The New Sudoku Players' Forum

[coloin]

!8 Clue puzzles ... they have an average of 2 clues per box !
Some 18C have a box distribution of 222222222 or 321222123 - and these all have 6 clues per band.

When some lobsidedness creeps in we get puzzles which have more than 6 clues per band and more than 6 clues in one of the diagonals

This puzzle has 13 clues in the diagonal [544] in [B1B5B9] ie a 13plus5 18C puzzle ..... probably there wont be an 18C with 14 clues in the diagonal. [see later]

Code: Select all

.2.3....4.59......78............2.......4...3....85.........95.......8.23..1.....

Code: Select all

+---+---+---+
|.2.|3..|..4|
|.59|...|...|
|78.|...|...|
+---+---+---+
|...|..2|...|
|...|.4.|..3|
|...|.85|...|
+---+---+---+
|...|...|95.|
|...|...|8.2|
|3..|1..|...|
+---+---+---+   13plus5 clues = 18C


A while ago I searched specifically for these and ended up with only 74 of them ... and no 14plus4 puzzle ... ive either got 10%,50%, or 90%

How many can others find ?

[JPF]

I'm having trouble understanding the assignment :

This puzzle has 13 clues in the diagonal [544] in [B1B5B9] ie a 13plus5 18C puzzle ... this is probably the maximum.

A while ago I searched specifically for these and ended up with only 74 of them ... and no 14plus4 puzzle ... ive either got 10%,50%, or 90%

and where are the 74 you found?

JPF

[coloin]

This puzzle has 13 clues in the diagonal [544] in [B1B5B9] ie a 13plus5 18C puzzle ... this is probably the maximum

ie there wont be an 18C puzzle with 14 clues in the diagonal boxes and 4 clues only in the other six boxes ..
a quick look only just revealed 21C 17plus4 puzzles and no 20C 16plus4 puzzles [so unlikely to be 14plus4]

we have found a few 21 clue 18plus 3 puzzles recently [and no 20C 17plus3 puzzles] here

Code: Select all

+---+---+---+
|..1|...|...|
|654|...|...|
|.87|...|...|
+---+---+---+
|...|..6|..3|
|2..|754|...|
|...|.21|...|
+---+---+---+
|...|...|75.|
|...|...|4.6|
|...|8..|2.9|
+---+---+---+  18plus3=21C


and where are the 74 you found?

I havn't posted them yet - that would be giving you the answers !

Am currently repeating the process... and have found one new puzzle ...

[coloin]

a quick look only just revealed 21C 17plus4 puzzles and no 20C 16plus4 puzzles [so unlikely to be 14plus4]

overnight a few 16plus4 found ...

Code: Select all

+---+---+---+
|12.|...|..7|
|34.|...|...|
|5.6|...|...|
+---+---+---+
|...|...|..3|
|...|26.|...|
|...|987|...|
+---+---+---+
|...|...|.8.|
|..8|...|695|
|...|..4|.1.|
+---+---+---+ 16plus4 20C

So therefore so far to summarise present tally [clues-in-diagonal plus n]

Code: Select all

18 plus 3 puzzles [21C]          17 only found
16 plus 4 puzzles [20C]          13 found [and increasing]
13 plus 5 puzzles [18C]          75 found [and increasing]
11 plus 6 puzzles [17C]           7 only found

Code: Select all

+---+---+---+
|...|.3.|..9|
|.42|...|...|
|57.|...|...|
+---+---+---+
|...|.1.|..8|
|...|7.4|...|
|...|6..|...|
+---+---+---+
|...|...|75.|
|...|...|.4.|
|3..|.62|...|
+---+---+---+   11plus6  17C


[JPF]

after a few KWH spent here are some 13 plus 5 puzzles [18C]:

Code: Select all

...............123..4..5..6....14......63......7.2..8..6.....7..8.......31.......
........1.......23.....4..5....6.......325.....4...7...2........5...84..639......
........1.......23.....4..5....6.......325.....4...7...28.......5...94..63.......
........1.......23.....4..5....6.......325.....7...4...28.......5...19..63.......
........1.......23.....4..5....6.......325.....7...8...2........5...74..639......
........1.......23.....4..5....6.......325.....7...8...29.......5...74..63.......
........1.......23.....4.5.....21......36......4...7...1...54...28......63.......
........1.......23.....4.5.....21......36......4...7...1...84...2.......635......
........1.......23.....4.5.....3.......52......1.6.7...8...94..27.......35.......
........1.......23.....4.5.....35......26......7...1...38.......5...14..62.......
........1.......23.....4.5.....6.......235.....7...8...38.......5...79..62.......
........1.......23.....4.5.....6.......325.....7...8...39.......5...84..62.......
........1.......23..4..5..6....2........4.7.....316....3.......51.......7....84..


JPF

[coloin]

Yes they are there in my clutch ... but difficult to find. Thanks.
However with more advanced and extensive methods more have been found !

I have altered the post topic as maybe more descriptive and reasonable ....

Update with the script still running

Code: Select all

24 plus-12 minimal puzzles [36C]            5 found
24 plus-3  minimal puzzles [27C]         5174 exactly found
18 plus-3  puzzles         [21C]           17 exactly found
16 plus-4  puzzles         [20C]          782 found [and increasing]
15 plus-4  puzzle          [19C]            1 found
13 plus-5  puzzles         [18C]          107 found [and increasing]
11 plus-6  puzzles         [17C]            7 presumed exactly found

Even with more 16 plus-4 puzzles found it seemed that they were precluded- until one emerged .....
Will leave it open for a few days for anyone to have a go at finding it - Good luck !!!

[m_b_metcalf]

I must confess that I'm completely confused about what you're both searching for. Where does 18C come into it? What about 10plus9? Could someone please clarify a little?

thanks,

Mike

Code: Select all

 . . . . 4 . . . 9
 2 1 . . 5 . . . .
 3 . . . . 8 . 6 .
 . . . 1 . 6 . . .
 8 . . . . . . . .
 . . 4 . . . . . 8
 . . . . . . 5 3 4
 . . . . . . . . .
 7 . . . . . 6 1 .  10plus9  19C

[coloin]

Code: Select all

+---+---+---+
|xxx|...|...|
|xxx|...|...|
|xxx|...|...|
+---+---+---+
|...|xxx|...|
|...|xxx|...|
|...|xxx|...|
+---+---+---+
|...|...|xxx|
|...|...|xxx|
|...|...|xxx|
+---+---+---+  Diagonal box pattern


All 18C puzzles have at least 6 clues in one or more of the 6 diagonal box patterns.
In unsymmetrical puzzles ,commonly there is one diagonal which has more clues than other diagonals. Usually there is one diagonal which has most.

With regard to the 18C distribution
There are puzzles found for - 6plus12, 7plus11, 8plus10, 9plus9, 10plus8, 12plus8, 11plus7,12plus6, and 13plus5. Only 13plus5 is rare !

Here is a 13plus5 18C puzzle with 13 clues in the B159 diagonal and 5 other clues

Code: Select all

+---+---+---+
|.2.|3..|..4|
|.59|...|...|
|78.|...|...|
+---+---+---+
|...|..2|...|
|...|.4.|..3|
|...|.85|...|
+---+---+---+
|...|...|95.|
|...|...|8.2|
|3..|1..|...|
+---+---+---+  18C   There are 13 clues in the diagonal boxes B1B5B9 and 5 others in B2B3B4B6B7B8

With regard to the 19C distribution
All 19C puzzles have at least 7 clues in one or more of the 6 diagonal box patterns.
There are puzzles found for - 7plus12, 8plus11 ......... only 14plus5 and 15plus4 are rare

Homework challenge hard search [whilst patterns game is inoperative] is for a puzzle with a 15plus4 clue pattern

Code: Select all

+-+-+-+
|4|1|0|
+-+-+-+
|1|5|1|
+-+-+-+
|1|0|6|
+-+-+-+  15plus4 pattern with 19C [at least one valid puzzle exists!]

Good luck again !!

[m_b_metcalf]

Now it's clearer what you're getting at. Nothing new to report, just near misses:

Code: Select all

153......42....6...6......7....64......183...9..............51.......9.8.7...2...  15plus5  20C
1..2....6.........4......35.....78....5.8......7.31....7...8.....9.....2......1.4  9plus10  19C

[JPF]

14 plus 5 are not so rare:
Here is a sample (226 19C)

Hidden Text: Show

Code: Select all

................12.....34.5....5.......126.....64..7...4...78..29.......51.......
................12.....34.5....65......12......74...8..23.......5...8.9.16.......
...............123.....4..5....15......3.6.....7.2..8..32.......6...7.9.81.......
...............123.....4..5....15......3.6.....7.2..8..32......4....7.9.81.......
...............123.....4.56.....78...12......53...........2.......586.....81..7..
...............123..4..5..6....6.......13.......7.4.8..2...8.7.53.......61.......
...............123..4..5..6....617.....32.......8......1...78..52.......63.......
...............123..4..5..6....64.7....31.......8......2...7.8.51.......63.......
........1.......2......1.34....2.......453.....5.6.7....7..85...26......94.......
........1.......2......1.34....2.......453.....5.6.7....8..75...26......94.......
........1.......2......3.45....1.......265.....6.7.8...17......82.......9....86..
........1.......2......3.45....1.......625.....6.7.8...17.......4...96..82.......
........1.......2......3.45....1.......625.....6.7.8...17......3....96..82.......
........1.......2......3.45....6.......415.....6.7.3....2..86...17......94.......
........1.......2......34.5....16......4.5.....2.7..8..4.......6....2.9.817......
........1.......2......34.5....16......4.5.....7.2..8..4.......6....7.9.812......
........1.......2......3456.....78...14......52...........1.......286.....8.4.7..
........1.......2......3456.....78...14......52...........1.......286.....8.4.9..
........1.......2...3..4.56....15......23......76..8...4.......12.......8.9...7..
........1.......2...3..4.56....15......3.2.....76..8...4.......12.......8.6...7..
........1.......2...3..4.56....15......3.2.....78..9...4.......12.......9.6...7..
........1.......2...3..4.56....15......7.2.....8.3.9...7.......12.......9.6...8..
........1.......2...3..4.56....15......7.2.....8.4.9...4.......12.......9.6...8..
........1.......2...3..4.56....15......7.2.....83..9...4.......12.......9.6...8..
........1.......2...3..4.56....51.......72.....83..9...67......12.......9.....8..
........1.......2...3..4.56....51.......72.....83..9...76......12.......9.....8..
........1.......2...3..4.56....7.......12.......8.39...3...98..24.......51.......
........1.......2...3..45.6....16......2.......578.4...4.......128......6....3...
........1.......2...3..45.6....17......25......86..4...4.......126......7.....8..
........1.......23.....145.....5.......326.....74..8...2........6...87..35.......
........1.......23.....145.....6.......235.....47..8...3........5...49..62.......
........1.......23.....145.....6.......235.....47..8...3........5...89..62.......
........1.......23.....145.....6.......235.....74..8...3........5...79..62.......
........1.......23.....145.....6.......235.....74..8...3........5...89..62.......
........1.......23.....145.....6.......235.....78..9...3........5...78..62.......
........1.......23.....145.....6.......325.....47..1...3........5...89..72.......
........1.......23.....4..5....16......3.7.....82..4...32.......7...98..41.......
........1.......23.....4.5.....1.......236.....75..8...6...14..53.......82.......
........1.......23.....4.5.....1.......236.....78..9...5...94..13.......26.......
........1.......23.....4.5.....1.......325.....56..4...1...78..26.......93.......
........1.......23.....4.5.....1.......326.....57..4...6...89..13.......92.......
........1.......23.....4.5.....1.......326.....75..8...6...14..53.......82.......
........1.......23.....4.5.....1.......326.....78..4...3...96..21.......85.......
........1.......23.....4.5.....1.......632.....75..8...5...84..16.......23.......
........1.......23.....4.5.....2.......165.....7.8.9...13......82.......9....76..
........1.......23.....4.5.....2.......3.5.....678.4...27.......3.......98...16..
........1.......23.....4.5.....2.......3.6.....178.6...28......6....54..9.3......
........1.......23.....4.5.....2.......3.6.....178.6...28......7....54..9.3......
........1.......23.....4.5.....2.......3.6.....178.6...29......6....54..7.3......
........1.......23.....4.5.....2.......315.....56..4...7...18..13.......62.......
........1.......23.....4.5.....2.......316.....57..4...6...89..13.......92.......
........1.......23.....4.5.....2.......316.....7.8.4...18.......4...36..29.......
........1.......23.....4.5.....2.......316.....78..9...6...98..13.......24.......
........1.......23.....4.5.....2.......34......167.8...62......8.3......9....54..
........1.......23.....4.5.....2.......356.....17..8...6...87..25.......39.......
........1.......23.....4.5.....2.......356.....67..4...1...87..53.......82.......
........1.......23.....4.5.....2.......361.....7.8.6...35......62.......9....74..
........1.......23.....4.5.....2.......361.....78..4...1...89..52.......63.......
........1.......23.....4.5.....2.......536.....17..8...6...87..25.......39.......
........1.......23.....4.5.....2.......631.....54..7...1...84..63.......72.......
........1.......23.....4.5.....2.......631.....57..8...1...74..63.......82.......
........1.......23.....4.5.....2.......635.....78..9...5...98..43.......62.......
........1.......23.....4.5.....21......3.......167.8...27......6....54..9.3......
........1.......23.....4.5.....21......3.......167.8...27......8....54..9.3......
........1.......23.....4.5.....21......3.......167.8...29......6.3......8....54..
........1.......23.....4.5.....25......3.......671.8...5...84..72.......93.......
........1.......23.....4.5.....26......3.7.....41..8...31.......7...94..82.......
........1.......23.....4.5.....3.......215.....67..4...1...89..29.......37.......
........1.......23.....4.5.....3.......216.....75..8...5...84..12.......36.......
........1.......23.....4.5.....3.......216.....78..4...6...98..52.......83.......
........1.......23.....4.5.....3.......245.....6.7.8...27.......8...14..39.......
........1.......23.....4.5.....3.......245.....6.7.8...27.......8...94..3.1......
........1.......23.....4.5.....3.......245.....6.7.8...27.......9...14..38.......
........1.......23.....4.5.....3.......245.....6.7.8...27.......9...84..3.1......
........1.......23.....4.5.....3.......245.....6.7.8...27......3........85...94..
........1.......23.....4.5.....3.......245.....6.7.8...27......3.1......6....84..
........1.......23.....4.5.....3.......245.....6.7.8...27......3.1......6....94..
........1.......23.....4.5.....3.......256.....17..8...6...87..29.......35.......
........1.......23.....4.5.....3.......261.....45..7...6...89..25.......34.......
........1.......23.....4.5.....3.......261.....78..4...6...98..52.......83.......
........1.......23.....4.5.....3.......265.....71..8...5...14..62.......93.......
........1.......23.....4.5.....3.......267.....18..4...7...69..28.......35.......
........1.......23.....4.5.....3.......526.....17..4...6...78..29.......35.......
........1.......23.....4.5.....3.......621.....78..4...8...59..27.......31.......
........1.......23.....4.5.....31......67......8.2.4...1...97...32......5.4......
........1.......23.....4.5.....35......24......6.7.8...27.......5...14..39.......
........1.......23.....4.5.....35......24......6.7.8...3.......279......5....14..
........1.......23.....4.5.....36......27......8.5.4...31.......6...98..72.......
........1.......23.....4.5.....4.......325.....67..8...5...84..72.......93.......
........1.......23.....4.5.....4.......326.....75..8...6...14..28.......35.......
........1.......23.....4.5.....4.......326.....75..8...6...14..53.......82.......
........1.......23.....4.5.....4.......326.....75..8...6...94..28.......35.......
........1.......23.....4.5.....4.......326.....75..8...6...94..53.......82.......
........1.......23.....4.5.....45......23......6.7.8...3.......278......5....14..
........1.......23.....4.5.....5.......326.....17..8...9...84..28.......53.......
........1.......23.....4.5.....5.......326.....78..9...1...94..35.......62.......
........1.......23.....4.5.....6.......127.....53..7...6...84..31.......72.......
........1.......23.....4.5.....6.......127.....83..7...6...94..17.......23.......
........1.......23.....4.5.....6.......137.....52..8...7...84..31.......92.......
........1.......23.....4.5.....6.......231.....45..7...7...86..25.......34.......
........1.......23.....4.5.....6.......231.....45..7...8...96..43.......52.......
........1.......23.....4.5.....6.......231.....75..8...1...54..63.......82.......
........1.......23.....4.5.....6.......235.....41..7...5...18..62.......73.......
........1.......23.....4.5.....6.......235.....41..7...5...89..62.......73.......
........1.......23.....4.5.....6.......235.....71..4...5...18..62.......93.......
........1.......23.....4.5.....6.......235.....71..4...5...89..62.......93.......
........1.......23.....4.5.....6.......235.....71..8...5...14..62.......93.......
........1.......23.....4.5.....6.......235.....71..8...5...84..62.......83.......
........1.......23.....4.5.....6.......235.....74..8...5...94..62.......73.......
........1.......23.....4.5.....6.......235.....78..9...5...84..62.......73.......
........1.......23.....4.5.....6.......235.....78..9...5...94..62.......93.......
........1.......23.....4.5.....6.......235.....78..9...5...96..43.......82.......
........1.......23.....4.5.....6.......237.....51..6...7...89..13.......42.......
........1.......23.....4.5.....6.......237.....65..4...7...89..53.......92.......
........1.......23.....4.5.....6.......321.....78..4...6...59..53.......82.......
........1.......23.....4.5.....6.......325.....67..8...8...14..31.......72.......
........1.......23.....4.5.....6.......325.....78..4...5...19..62.......93.......
........1.......23.....4.5.....6.......325.....78..9...5...94..62.......93.......
........1.......23.....4.5.....6.......325.....78..9...5...98..62.......73.......
........1.......23.....4.5.....6.......327.....51..4...7...89..42.......63.......
........1.......23.....4.5.....6.......327.....58..4...7...18..63.......82.......
........1.......23.....4.5.....6.......327.....58..4...7...19..42.......63.......
........1.......23.....4.5.....6.......327.....58..4...7...98..63.......82.......
........1.......23.....4.5.....6.......327.....81..7...6...94..21.......37.......
........1.......23.....4.5.....61......73......8.2.4...1...97...32......5.4......
........1.......23.....45......1.......326.....67..8...5...84..19.......23.......
........1.......23.....45......1.......326.....67..8...8...59..14.......23.......
........1.......23.....45......21......3.6.....4.7.8...37.......6...94..82.......
........1.......23.....45......26......3.1.....47..8...27.......6...94..83.......
........1.......23.....45......51......36......7.8..6..2...7.8..54......63.......
........1.......23.....45......51......36......7.8..6..54......63.......9....7.8.
........1.......23.....45......53......16......7.8..6..2...7.8..54......61.......
........1.......23.....45......67......32......45..8...2........7...94..365......
........1.......23.....456......64...27.......83..........29......3.....5..71.9..
........1.......23.....456......74...28.......73..........26......3.....5..89.7..
........1.......23.....456......74...28.......93..........6.......231...9..4..8..
........1.......23.....456.....1.......23......65..4...1...78..53.......72.......
........1.......23.....456.....1.......23......75..4...1...89..53.......82.......
........1.......23.....456.....1.......235.....7...8...5...64..12.......34.......
........1.......23.....456.....1.......237.....45..8...3........7...64..21.......
........1.......23.....456.....1.......237.....56..8...2........7...54..63.......
........1.......23.....456.....1.......237.....68..9...3........7...94..21.......
........1.......23.....456.....1.......326.....57..8...3.......27.......9....54..
........1.......23.....456.....1.......326.....75..4...3.......52.......6....89..
........1.......23.....456.....1.......327.....56..8...3.......12.......7....54..
........1.......23.....456.....2.......3.6.....78..9...6...14..82.......93.......
........1.......23.....456.....2.......316.....75..4...3.......52.......6....89..
........1.......23.....456.....2.......346.....17..8...3.......27.......5....84..
........1.......23.....456.....2.......356.....78..4...3........6...19..82.......
........1.......23.....456.....2.......36......17..4...6...58..72.......83.......
........1.......23.....456.....2.......36......57..4...8...91..63.......92.......
........1.......23.....456.....2.......36......57..8...6...14..72.......93.......
........1.......23.....456.....2.......367.....1...4...7...58..28.......36.......
........1.......23.....456.....2.......367.....1...4...7...89..25.......36.......
........1.......23.....456.....2.......367.....1...4...7...89..29.......36.......
........1.......23.....456.....2.......367.....78..4...2........8...57..63.......
........1.......23.....456.....2.......367.....85..4...2.......63.......7....98..
........1.......23.....456.....2.......371.....65..8...3........7...64..92.......
........1.......23.....456.....2.......375.....68..7...3........5...94..72.......
........1.......23.....456.....2.......376.....85..4...3........6...19..52.......
........1.......23.....456.....2.......731.....5...8...1...64..73.......82.......
........1.......23.....456.....2.......731.....5...8...1...94..73.......82.......
........1.......23.....456.....2.......731.....6...8...1...54..73.......82.......
........1.......23.....456.....2.......731.....6...8...1...94..73.......82.......
........1.......23.....456.....2.......736.....45..8...3........6...94..72.......
........1.......23.....456.....21......3.......5.7.4...1...89...37......42.......
........1.......23.....456.....26......3.......47..8...35.......6...14..72.......
........1.......23.....456.....26......3.......578.9...3.......27.......6....54..
........1.......23.....456.....3.......257.....56..4...2........7...89..63.......
........1.......23.....456.....3.......26......17..8...7...54..28.......36.......
........1.......23.....456.....3.......261.....65..4...2........7...89..53.......
........1.......23.....456.....3.......265.....7...8...5...14..63.......82.......
........1.......23.....456.....3.......265.....7...8...5...94..63.......82.......
........1.......23.....456.....3.......267.....15..2...6........7...89..23.......
........1.......23.....456.....3.......271.....5...8...1...64..82.......93.......
........1.......23.....456.....3.......271.....5...8...1...94..62.......83.......
........1.......23.....456.....3.......271.....58..4...1...67...2.......83.......
........1.......23.....456.....3.......276.....51..8...3........6...89..72.......
........1.......23.....456.....3.......62......14..7...8...54..27.......36.......
........1.......23.....456.....3.......62......14..7...8...94..27.......36.......
........1.......23.....456.....3.......627.....1...4...1...89..52.......63.......
........1.......23.....456.....3.......627.....1...4...4...89..25.......36.......
........1.......23.....456.....3.......712.....5...4...4...87..23.......91.......
........1.......23.....456.....3.......712.....5...4...6...87..19.......32.......
........1.......23.....456.....3.......721.....5...8...1...64..73.......82.......
........1.......23.....456.....3.......721.....5...8...1...94..73.......82.......
........1.......23.....456.....31......72......5...4...1...87...39......2.6......
........1.......23.....456.....36......27......18..7...2.......13.......8....94..
........1.......23.....456.....36......27......5...8...27.......6...54..83.......
........1.......23.....456.....4.......326.....57..8...3........9...54..27.......
........1.......23.....456.....4.......326.....57..8...3........9...84..27.......
........1.......23.....456.....4.......326.....57..8...3.......27.......9....14..
........1.......23.....456.....5.......13......62..4...7...89..12.......43.......
........1.......23.....456.....5.......137.....6...8...7...94..13.......82.......
........1.......23.....456.....5.......236.....7...8...6...84..52.......93.......
........1.......23.....456.....5.......236.....7...8...6...94..52.......73.......
........1.......23.....456.....5.......237.....41..8...2........7...94..31.......
........1.......23.....456.....5.......237.....86..4...2........7...98..36.......
........1.......23.....456.....5.......237.....86..4...2.......63.......7....18..
........1.......23.....456.....5.......317.....6...8...7...94..13.......82.......
........1.......23.....456.....5.......326.....78..9...3........6...94..52.......
........1.......23.....456.....5.......327.....86..4...3........7...98..52.......
........1.......23.....456.....6.......23......17..8...7...54..28.......36.......
........1.......23.....456.....6.......23......17..8...7...54..28.......63.......
........1.......23.....456.....6.......23......75..8...5...84..23.......96.......
........1.......23.....456.....6.......231.....47..8...1...54...2.......37.......
........1.......23.....456.....6.......231.....57..8...1...54...2.......37.......
........1.......23.....456.....6.......231.....57..8...1...84...2.......37.......
........1.......23.....456.....6.......231.....57..8...2........9...54..37.......
........1.......23.....456.....6.......231.....7...8...1...64..37.......82.......
........1.......23.....456.....6.......235.....7...8...5...14..36.......82.......
........1.......23.....456.....6.......235.....7...8...5...14..63.......82.......
........1.......23.....456.....6.......235.....7...8...5...94..36.......82.......
........1.......23.....456.....6.......235.....7...8...5...94..63.......82.......
........1.......23.....456.....6.......237.....51..8...6.......23.......9....54..
........1.......23.....456.....6.......32......15..7...5...84..27.......63.......
........1.......23.....456.....6.......32......17..8...7...94..36.......52.......
........1.......23.....456.....6.......32......17..8...7...94..36.......82.......
........1.......23.....456.....6.......32......75..1...5...84..29.......63.......
........1.......23.....456.....6.......32......75..1...5...84..36.......92.......
........1.......23.....456.....6.......321.....15..7...2.......36.......5....78..
........1.......23.....456.....6.......321.....47..8...2........9...54..37.......
........1.......23.....456.....7.......23......81..4...6...59..12.......39.......
........1.......23.....456.....7.......231.....5...8...1...94..62.......83.......
........1.......23.....456.....7.......231.....56..4...1...89...2.......63.......
........1.......23.....456.....7.......231.....6...8...1...94..52.......83.......
........1.......23.....456.....7.......231.....8...4...7...59..41.......62.......
........1.......23.....456.....7.......235.....46..8...2........5...94..63.......
........1.......23.....456.....7.......235.....86..4...2........5...19..36.......
........1.......23.....456.....7.......236.....18..9...3........6...94..72.......
........1.......23.....456.....7.......236.....5...4...6...89..53.......72.......
........1.......23.....456.....7.......236.....5...8...6...84..72.......93.......
........1.......23.....456.....7.......236.....58..4...3........6...19..72.......
........1.......23.....456.....7.......236.....8...9...6...54..72.......83.......
........1.......23.....456.....7.......236.....8...9...9...14..27.......35.......
........1.......23.....456.....7.......238.....16..4...2.......63.......8....59..
........1.......23.....456.....7.......238.....96..4...2........8...59..36.......
........1.......23.....456.....7.......321.....5...4...7...68..83.......92.......
........1.......23.....456.....7.......321.....56..8...1...59...2.......73.......
........1.......23.....456.....7.......321.....56..8...1...89...2.......73.......
........1.......23.....456.....7.......321.....58..7...3.......72.......9....54..
........1.......23.....456.....7.......325.....8...9...2...14..65.......73.......
........1.......23.....456.....7.......325.....86..4...3........5...18..72.......
........1.......23.....456.....7.......326.....5...8...6...14..72.......93.......
........1.......23.....456.....7.......326.....5...8...6...84..53.......72.......
........1.......23.....456.....7.......326.....8...9...6...14..53.......72.......
........1.......23.....456.....7.......632.....5...8...6...14..73.......82.......
........1.......23.....456.....7.......632.....5...8...6...94..52.......73.......
........1.......23.....456.....7.......632.....5...8...6...94..73.......82.......
........1.......23..4..5..6....1.......2.6.....738.5...5.......128......6....4...
........1.......23..4..5..6....14......3.......672.8...5.......137......8....6...
........1.......23..4..5..6....17......2.......839.5...5.......129......7....4...
........1.......23..4..5..6....2.......3.6.....781.5...5.......328......6....4...
........1.......23..4..5..6....2.......3.7.....681.5...5.......328......7....4...
........1.......23..4..5..6....27......18......9.3.5...58......21.......7.....9..
........1.......23..4..5.6.....1.7.....326......8......2.......13.......65...79..
........1.......23..4..5.6.....16......42......57..8...3....7..216......7........
........1.......23..4..5.6.....16......42......57..8...3....7..216......8........
........1.......23..4..5.6.....16......72......58..9...3....8..216......9........
........1.......23..4..5.6.....17......2.......638.5...5.......128......7....4...
........1.......23..4..5.6.....27......38......9.1.5...5.......236......8.....9..
........1......23......4.5.....15......34......6..78...17......23.......4....69..
........1......23......4.5.....25......3.6.....7.8...9.38......6....7..492.......
........1......23......4.5.....3.......615.....62..7...32......41.......7....86..
........1......23......4.56....1.......37......8.2.9...19.......5...87..23.......
........1......23...4..5.6.....2.......316......7..8...37......5....84..61.......


I stopped the search of those 14+5

JPF

[JPF]

without using "more advanced and extensive methods"
I got this 15+4 puzzle:

Code: Select all

+---+---+---+
|12.|...|...|
|...|...|.3.|
|456|...|...|
+---+---+---+
|...|5..|...|
|.7.|..4|.8.|
|...|631|...|
+---+---+---+
|...|...|145|
|...|.8.|..9|
|...|...|6..|
+---+---+---+


JPF

[coloin]

without using "more advanced and extensive methods"

Using extensive methods... I had not found that one !!! Well done !

Here is the different one that I found !

Code: Select all

+---+---+---+
|..1|..7|...|
|.23|...|...|
|.4.|...|...|
+---+---+---+
|...|2..|..4|
|9..|16.|...|
|...|43.|...|
+---+---+---+
|...|...|.13|
|...|...|29.|
|5..|...|76.|
+---+---+---+   15plus4-19C-#2

[coloin]

without using "more advanced and extensive methods" I got this 15+4 puzzle:

Code: Select all

+---+---+---+
|12.|...|...|
|...|...|.3.|
|456|...|...|
+---+---+---+
|...|5..|...|
|.7.|..4|.8.|
|...|631|...|
+---+---+---+
|...|...|145|
|...|.8.|..9|
|...|...|6..|
+---+---+---+    15plus4-19C-#1


Thinking about it more ...... I cant see how you found this puzzle !!!
EDIT
taking a {-2+1}x2 on the known 18plus3 [21C] puzzles fails to provide
taking a {-1+2}x2 on the known 11plus6 [17C] puzzles also fails to provide

I take it that you didn't generate masses of minimal and non-minimal 15plus5 or 16plus4 puzzles ! like I have done - and I still haven't found your puzzle or others

The B159 maybe has a low sol count ? But it has at least 882 different +4 completions and no +3 completions ... so that cant have been the way either !

I think I've reached near the end of the 18C 13plus5 search ....144 puzzles found - initially I had only 74.

A very remote

Code: Select all

+---+---+---+
|123|...|...|
|45.|...|...|
|...|...|..6|
+---+---+---+
|...|736|...|
|...|8..|...|
|5..|...|1..|
+---+---+---+
|...|...|451|
|...|...|8..|
|..7|6..|...|
+---+---+---+   13plus5 #144


Status of search

Code: Select all

24 plus-12 minimal puzzles [36C]           40 found ..... 
24 plus-3  minimal puzzles [27C]         5144 exactly found
18 plus-3  puzzles         [21C]           17 exactly found
16 plus-4  puzzles         [20C]         3374 found ? 90% **
15 plus-4  puzzle          [19C]            2 found [and static]
13 plus-5  puzzles         [18C]          144 found [and static]
11 plus-6  puzzles         [17C]            7 exactly found

As a by-product there was generation of:
12 plus-6  puzzles         [18C]        41000 found  ? 95% **
444111111  puzzles         [18C]        12430 found  ? 95% **
11 plus-7  puzzles         [18C]      1600000 found  ? 75% **         ** guestimate made on % new puzzles found each time                                                                                     


Here is the gang of 144 13plus5 18C puzzles for posterity,
Perhaps I can group them together better ....

Hidden Text: Show

Code: Select all

.2...6....56......789.........59.......8..4..3...7.1.......1...........9.......85
.2...6...45.......789.........59.......8..4..3...7.1.......1...........9.......85
.1....6...5.......489.........59.......8.....6..2..7.......7.3......4..9.......85
.2....6...5.......389.........89.......5.....4..2..1.......4........7.39.......85
.4....6..65........89.........59.......8.....3..2..1.......1..3.....7..9.......85
.4....6...5.......789.........59.......8.....3..2..1.......1..3.....7..9.......85
.42...6...5........89.........59.......8.....3..2..1.......1.3......7..9.......85
.23...6...5........89.........59.......8.....6..2..1.......1.3......7..9.......85
.2....6...5.......489.........59.......8.....6..2..1.......4.3......7..9.......85
.2....6...5.......489.........59.......8.....3..2..1.......4........7.39.......85
.2....6..45........89.........59.......8.....3..6..1.......1..4.....7..9.......85
.2....3..45........89.........59.......8.....3..6..1.......1.4......7..9.......85
.24...3...5........89.........59.......8.....3..4..1.......17.......7..9.......85
.24...3...5........89.........59.......8.....3..4..1.......1.2......7..9.......85
.7....6...56.......89.........59.......8.....3..2..1.......1.3......7..9.......85
42....6...5........89.........59.......8.....3..2..1.......1.3......7..9.......85
.24...6...5........89.........59.......8.....3..2..1.......1.3......7..9.......85
.2....6...5.......489.........59.......8.....3..2..1.......1.3......7..9.......85
.2....3..45........89.........592......8.....3.....1.......1.4......7..9.......85
.74...6...5........89.........59.......8.....3..2..1.......6..3.....7..9.......85
..4...7..35........89.........59.......8.....6..2..1.......4.3......7..9.......85
12....3..74.........9........859.......8........6..1.......1.4......7..9.......85
..1...2..35........89.........59.......8.....6..4..3.......1.7......2..9.......85
.2....3..45........89.........59.......8.....6.....1.......1.4......26.9.......85
.1....6..45........89.........59.......8.....3.....7.......7.4......1..9......285
.2....6..45........89.........95.......8.....3.....1.......1.4......2..9......385
.2....6..45........89.........95.......8.....3.....1.......1.4......2..9......785
.2....6..45........89.........59.......8.....3.....1.......124......7..9.......85
.2....6..45........89.........59.......8.....3.....1.......134......7..9.......85
.2....6..45........89.........59.......8.....3.....1.......174......7..9.......85
.2....6..45........89.........59.......8.....3.....1.......1.4......72.9.......85
.2....6..45........89.........59.......8.....3.....1.......1.4......7..9......285
..2...6..45........89.........59.......8.....3.....1.......124......7..9.......85
..2...6..45........89.........59.......8.....3.....1.......134......7..9.......85
..2...6..45........89.........59.......8.....3.....1.......174......7..9.......85
..2...6..45........89.........59.......8.....3.....1.......1.4......73.9.......85
..2...6..45........89.........59.......8.....3.....1.......1.4......7..9......385
..7...6..45........89.........59.......8.....3.....1.......134......7..9.......85
..7...6..45........89.........59........8....3.....1.......134......7..9.......85
..7...6...54.......89.........59.......8.....3.....1.......1.4......7..9......285
.2....6...5.......189.........89.......5.....6.....7.......6.1......3..9......485
.732......5........89...........4..1....89..7.....5.........59.......8.34..1.....
.291....3.57.......8...........4.........2..1....85.........75.......8.26..4.....
.246....1.59.......8....................42..6....85.........95.......8.23..7.....
.2.6....7459.......8....................42..6....85.........95.......8.23..7.....
.2.1....4.59......38...........4.........2..1....85.........95.......8.27..4.....
.291....6.57.......8...........4.........2..1....85.........9........5823..6.....
.2.1....495........83.........3....6.....2.......85.........95.......8.27..4.....
.2.1....6.57......38............9........2..1....85.........7........8526..4.....
.2.1....3.57......68............9........2..1....85.........7........8521..4.....
.2.1....3.59......68............3........2..4....85.........9........8527..4.....
.2.1....6457.......8...........4...1.....2.......85.........75.......8.21..3.....
.2.1....7.59.......8...........3.........2..1....85.........9........8527..6...3.
.2.1....6.59.......8...........4.........2..7....85.........9........8526..3...4.
.2.1....6.59.......8...........4.........2..1....85.........75.......8.21..3..9..
.2.1....495.......38..........3....6.....2.......85.........95.......8.27..4.....
.2.7....1.59......68...........4.........2..7....85..........9.......8523..1.....
.2.7....1.59.......86..........4.........2..7....85..........9.......8523..1.....
.2.7....4.59.......81..........4.........2..7....85.........9........8523..1.....
.2.7......59.......84...........9..1.....6..4....85.........5........8926..1.....
.2.1....3.59......68...........4.........2..7....85..........9.......5823..6.....
.2.7....1.56.......89..........4.........2..7....58..........9.......8523..6.....
.2.7....3659.......8...........4.........2..7....85.........9........8523..1.....
.2.7....3659.......8............4........2..7....85.........9........8523..1.....
.2.7....4.59.......81..........4.........2..7....85.........95.......8.23..4.....
.2.7....4.59.......81...................12..7....85.........95.......8.23..4.....
.2.1....3659.......8............4........2..1....85.........9........8521..7.....
.2.1....6.59.......83..........4.........2..1....85.........95.......8.23..4.....
.2.6....4.59.......83...................12..6....85.........95.......8.23..7.....
59.......8.6......4..3..1......2........58........97....3.....9..7.....6.......85
59.......8........4.23..1......2........58........97....3.....9..7.....6.......85
.4....3...5.......289.........5.4......89....3.....1.......3.2......7.9........85
.2.3....4.59......78............2.......4...3....85.........95.......8.23..1.....
.7...3..4689.......5..........4..1.....98.......5...........259.......8.3....1...
.6.1......82......59............8.......95...7....4..3......8.7......95.4..3.....
.2.7....1659.......8...........3...7....9........85.........58....6..9.37........
..23....4.51......98............9.......4...3....85.........586......9..7..1.....
6..3....4.51......98............9.......4...3....85.........586......9....21.....
9..3....1.56.......84...........2.......4...6....58.........95.......8.2..76.....
.2.1....4.59......78............6.......7...3....85........8952......8..4........
..13....4.59.......8............7......26...3....85........895.......8..4.....2..
...3....4259.......8............7......26...3....85........895.......8..4.....6..
.2.3....6459.......8..........7.6...........4....85.........9........8527..4.....
.2.3....6459.......8............6...........4...185.........9........8527..4.....
...3...4..5.......689...........9......4....3....85.........59.......8.24..1..6..
.2.1....4.59......78...........9...1....4........85..................8523..7...9.
2..3....4.59......81............1.......4...3....85.........582......1....69.....
.2.3....1.87......65...........8......39.........65.........57.......8.24..1.....
.2.3....7.96......58............9.......85.....32...........86.......9.21..7.....
.2.1....4.59......78...........76...........3....85........8952......8..4........
2..3....7.59.......18...........1.......4...3....85.........582......1....69.....
.2.3....765........8..........7.6...........4...185.........85.......6..4.3....1.
..13....4.59.......8............9.......6...3...581........895.......8..4......2.
.2.3....4.65.......8..........134...........9....85.........85......86..4......1.
.2.9....1.87.......5............7.......2...3....85.........4........8526..3...7.
.2.3....4.58......79..........4........7.6.......9.5........85.......9.24..1.....
..13....4.59.......8............7......26...3....89........85........87.4......9.
.2.3....1.59.......84...........4...........3...285.........45.......8.76..1.....
.2.1....4.59.......87...................239......58.........51.......8.26..4.....
.2.1....3.59......78............85.....3........64..........95.......8.23..4.....
...1...4..59......38..........695...........3....8..........59.......8.21..7..6..
..47....6.85.......93...........2.......3...7....89.........9........83.2..5..1..
...1....4.59.......8............7......26...3....89........85........87.4......96
..21....4.59.......8............7......26...3....89........85........87.4......9.
..63....4.59.......8............7......26...3....89........85........87.4......9.
...2...1..59......38..........695...........3....8..........59.......8.21..7..6..
...1....4.59.......8...........7.......26...3....89........85.2......87.4......9.
.2.1....4.59......78...........87...........9...4.5.........873......5..1..2.....
...3....7.56......784...........85.....1.........45.........852......6..1..7.....
...3....7356.......84...........85.....1.........45.........852......6..1..7.....
...3....7.56......784...........85.....2.........45.........852......6..1..7.....
...3....7.56......784..........485.....1..........5.........852......6..1..7.....
...3....7356.......84...........85.....2.........45.........852......6..1..7.....
...3....7356.......84..........485.....1..........5.........852......6..1..7.....
...3....7.56......784..........485.....2..........5.........852......6..1..7.....
...3....7356.......84..........485.....2..........5.........852......6..1..7.....
...3....9.81......45...........1.......92........856........82.......5.39..4.....
6...3...4.59......78...........46.......2.5......17.........85.......9..4.2......
.2.3......45....8...8...........4.......9...1....58.........9........85.3..1..6.7
.2.4....7956.......8...........285...............65.........65.......2.43..7.....
.2.1.....95........83...5.......5.......7...4....83..........6.......8521..4.....
4.29......53....8..8............3.......6...7....58..........6.......8527..4.....
9..3....4.52......81..........6.1...........7....85.........586......1..3..9.....
........4956..8....82.........7.2...........3....85.........5........8921..3.....
..43....1.5.......689..............3....7........85..........57......8.21..9..6..
.2.3....1.5.......689..............3....7........85..........57......8.21..9..6..
..43....1.5.......689..............3....75.......8...........57......8.2..19..6..
.2.3....1.5.......689..........1...3.....2........5..........57......8.21..9..6..
....3...4195.......8............8......24...3....69.........95......58..4.....6..
....3...4195........8...........8......24...3....69.........95......58..4.....6..
1......37.5.......68...........16........2..9....85.........8........652..47.....
.1.....47.5.......689.........1.6........9..2....85.........98.......6....32.....
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1......475........689.........1.6........9..2....85.........98.......6....32.....
.1.....47.5.......689.........186........9..2.....5.........98.......6....32.....
.1.....47.5.......689.........186........9..3.....5.........98.......6....32.....
1......475........689.........186........9..2.....5.........98.......6....32.....
1......475........689.........186........9..3.....5.........98.......6....32.....
1....28..456........3.......7..........56...4...41.........8.........2.6.......41
2146.......9.......7....5......7.........2..4....58.........9...5....87....4....6
2146.......9.......8....5......7.........2..4....58.........9...5....87....4....6
3246.......9.......7....5......7.........2..4....58.........9...5....87....4....6
2146.......9.......8....5......7.........1..4....58.........9...5....87....4....6
123......45...............6...736......8.....5.....1........451......8....76.....