## Uniqueness Question

Post the puzzle or solving technique that's causing you trouble and someone will help

### Re: Uniqueness Question

http://hodoku.sourceforge.net/en/tech_ur.php covers the following:
Unique rectangles types 1-6
Hidden rectangle types 1-2 {avoidable}
B.u.g http://forum.enjoysudoku.com/the-bug-bivalue-universal-grave-principle-t2352.html
B.u.g lite (bug+1)

http://forum.enjoysudoku.com/post63659.html#p63659
Unique rectangle 1.1
{creates the use of UR's missing 1 candidate}

M. U. G http://forum.enjoysudoku.com/post21050.html#p21050
Aur http://forum.enjoysudoku.com/post22180.html#p22180
Revers bug http://forum.enjoysudoku.com/the-reverse-bug-t4431.html
Reverse bug lite http://forum.enjoysudoku.com/reverse-bug-lite-t4957.html

Chains/technique ± any uniqueness argument

Are all based around avoiding any one of the unavoidable sets
Which can be as simple as 4 cells and two digits to the monster of an empty grid.

I'll provide hyper links
To the list later tonight.
Last edited by StrmCkr on Sat Dec 24, 2016 3:36 am, edited 2 times in total.
Some do, some teach, the rest look it up.

StrmCkr

Posts: 862
Joined: 05 September 2006

### Re: Uniqueness Question

ghfick wrote:I suppose the empty puzzle has the maximum solution count. [combinatorics here?]. I wonder what the maximum solution count would be for a puzzle with 17+ givens?

The empty grid should have 6670903752021072936960 solutions, 5472730538 of them being essentially different (see here and here).
I guess, that it is not easy to calculate the maximum for puzzles with N givens (apart from trivial cases N=1 or N>76)

Could you please post a list of 100 puzzles with the first hundred solution counts?

Here is an arbitrary list:
Hidden Text: Show
.32.9...5..7.5..3........14..628.....5.6....3.4..35.....4......7.....65..9.1..... #1
1..7...2..7.48....6..5.3.4.3.1.....4.5..372........3......7.5.....9.1.7..683.4... #2
8.....6..5..21.3..1..3.7..5.6...8.....4.5..8.2.1...........5.2..589.4.7.........3 #3
.2.97..8.98..6...4...8...2..76.3.29.2..........329..455....4......3..7.........3. #4
..85.......6....289...3............6..9.7.28.....18..3.1276....7.5....4..8.9..752 #5
...9...6.8...4..13....1......2....4..7...45.16.8..2...2.4.3.8.......9....1....7.. #6
3.7.......6.....84.2.1.4.6.....1......18976......42.....84.....7.4.25....12..8.7. #7
..6.2.1........3.685......2.8..5647..37....1.5..8......9.26........917.8......... #8
.8..12...3...9..8.6.4....7..2.1..4....8...2...7.6..............865..9..3..9.....8 #9
.....67.8.5.2......4.....1..3..84.51...7..4.2..962....2..........4.....9.7.85.... #10
754..91.........5281.65.4...4...5...59.8.......6..2...4....17........6.....376..1 #11
.......966.1.32...........7..9......12....74...4..93.2.38.2.5.....9.78.......5..1 #12
.2.6...1......4.92..........6...385..........1...25.3.61..3...57...821.39.....74. #13
.....9.7.6..3....2.2.1......1..7...32..5...8..6.....91....428..1.5.3.9.....6..... #14
....9.7651..2......4.........2....4......93.....8479..9.31....68.53.6............ #15
....4.81.9...52......8...6..3.2.......4.9..81.....625...3.6...7....1.6.4.5....... #16
.7........38.1.2..6..98.4....7...5.49..4...3...1......1..67...9........3....9..6. #17
.......1....8.4..3......564.7.4....5.29..5.8.38...7..2......9785....6.......1.... #18
..8....7..39....4.71..9.8....3..7.18......9.35...3..642....6......5.4..73.....68. #19
...9..7..4.......86.94..1...1......23...7.8..2.53....4.....7..6..3......146..5... #20
...47.3.6....1...8.7.6.5...5.6.2....1.......9.4..9.8.76.5....8.......4.58....7... #21
...4......78....2.9.4..6....2......3.6....847..1.6........78.5.5.2..94....7.24..6 #22
.7.....5.......8..9..51..2........7.294.....1.3.69..84.......9...23....67..461.35 #23
.8.....957...81..4.69.2..3....2...1..5....3........9....8....2....4.85.63........ #24
......9.....65....9..8...47.4....6..8.1.63..5.....53..3.6.7.....82...........2..8 #25
.2......84..7........9...5...9....7.7...6..4...3.7456....3.........4...2.68.1.4.. #26
......7.6..4..1...........879.1.8...2........3...671...17..2......5..69193....5.. #27
7.2.....68.14.....3...9.....2.7...93..4..8.72..36.9.........35.2...8..1......7... #28
..1.9.65436........5.......7.3.5....28..4..7..9.8...2.....1.2.86.2....19..8265... #29
1.8.7....6......7..5.8...4......6.14.15..78...2...93.7.8.4..7.12........9.7...... #30
..5...2..3.....9.....49...6...5..7.9...3.1...5.2....48..78...5......6...81...4..3 #31
.8.1...27....5.....4...........2.5..8.....1...719.....9.5..82...1..69.4..24...96. #32
..8.....4.21...5.935..6....41...........5.48.......3.7..5.34...1.3..7.9.2.....6.. #33
8.5..4.13..............39.....2...8.....3....1.4..9...6..8..1..5.......6.9.7..43. #34
......947..734..6...4.62.....6.........6........57.32.3..4.1.9.579.........2...3. #35
1.4.....2..58.......3421......2..81.....89...29....5.6..2.364...6795.......1..... #36
42......6.........7...951.......7.25.739......48...6........5.1..2.4..6..8.53.... #37
6.93.8..5.1.....2...5.....92...5.8..48..1......62.....83.726..49...........8...6. #38
3...46..2.5.8..7.39...1.5....2.5...7..3.....8..42...1.....9...16.....8......8..2. #39
52..1......4....39..........3...52.6...83....19...4..3.5.1....8......56....4.87.2 #40
1....2..42...56.....93...76...4.......7......52...7.3...12..59....1....393...5... #41
.....19....34.7..........76...975...5.7.........2....9...1.9..3.28.....1..536.... #42
6..............5.....3..2187.3....8.4....8..7.9.2.....51.9........87.4..8...61... #43
9.......6156..78.....9..3.4.....9.1.......92..8.1......7..5..4..1.8...6...4...... #44
.....64.94..........53.8.1.68...2.5.75...91....1...9...........1....3.6839....7.. #45
..3...8....8....5.....6.9.24...2...88..4.6...37...5..91...8...3......5....5....76 #46
..6.52.9...7.8.......9...48...1.5.2.16..4.7..............3...8...8.96.......7.9.6 #47
....7.......8327....5....43...5.41....4...3.5.1.....6.682..75......1.9...4....... #48
4...285.7..2..1......5....1..69.4.8..2.8.7.359.8.....6....4...9.4....3..3......1. #49
4569..7..8......5..13.2.....6....1.....196342.2.....6....56..78.8...2...........5 #50
6.85.....543........1......8..1....57...9..81...8....6...2.651..3.97.64.....1.72. #51
6.2.18...1....5.23..32......16....3..4.5.1...2....9.....7........4..2........4965 #52
..24.5.7....8....295...3.1.5..68...72.7.......8.....9.8...6..43...7......1..5...8 #53
..1.5.......7....8.....8....9.......74.3...855..6713.9..9.82.3.......9.1...4.3... #54
....5.8...2..6....847.3..........659..........6318..4.3..8..5.7...7.....2.4...... #55
......8622..8....5.864..............3....4.9...19865...6..57....1...9.8..2..4.... #56
.....5.8..69.....78.....421....34..9.7.9.6.4....1.....4..3..........1.346.....8.2 #57
...4875.3...95612..6......9.3......49.......6....32.5.6..8...1...12...7...3...... #58
..31.....1..6..9.....8...7.9...6......478....875.9.436.9..2.........8..7...35...2 #59
...9.........7.6417.1..5...........8.1..6.29.97.4.........8.9..498..1....56..9... #60
...7.5.1...6......82....7.6...85...1.6.4.......5..72.86.....93.7........3...8.... #61
....5..9.6.....7..2.....1.5..76.......87..5.34....5....2...7..1.9.23.86....9..... #62
7..5.3...92...1...863.9.5.4.....79...4.8...5.1........2......76.....438...7....95 #63
.....5.....9....3....3.8764638.79.5....23.986...............1.....9....821.4..6.. #64
...1..5.31.6.34..9...6......79....2........7..6...2.4....9.813...8.4...63....1... #65
7.15...8....3...1.6.38..9....4..5....52.7.6........8.9..7.8....8..94............. #66
....51...2.83...4..164....7....1.4......83.5........6....9.5.28.....7..6.5.....9. #67
......6.8.17...95.....29.3.5....7..4.....6..33.6......2...1.3.764.......17.....9. #68
.....2.84......7....69.8..35......9..8...5....4..7.......4..237..3.....5..5...81. #69
....5...8..872..6....1.3..2...3..8..3..8..........1..4.5............697.6..4785.3 #70
.......8...4...31.....4....2.843....4.7.1.2....6...5.77.3....2....158...8.....16. #71
.1..95.3....1.........8.17....9.6........7.96.2.451...3.5.7.46..9.......7........ #72
........8...67.....7..5.94.6........432.1..5.8..79346.5...3............7.4.....91 #73
75.6...3.3...79..5..8..2...9.......4.2...1.5..61.......7..........5..3...96.8...2 #74
.5......1..4....9..834..........92..8.72...5.2...1..3..4..7....726.8.......3...82 #75
.1...82..964.....7......6..39.2.....4.6.93.1.1..6............48....25.....8.4.... #76
....5...9..54..2.7...9.68....2...16.51.2..........7.......8.39.48.....1.....3.... #77
.7.59............3....4..5..3...9..26.2.14....4..821.9.8....52...7.....612....798 #78
.3.........6....41...9.17..1.4.....729.8.7..38....6......2..8..5.7...3...4......6 #79
..3.8....4...2.1...1.7........6...38.7.4.....2.5.9...6...2.1..7.4...5..2......3.. #80
..861..7...9..4..63.5.......9.2..31..52...6..........8........2...7.9..4..7..3.59 #81
3..2.5..6.......5......68.3...63.9...76....1....81......5...68.78......51....4..9 #82
1....45...4..723..835...........1....8.......6......7....76.1.....4......72.5.4.. #83
8..3....25......9.......3.....9.75...89.5........38.79....6.....43....57.518..6.. #84
5....9........857....5....31.7.........3...8.4...95....3.7..65..54.1....6.8....2. #85
......19..5.823....2.9.4...5...3....8.3....7......1..3.....92..97...5.....52..8.. #86
.......9.4.2789...9......4....24..3.6.1....54..5..89....7.....526..5.7..5..1..3.. #87
......5.....34.1........973....6.2.5....89..43....4..6.31..5....489..6....9...4.. #88
..3..........769.3.6......1.5......7.87.4....3.....65..29...5......3.4......8.7.9 #89
.....73.....8...7..8.5..9....4......6...3..2.3....8..9..56..1...2..9........2.... #90
1..8.....2.7..9..8.....26916.........49...1...1.23....3.6.2.4.....4..3..9..6..... #91
..876.1.....5.9.2...9.1..6....49.8.6..46.........51...4......9..8.......7....25.3 #92
87..1.....6.....1..4567.2.8...5....1....62.9..1..9...7........9.....6...4....86.5 #93
..3.5..9....67.4..245.....7.......545.8............1.8...5.7.......3..6..7...4... #94
..85.3..........9.....9.4.....1.5.8.751.....43..7...65.94....3...5.16.......49... #95
.7.42.63.15.......4...9.....3...2...9..7....6.8..61..37.....56.31...6...2.6..9..7 #96
.4.8......7....6.956..73.1....5...4.1.....76........2....6..18.4.8....3.....3...2 #97
4...1...2.............254..9..56.2.47..1.4.6.56.........9....871..8.79.63........ #98
...1..3.....7..9......23.419.........6......8...8...27...9.4..6..3...5..74...68.9 #99
4....82...7.9......3.....1..24.5..3..........79.6.35..2..7.....1.32.576.....91... #100

Note that for each solution count you may have puzzles with so different solution paths as you have with unique puzzles.
eleven

Posts: 1873
Joined: 10 February 2008

### Re: Uniqueness Question

ghfick wrote:I now see we also have MUG [Multi-Value Universal Grave] and so I found:
layered-bug-lite-t4432.html
Again MUGs could be findable by humans but slightly tougher, for sure.
The examples found are very helpful. Is there a place that gives precise definitions for these terms?

Forming MUGs from BUG-Lite composites
Layered BUG-lite
You will see, that it is not trivial to decide, if a pattern is a MUG. I don't know, if there is an academic definition for a MUG, e.g. i think, that two independent MUG's "combined" would not be called a MUG.
But the basic property is (as for BUG lites), that whatever numbers/candidates you have outside the MUG pattern, there would always remain at least 2 solutions (inside the MUG cells).
eleven

Posts: 1873
Joined: 10 February 2008

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