..1........7..2.9.........123......456..2...789...41............2..95.......6
...9..1........4..8.6.........123...9..456...6..789..2.4.5.............6........8
...9..17.......5..8...........123......456...6..789..2.1.5.............6.9......8
..3........2.9..........16....123....7.456.1....789.........2.946........1.......
..3.9......2............16....123....7.456.1....789.........2.846........1.......
..3.9......2............16....123....7.456.1....789.........3.946........1.......
..5........2.9..........16....123....7.456.1....789.........2.946........1.......
..7.......5......9...2........1234.....456....6.789...........8....9..564.2......
..7.9..3................16....123......456.1...2789.........2.916.......4........
..73..1..8.....4..5.9.......6.123......456......789....1..............9........58
.2.....4..9..........5..17....123...3..456......789.........2..4..6...........8.9
.26.......9....8.....5...4....123......456.7....789.........2.91.4..............8
.52..8......6..1...8.......7..1236.....456......789..........98.......5.1........
.6.........9.........5..14.58.123......456......789.........2.64..3...........8..
.8.3..2............59......4..1237.....456......789...3...............59..46.....
2..3..4............9.......8..1235.....456......789..........97........61.52.....
36...................5...4....123.9..8.456.....4789.1.......6.81..9..............
62........9....8.....5...1....123......456.7....789.........2.91.4..............8


cant be many more.............

C
coloin
 
Posts: 1547
Joined: 05 May 2005

Re: 9plus12 game

Postby m_b_metcalf » Fri Oct 28, 2011 12:50 pm

coloin,
Could you kindly check this list against yours for isomorphs? I generated it from your list (first serial number) using some ancient patterns game program.

Thanks,

Mike Metcalf

Code: Select all
...........1.2..3.......45....463......785.4...6192.........6.245.......7........ 1                 1
..........12.........3..45....567....6.831..7...492..........914..7.............6 5                 2
..........12.........3..45....567....6.891..7...432..........914..7.............6 5                 3
.........1.2.........3..45....426......578...6..913..7.4.7.............6.......81 9                 4
.......1.2...........3..45..1.453......167...7..829....4.6.............7.......92 12                5
.......1..23.........4..5..4..567.8....149......823.........6.35..7...........2.. 13                6
......1.....2..3..4.5.........346......782..4...195...71.8.............52.......9 18                7
......1.....2..3..4.5.........346......789..4...125...73...............58....4..9 19                8
......1.....2..3..4.5.........346......789..4...125...73............4..58.......9 20                9
......1...23.4.5...6.......4..1573.....823......964..........2........6.1....5... 21                10
......1.2.3........45.........2167...5.738......945..........5........382..1..... 23                11
......1.2.3........4..5....6..1725.....8352.....649...1............8..3.2........ 24                12
......12.3........4.5.........216.7....845...5..739....2.1.............5......9.3 26                13
.....12............34......5..2167.....347......589...6....2..........481......9. 40                14
...1..2..3.4......5.....6.....214......756...4..839....2.6.............49.......3 42                15
...1..2..3.4......5.....6.....214......736...4..859....2.6.............49.......3 42                16
...1....2.3........4.......5..6217.....748......593...1..2...........84.6......3. 44                17
...1..2.3..........45......6..2713.....348......659...................482..7...9. 54                18
...1..2.3.4........5.......6..2713.....358......649..........9........582..7..... 55                19
...1..23.4...............5..3.251......367...7..849....2.6.............7.......94 57                20
...1..23..4........5.......3..2617.....758......349..........94........87..6..... 62                21
...1..2............34....5.6..7214.....843......695...1.......9.......3.7..2..... 63                22
...1..2....3.......45.........6217.....735......849...1............5.93.8......5. 64                23
...1..2....3.......45.........6718.....835......249...1............5.93.6......5. 64                24
...1..2....3.......45.........6217.....735......849...1............5.93.6......5. 64                25
...1..2...34........5.........6217.....834......759...1............4.9.58.......4 71                26
...1..2........3..4.5.........346......781..4...295...73.8.............51.......9 78                27
...1..2........3..4.5.........346......789..4...215...72...............58....4..9 92                28
...1..2........3..4.5.........346......789..4...215...72............4..58.......9 93                29
...1..2........3..4.5.........267...1..385...5..941..6.3.8.............4........5 94                30
..1.2......3............45....413....6.785.4....692.........1.275........4....... 97                31
..1.2......3............45....416....7.835.4....792.........1.285........4....... 97                32
..1........2.3..........45....412....6.785.4....693.........2.375........4....... 99                33
..1........2.3..........45....412....6.785.4....693.........1.975........4....... 99                34
..1.2..3................45....463......785.4...6912.........6.245.......7........ 101               35
.12.......3....4.....5...6....617......852.9....943.........1.38.6..............4 104               36
.1.2..3............45......6..7328.....649......815...2...............54..69..... 107               37
12...................3...4....561.7..8.432.....4987.5.......8.25..7.............. 109               38
12........3....4.....5...6....728......651.9....943.........2.36.7..............4 110               39
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Re: 9plus12 game

Postby coloin » Fri Oct 28, 2011 8:24 pm

Well these two were the only ones not in my list of 110

Code: Select all
...1..2..3.4......5.....6.....214......736...4..859....2.6.............49.......3
...1..2..3.4......5.....6.....214......756...4..839....2.6.............49.......3


i probably havnt searched the removal of clues from the central box .....

C
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Joined: 05 May 2005

Re: 9plus12 game

Postby coloin » Thu Aug 09, 2012 10:49 pm

So I appear stuck at 112 of these box "9plus12"s. There are many many 9plus13s of this type though.

Of course there is another type

a vertical "9plus12" - and there are definitely rather more of these [easily found by looking at 17 clue puzzles with 5 clues in a column or row]
eg
Code: Select all
+---+---+---+
|97.|.1.|...|
|...|.2.|.85|
|6..|.3.|...|
+---+---+---+
|..8|24.|...|
|...|.5.|1..|
|...|.6.|9..|
+---+---+---+
|.9.|.76|...|
|...|.8.|.2.|
|...|.9.|...|
+---+---+---+

There is no danger of the 12 other clues ever being symmetrical around c5. Which means there is no symetrical 6plus12 - most examples found recently have been vertical "2plus16" here

For completeness
If we take a complete 9 clue rookery - a valid puzzle can be found with adding 13 clues [not 12]
Code: Select all
+---+---+---+
|1..|...|...|
|23.|1..|...|
|...|4..|1.5|
+---+---+---+
|.16|...|7..|
|..4|51.|...|
|...|.2.|.1.|
+---+---+---+
|..1|..7|...|
|...|..1|..2|
|...|8..|.31|
+---+---+---+ 9plus13


C
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Posts: 1547
Joined: 05 May 2005

Re: 9plus12 game

Postby coloin » Mon Aug 20, 2012 1:19 am

These 12 more bring the total to 124 [box-9plus12s].
Code: Select all
.......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

Found a little bit easier by using 2 versions of gridchecker

C
coloin
 
Posts: 1547
Joined: 05 May 2005

Re: 9plus12 game

Postby coloin » Mon Aug 27, 2012 4:01 pm

coloin wrote:There is no danger of the 12 other clues ever being symmetrical around c5. Which means there is no symmetrical 6plus12

here is my first 51 horizontal-9plus12s out of the pot !
Code: Select all
123456789.......1.....3................1...2..36..............5.....76.348.......
123456789.......1.....3................1...4..36..............5.....26.328.......
123456789.......1.....3................1...4..36..............5.....76.328.......
123456789.......1.....3................1...4..36..............5.....96.328.......
123456789.......1.....3................1...4..36..............5.....96.378.......
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.......
123456789.......4.....3................9...1..36..............5.....76.398.......
123456789.......4.....3................9...2..36..............5.....76.398.......
123456789.......1.....3................2...4..36..............5.....76.328.......
123456789.......1.....3......5.9.....6...8.2................3.5.8...7........1...
123456789.......1.....3......5.9.....7...8.2................3.5.....7....8...1...
123456789.......1.....3......5.9....6....8.2................3.5.....7...8....1...
123456789.......1.....3......5.9....7....8.2................3.5.....7...8....1...
123456789.......1...4.3........9....6....8.2................3.5.....7...2....1...
123456789.......1...4.3........9....6....8.2................3.5.....7...8....1...
123456789......1....4.........1........278.....9.....6.1............3..4.7.......
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...
123456789......3.....2.......5..........789..4.2..............5........4.7...3...
123456789......1.....2.......5..........789..4.2..............5........4.7...1...
123456789......1.....2.......5.....2....7.........1..3........543...9....1.......
123456789......1.....2.......5.....2....7.........1..6........5.1.......36...9...
123456789......1.....2.......5.....2....7.........1..6........5.1.......96...3...
123456789......1.....2.......5.....2....7.........1..6........546...9....1.......
123456789............2.....2.......57..9..........8.3...8..7...........4.....12..
123456789.......5.4..........5....63............2....8..8.6............4.....12..
1234567897............9..............49...........2.7.8...67...........4.....12..
1234567897............9..............49...........8.7.8...67...........4.....12..
1234567897............9.....45....................2.7.8...67...........4.....12..
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...
123456789......2......13........8...6........41......2..8..7...........4.......1.
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
1234567898...........2..........41....2.......59......3....7..........1........52

The first ones of this list were gleaned from the 17s with 5 clues in a row or column [28 of these] and the rest are close.

I am not sure ultimately how many there are ? 1000 [guess]

Notably none of these puzzles has this pattern in the first band
Code: Select all
xxxxxxxxx
........x
........x

which to me confirms how unlikely it is that a symmetrical 18-clue 9plus12 exists

C
coloin
 
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Re: 9plus12 game

Postby coloin » Tue Oct 02, 2012 8:43 am

coloin wrote:I am not sure ultimately how many there are ? 1000 [guess]

Well it seems that i overestimated how many more there are - and these next 11 werent found easily.

Code: Select all
123456789.....2...7.......1....9.....8.....2..6.....4.9...7...5.......6..........
123456789....9....4..........9....36...1.............8..8.6...........4.....2.1..
123456789....9....4..........9....62...1.............8..8.2...........4.....6.1..
123456789....9....4..........9....26...1.............8..8.6...........4.....2.1..
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...


If anyone was to contemplate furthur proof that a 16 puzzle doesnt exist - one could be tempted to suggest that 4 clues in a box/row/column is a non-starter.

C
coloin
 
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Re: 9plus12 game

Postby coloin » Wed Oct 24, 2012 11:24 pm

And 7 more
Code: Select all
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...


Getting harder to find now.
coloin
 
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Re: 9plus12 game

Postby coloin » Wed Jan 23, 2013 11:26 pm

Im obsessivly trying to find these puzzles - even a 9plus13 is hard to find de novo......

but, improving my method even furthur these 19 box-9plus12s brings the total to 143

Code: Select all
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...............

and the last one is unusual in that it has only 3 clues in one of the bands
Code: Select all
+---+---+---+
|59.|...|...|
|8..|...|.2.|
|...|3..|.1.|
+---+---+---+
|..4|123|...|
|...|456|7..|
|...|789|5..|
+---+---+---+
|...|..5|8..|
|..1|...|...|
|...|...|...|
+---+---+---+

C
coloin
 
Posts: 1547
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Re: 9plus12 game

Postby dobrichev » Thu Jan 24, 2013 12:54 pm

Congratulations for the new findings!

Are you still digging for the first rookery 9+12?

BTW I can't get the difference between "horizontal" and "vertical" 9+12's. Aren't they morphs of each other?
dobrichev
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Re: 9plus12 game

Postby coloin » Thu Jan 24, 2013 4:01 pm

dobrichev wrote:Are you still digging for the first rookery 9+12?

no, i seem to recall that 13 clues minimum are necessary to cover a 7-rookery/template combination

dobrichev wrote:BTW I can't get the difference between "horizontal" and "vertical" 9+12's. Aren't they morphs of each other?

yes they are the same !
just easier to handle the horizontal 123456789 initially. The vertical aspect was to pander to the search for 18s with vertical symmetry. This would appear unlikely with 6 clues in column 5.

Its either coincidence or design that there may be x2 more box9plus12s than horizontal9plus12s

Possibly a few more of each .........

C
coloin
 
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Re: 9plus12 game

Postby coloin » Thu Jan 24, 2013 4:17 pm

pm from mauricio
he has made 70 horizontal 9plus12s
bearing in mind there were 69 previously posted puzzles

Is it significant that only one was new ! ?

well done
Code: Select all
12345678945................7..........8..9.......4.2....9..8.......1.42..........

C
coloin
 
Posts: 1547
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Re: 9plus12 game

Postby dobrichev » Thu Jan 24, 2013 6:09 pm

Since most probably you use the same methods (vicinity search) and the same source structures (17's), it is not surprising that the results match.

143 box / 70 row / ~34 rookery 9+12s? Or 290/143/70, or 143/100/70?
dobrichev
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Re: 9plus12 game

Postby coloin » Fri Jan 25, 2013 10:18 am

dobrichev wrote:Since most probably you use the same methods (vicinity search) and the same source structures (17's), it is not surprising that the results match.

Well i think to get the last few ones you have to search the vicinity further ....... it depends how mauricio and i searched.
I think i searched for non minimal 6plus13s with alternating [-1+1]without the pattern and [-2+2] within the pattern.

I will revisit it after i have done with the box 9plus12s. I improved the search technique by generating 5plus13s. Performing a {-1+1} on these generates a 6plus12 if there is one ! and is a lot more efficient.

dobrichev wrote:143 box / 70 row / ~34 rookery 9+12s? Or 290/143/70, or 143/100/70?

maybe its 143/70/0

wrt to the rookery9plus12 search......
dukuso surmised from the 17s that you need minimum
17 clues for an 8 and 9 rookery
13 clues for a 7-rookery ...............
this is born out as there are 778 4 plus13s in the 17-puzzles, with no 5plus12.
finding new rookery9plus13s is fairly difficult - they tend to be more apart than -2+2
so maybe not hopeful for a rookery-9plus12 ?

C
coloin
 
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