Nick70 wrote:The search is finished and I confirm there are 36 puzzles on that pattern.
... .+. ...
... .+. ...
... .+. ...
... .+. ...
+++ +++ +++
... .+. ...
... .+. ...
... .+. ...
... .+. ...
gfroyle wrote:Does *your* exhaustive search program work by filling in the pattern in all possible (legal, inequivalent) ways, and then checking each one in turn?
gfroyle wrote:If so, then a 20-cell pattern is surely a gargantuan search?
Moschopulus wrote:Since we've done multiplication (the X pattern) what about addition (the + pattern) ?
- Code: Select all
... .+. ...
... .+. ...
... .+. ...
... .+. ...
+++ +++ +++
... .+. ...
... .+. ...
... .+. ...
... .+. ...
The search space is very small, maybe this can be done by hand...
coloin wrote:I dont think there can be 4 empty boxes though - even with 32 clues in Boxes 2,4,6&8. ?
000000000063000029780000104000149000000503000000726000601000045900000700270000830
000000000706000025052000896000052000000961000000304000900000080001000072370000410
000000005107000200560000194000040000000652000000397000702000600098000041015000900
000000005843000601120000380000819000000236000000070000009000078260000900017000003
000000006276000081340000705000800000000450000000127000167000009009000024008000650
000000007781000409420000380000090000000176000000240000650000730043000062090000100
000000009034000708758000320000487000000102000000360000290000006306000405500000190
000000010200000043397000608000540000000601000000092000805000020003000106061000980
000000010300000204754000630000894000000605000000023000840000070006000300005000429
000000017025000004860000200000067000000014000000938000408000509200000030309000071
000000017067000200892000360000010000000409000000568000056000070029000806308000024
000000020105000308493000005000170000000302000000864000836000497900000180010000600
000000030120000908509000400000406000000387000000009000410000670087000592050000100
000000030910000604528000900000045000000380000000710000059000207270000015060000040
000000037846000900020000060000540000000731000000086000590000300001000025064000810
000000038500000010094000762000312000000054000000068000020000674360000820100000000
000000039780000100069000527000975000000064000000301000302000090004000005871000402
000000040654000108800000320000830000000514000000609000420000006900000801307000290
000000050075000384060000072000950000000710000000384000180000006003000025200000431
000000050170000620029000187000905000000014000000270000600000500005000970800000312
000000057100000602694000030000807000000265000000039000009000570530000108076000040
000000084901000067700000501000030000000579000000864000030000006620000039840000050
000000089104000600870000150000697000000180000000302000300000006510000927260000800
000000089350000200102000450000003000000970000000125000489000007070000503530000028
000000090007000103134000607000876000000031000000209000648000320090000004300000705
Ocean wrote:
Sudokus with 4 empty boxes are not too common, but quite simple to generate. (Don't think I've seen 5 emtpy boxes though.)
*.*.*....
.......*.
*........
.*.*.*...
......*.*
...*.....
....*.*..
.*.....*.
*..*.....
1.2.3...........6.4.........7.8.6.........1.4...5.........1.2...6.....8.5..3.....
1.2.3...........6.4.........7.6.8.........1.4...9.........1.2...6.....8.5..3.....
1.2.3...........6.4.........7.6.8.........2.1...9.........1.3...6.....8.5..2.....
1.2.3...........6.4.........7.6.8.........2.4...7.........2.1...6.....8.5..9.....
1.2.3...........6.4.........7.6.8.........2.3...7.........1.3...6.....8.5..9.....
1.2.3...........6.4.........7.6.8.........1.4...7.........1.2...6.....8.5..9.....
1.2.3...........6.4.........7.6.8.........5.2...7.........2.1...6.....8.5..3.....
1.2.3...........6.4.........7.6.8.........2.5...7.........2.1...6.....8.5..3.....
1.2.3...........6.4.........7.6.8.........2.4...7.........2.1...6.....8.5..3.....
1.2.3...........6.4.........5.6.7.........9.2...3.........2.1...6.....7.5..8.....
1.2.3...........6.4.........3.7.6.........4.1...8.........1.2...6.....8.5..9.....
1.2.3...........6.4.........3.7.6.........4.1...8.........1.2...6.....7.5..9.....
1.2.3...........6.4.........3.6.7.........4.1...8.........1.2...6.....7.5..9.....
1.2.3...........6.4.........3.6.7.........5.1...3.........1.2...6.....7.5..8.....
1.2.3...........6.4.........3.6.7.........4.1...3.........1.2...6.....7.5..8.....
1.2.3...........6.4.........3.6.7.........1.5...3.........1.2...6.....7.5..8.....
1.2.3...........5.4.........6.7.8.........4.9...5.........4.2...5.....8.3..6.....
1.2.3...........5.4.........6.7.8.........9.4...5.........4.2...5.....7.3..6.....
1.2.3...........5.4.........6.7.5.........1.4...1.........1.2...5.....7.3..8.....
1.2.3...........5.4.........6.5.7.........6.4...8.........4.2...5.....7.3..9.....
1.2.3...........5.4.........6.5.7.........9.4...8.........4.2...5.....8.3..6.....
1.2.3...........5.4.........6.5.7.........4.9...8.........4.2...5.....8.3..6.....
1.2.3...........5.4.........6.5.7.........9.1...8.........1.2...5.....8.3..6.....
1.2.3...........5.4.........6.5.7.........4.9...6.........4.1...5.....7.3..8.....
1.2.3...........5.4.........6.5.7.........4.2...6.........2.1...5.....7.3..8.....
1.2.3...........5.4.........6.5.7.........2.4...6.........2.1...5.....7.3..8.....
1.2.3...........5.4.........6.5.7.........1.2...6.........1.8...5.....7.3..2.....
1.2.3...........5.4.........6.2.7.........8.4...5.........4.1...5.....7.3..6.....
1.2.3...........5.4.........6.2.7.........4.8...5.........4.1...5.....7.3..6.....
1.2.3...........5.3.........6.7.8.........1.9...5.........1.2...5.....8.4..6.....
1.2.3...........5.3.........6.7.8.........9.1...5.........1.2...5.....7.4..6.....
1.2.3...........5.3.........6.7.8.........1.9...5.........1.2...5.....7.4..6.....
1.2.3...........5.3.........6.7.5.........1.9...8.........1.2...5.....8.4..6.....
1.2.3...........5.3.........6.5.7.........9.1...8.........1.2...5.....8.4..6.....
Mmm... that shows up bias in the way Gordon is searching for grids. If we take your first experiment, on which Gordon "scored" 36/36, and this new one on which Gordon scored 28/34, then the joint maximum likelihood estimator of the true number of 17s is ~36020. At this MLE, the first result looks lucky to the tune of 1-in-15 (p-value 6.67%) and the second looks unlucky to the tune of 1-in-25 (p-value 3.95%). Not a very good fit.Nick70 wrote:I did a complete search on another 17-clue pattern:
...
gfroyle's list had 28 puzzles on that pattern. I found 34:
Red Ed wrote:]Mmm... that shows up bias in the way Gordon is searching for grids. If we take your first experiment, on which Gordon "scored" 36/36, and this new one on which Gordon scored 28/34, then the joint maximum likelihood estimator of the true number of 17s is ~36020.
Moschopulus wrote:
None has been found with 5 empty boxes. Discussed before on this thread:
http://forum.enjoysudoku.com/viewtopic.php?t=1180
kjellfp wrote:Moschopulus wrote:
None has been found with 5 empty boxes. Discussed before on this thread:
http://forum.enjoysudoku.com/viewtopic.php?t=1180
There is no Sudoku with 5 empty boxes. As mentioned in the link, there are two non-isomorphic cases to consider...
000
0XX -> No unique grid (3 empty boxes in a row)
XXX
00X
00X -> No unique grid
XXX
00X
0X0 -> Probably none.
XXX
00X
0XX -> Probably none.
XX0
00X X0X
XX0 -> Many unique grids [Also isomporph to 0X0
XX0 X0X
000
XXX -> Obviously no unique grid.
XXX
00X
0XX -> Probably none.
XXX
00X
XX0 -> YES (subset of case with 4 empty boxes).
XXX
0XX
X0X -> YES.
XX0