Sudoku16 - Minimal Puzzles

For fans of Killer Sudoku, Samurai Sudoku and other variants

Re: Sudoku16 - Minimal Puzzles

Postby tarek » Fri Feb 22, 2019 9:21 am

The machine challenging collection would have:
1. TW only puzzles (no singles to start with, Euler’s classification in the 6x6 thread ;) )
2. High singles backdoor size

Possible extensions:
3. Low clue count
4. Filter with Human style techniques to have a high SE rating

With these puzzles it would be interesting to see how adding locked candidates/sets would add to the performance.

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Re: Sudoku16 - Minimal Puzzles

Postby Mathimagics » Fri Feb 22, 2019 9:32 am

m_b_metcalf wrote:That raises the question as to what is the purpose of generating puzzles at astonishingly impressive lightning speeds if only 0.1% of them can be solved by humans (see my previous post), and one doesn't know which ones, to boot?

I was looking into guess-strategies, so was focusing my tests on batches on low-clue puzzles, and these are mostly multiple-solution cases, so I started generating minimal puzzles to provide an alternative batch set. These are probably more useful in any case.


PS: come on guys, I ain't no Euler, not by a looooooooooong stretch! :?

You can call me Bruce! Although similarly inaccurate (he's in charge of the sheep dip, not me), it is less embarrassing :oops:
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Re: Sudoku16 - Minimal Puzzles

Postby blue » Fri Feb 22, 2019 10:58 am

dobrichev wrote:2) Essentially SAT is a brute force approach to a problem so it shouldn't be viewed as an alternative of brute force.

Mathimagics wrote:SAT is still "brute force", I agree

But "MiniSat" has "conflict driven clause learning" ... it's an "intelligent brute" 8-)

It's no panecea though, unfortunately.
One time, for a probelm it couldn't handle, I watched it chew up 2Gb of RAM (over several hours), before it finally crashed :(

Cheers.
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Re: Sudoku16 - Minimal Puzzles

Postby dobrichev » Fri Feb 22, 2019 12:33 pm

Yes, it is intelligent, by my point is that you never know why for 3 very similar problems A, B, and C SAT returns "Yes" for A, "No" for B, and crashes for C.

Off-topic: You can read this recent success story for using SAT. The task is defined here.
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Re: Sudoku16 - Minimal Puzzles

Postby Mathimagics » Fri Feb 22, 2019 1:12 pm

dobrichev wrote:The task is defined here.


Why did I not know about this site? :shock:

Can I "wrap up" Sudoku (ha ha) in the time available before the next competition? :?:

I ask the latter question because, once I go there, it is highly unlikely that I would ever come back … :lol:
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Re: Sudoku16 - Minimal Puzzles

Postby m_b_metcalf » Fri Feb 22, 2019 1:23 pm

Mathimagics wrote:I ask the latter question because, once I go there, it is highly unlikely that I would ever come back … :lol:

That's what hapenned to H(erbert)Kociemba :!:
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Re: Sudoku16 - Minimal Puzzles

Postby Mathimagics » Fri Feb 22, 2019 3:35 pm

I see that both Mladen (rank #22) and Herbert (rank #35) both performed very well in the recent competition. Congratulations to both of you! 8-)

And Mladen, at least, has come back unscathed …
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Re: Sudoku16 - Minimal Puzzles

Postby m_b_metcalf » Sun Feb 24, 2019 5:22 pm

tarek wrote:2. High singles backdoor size

FWIW, and if I've done it right, I could solve 496 of the 2000 puzzles using a single backdoor in the solution chain. I don't intend to try for higher.

Regards,

Mike
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Re: 206 tough puzzle list

Postby tarek » Sun Mar 03, 2019 10:27 am

List of 206 puzzles with 81-84 clues all originating from same parent puzzle. 1 puzzle Singles Backdoor size 3, 12 puzzles singles Backdoor size 4 & the rest are Singles Backdoor size 5. There is no correlation with difficulty if you are using anything other than singles to solve.

Not all are minimal. So this list is intended to test for minimal puzzles & backdoors.

206 16x16 puzzles: Show
.A729.BC.....3.16..B3....D..A.2........5.3..C8..1.9...86..4.............B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5.........G8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.....64.B2
.A72..BC.....3.16..B3...9D..A.2........5.3..C8..1.9...86..4.............B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5.........G8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.....64.B2
.A729.BC.....3.16..B3....D..A.2........5.3..C8..1.9...86..4.............B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5.........F8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.....64.B2
.A729.BC.....3.16..B3....D8.A.2........5.3..C8..1.9....6..4.............B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5.........G...34.827.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.....64.B2
.A729.BC.....3.16..B3....D8.A.2........5.3..C8..1.9....6..4.............B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5.........G8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.....64.B2
.A729.BC.G...3.16..B3....D..A.2........5.3..C8..1.9....6..4.....7.......B..92..8D.....E....2.........3.45....B7..4.3...D...71...9.1...A2.......74.6.............5.......F..8..3..827.9.1.4....65...C.......A...6....65..C7....A......423.1..859......8.9...64.B2
.A729.BC.....3.16..B3....D..A.2........5.3..C8..1.9....6..4.............B..92..8D.....E....2.........3.45....B7..4.3...D...71...9B1...A2.......74.6.....1.......5.........G8..3..827.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.....64.B2
.A729.BC.....3.16..B3....D..A.2........5.3..C8..1.9....6..4.............B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5.........G8..34..27.9.1.4....65...C......2A...6...865..C7....A......423.1..859......8.....64.B2
.A729.BC.....3.16..B3....D..A.2........5.3..C8..1.9...86..4.............B..9...8D.....E....2.........3..5...FB7..4.3...D...71...9B1...A2.......74.6.....1.......5.........E8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.....64.B2
.A729.BC.....3.16..B3....D..A.2........5.3..C8..1.9...86..4.............B..9...8D.....E....2.........3..5...FB7..4.3...D...71...9B1...A2.......74.6.....1.......5.........G8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.....64.B2
.A729.BC.....3.16..B3....D..A.2........5.3..C8..1.9...86..4.............B..92..8D.....F....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5.........G8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.....64.B2
.A729.BC.....3.16..B3....D..A.2........5.3..C8..1.9...86..4.....7.......B..92..8D..........2.......G.3..5....B7..4.3...D...71...9.1...A2.......74.6.....1.......5.......F..8..34..27.9.1.4....65...C.......A...6....65..C7....A......423.1..859......8.9...64.B2
.A729.BC.....3.16..B3....D..A.2........5.3..C8..1.9...86..4.....7.......B..92..8D..........2.........3..5.E..B7..4.3...D...71...9.1...A2.......74.6.............5.......F..8..34.827.9.1.4....65...C.......A...6....65..C7....A......423.1..859......8.9...64.B2
.A729.BC.....3.16..B3....D..A.2....4...5.3..C8..1.9...86..4.............B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......7..6.....1.......5.........G8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.....64.B2
.A729.BC.....3.16..B3....D..A.2........5.3..C8..1.9...86..4.............B..924.8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5.........G8..3...27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.....64.B2
.A729.BC.G...3.16..B3....D..A.2........5.3..C8..1.9...86..4.............B..92..8D.....E....2.........3.45....B7..4.3...D...71...9B1...A2.......74.6.....1.......5.........E...3...27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.....64.B2
.A729.BC.G...3.16..B3....D..A.2........5.3..C8..1.9...86..4.....7.......B..92..8D.....E....2.........3.45....B7..4.3...D...71...9B1...A2.......74.6.....1.......5.........E...3...27.9.1.4....65...C......2A...6....65..C7....A......4.3.1..859......8.....64.B2
.A729.BC.....3.16..B3....D..A.2........5.3..C8..1.9...86..4.............B..92..8D.....E....2.........3.45....B7..4.3...D...71...9B1...A2.......74.6.....1.......5.........G...3..827.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.....64.B2
.A729.BC.....3.16..B3....D..A.2........5.3..C8..1.9...86..4.............B..92..8D.....E....2.........3.45....B7..4.3...D...71...9B1...A2.......74.6.....1.......5.........G8..3...27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.....64.B2
.A729.BC.....3.16..B3....D..A.2........5.3..C8..1.9...86..4.............B..92..8D.....E....2.........3..5....B7A.4.3...D...71...9B1...A2.......74.6.....1.......5.........G8..3...27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.....64.B2
.A729.BC.....3.16..B3....D..A.2........5.3..C8..1.9...86..4.............B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1.4.A2.......74.6.....1.......5.........G8..3...27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.....64.B2
.A729.BC.....3.16..B3....D..A.2........5.3..C8..1.9...86..4.....7.......B..92..8D.....E....2.........3..5.C..B7..4.3...DG...1...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6.....5..C7....A......4.3.1..859......8.9...64.B2
.A729.BC.G...3.16..B3....D..A.2........5.3..C8..1.9...86..4.............B..92..8D.....E....2.........3..5....B7..4.3..FD...71...9B1...A2.......74.6.....1.......5..........8..3...27.9...4....65...C......2A...6....65..C7....A.G....423.1..859......8.9...64..2
.A729.BC.G...3.16..B3....D..A.2........5.3..C8..1.9....6..4.............B..92..8D.....E....2.........3..5....B7..4.3..D....71...9B1...A2.......74.6.....1.G.....5..........8..34.82..9.1.4....65...C.......A...6....65..C7....A......423.1..859......8.9...64.B2
.A729.BC.....3.16..B3....D..A.2........5.3..C8..1.9...86..4.............B..9...8D.....E....2.........3..5...GB7..4.3...D...71...9B1...A2.......74.6.....1.......5.........E8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.....64.B2
.A729.BC.....3.16..B3....D..A.2........5.3..C8..1.9...86..4.............B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5.........E8..34..27.9.1.4....65F..C.......A...6....65..C7....A......423.1..859......8.....64.B2
.A729.BC.....3.16..B3....D..A.2........5.3..C8..1.9...86..4.............B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5.........E8..34..27.9.1.4....65G..C.......A...6....65..C7....A......423.1..859......8.....64.B2
.A729.BC.....3.16..B3....D..A.2........5.3..C8..1.9...86..4.............B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5.........E8..34..27.9.1.4....65...C...F..2A...6.....5..C7....A......423.1..859......8.....64.B2
.A729.BC.....3.16..B3....D..A.2........5.3..C8..1.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5.........E8..34..27.9.1.4....65...C...F..2A...6.....5..C7....A......4.3.1..859......8.....64.B2
.A729.BC.....3.16..B3....D..A.2........5.3..C8..1.9...86..4.............B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5.........E8..34..27.9.1.4....65...C...G..2A...6.....5..C7....A......423.1..859......8.....64.B2
.A729.BC.....3.16..B3....D..A.2........5.3..C8..1.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5.........E8..34..27.9.1.4....65...C...G..2A...6.....5..C7....A......4.3.1..859......8.....64.B2
.A729.BC.....3.16..B3....D..A.2........5.3..C8..1.9...86..4.............B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5.........E8..34..27.9.1.4....65...C......2A...6.....5F.C7....A......423.1..859......8.....64.B2
.A729.BC.....3.16..B3....D..A.2........5.3..C8..1.9...86..4.............B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5.........E8..34..27.9.1.4....65...C......2A...6.....5G.C7....A......423.1..859......8.....64.B2
.A729.BC.G...3.16..B3....D..A.2........5.3..C8..1.9...86..4.............B..92...D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1......E5.........E8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.....64.B.
.A729.BC.G...3.16..B3....D..A.2........5.3..C8..1.9...86..4.............B..92..8D..........2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5.......G.E...34.827.9...4....65...C......2A...6....65..C7....A......423.1..859......8.....64.B2
.A729.BC.G...3.16..B3....D..A.2........5.3..C8..1.9...86..4.............B..92..8D..........2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5.......G.E8..34..27.9...4....65...C......2A...6....65..C7....A......423.1..859......8.....64.B2
.A729.BC.G...3.16..B3....D..A.2........5.3..C8..1.9...86..4.....7.......B..92..8D..........2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5.......G.E...34.827.9...4....65...C......2A...6....65..C7....A......4.3.1..859......8.....64.B2
.A729.BC.G...3.16..B3....D..A.2........5.3..C8..1.9...86..4.....7.......B..92..8D..........2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5.......G.E8..34..27.9...4....65...C......2A...6....65..C7....A......4.3.1..859......8.....64.B2
.A729.BC.....3.16..B3..E.D..A.2........5.3..C8..1.9....6..4.............B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5.........G8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.....64.B2
.A729.BC.....3.16..B3....D..A.2........5.3..C8..1.9...86..4......6......B..9...8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5.........G8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.....64.B2
.A729.BC.....3.16..B3....D..A.2........5.3..C8..1.9...86..4.............B..92..8D.....E9...2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5.........G8..34..27.9.1.4....65...C......2A...6.....5..C7....A......423.1..859......8.....64.B2
.A729.BC.....3.16..B3....D..A.2........5.3..C8..1.9...86..4.............B..9...8D.....E....2.....2...3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5.........G8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.....64.B2
.A729.BC.....3.16..B3....D..A.2........5.3..C8..1.9...86..4.............B..92..8D.....E....2.......9.3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5.........G8..34..27.9.1.4....65...C......2A...6.....5..C7....A......423.1..859......8.....64.B2
.A729.BC.....3.16..B3....D..A.2........5.3..C8..1.9...86..4.............B..92..8D.....E....2.........36.5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5.........G8..34..27.9.1.4....65...C......2A...6.....5..C7....A......423.1..859......8.....64.B2
.A729.BC.....3.16..B3....D..A.2........5.3..C8..1.9...86..4.............B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.....E.74.6.....1.......5.........G8..3...27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.....64.B2
.A729.BC.....3.16..B3....D..A.2........5.3..C8..1.9...86..4.............B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1......C5.........G8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.....64.B.
.A729.BC.....3.16..B3....D..A.2........5.3..C8..1.9...86..4.............B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5.........G8..34..27.9.1.4....65F..C.......A...6....65..C7....A......423.1..859......8.....64.B2
.A729.BC.....3.16..B3....D..A.2........5.3..C8..1.9...86..4.............B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5.........G8..34..27.9.1.4....65...C.......A...62...65..C7....A......423.1..859......8.....64.B2
.A729.BC.....3.16..B3....D..A.2........5.3..C8..1.9...86..4.............B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5.........G8..34..27.9.1.4....65...C......2A...6.....5F.C7....A......423.1..859......8.....64.B2
.A729.BC.....3.16..B3....D..A.2........5.3..C8..1.9...86..4.............B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5.........G...34.827.9.1.4....65...C.......A...6....65..C79...A......423.1..859......8.....64.B2
.A729.BC.....3.16..B3....D..A.2........5.3..C8..1.9...86..4.............B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5.........G8..34..27.9.1.4....65...C.......A...6....65..C79...A......423.1..859......8.....64.B2
.A729.BC.G...3.16..B3....D..A.2........5.3..C8..1.9...86..4.............B..92E.8D..........2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5.........G...3..827.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.....64.B2
.A729.BC.G...3.16..B3....D..A.2........5.3..C8..1.9...86..4.............B..92E.8D..........2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5.........G8..3...27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.....64.B2
.A729.BC.....3.16..B3....D..A.2........5.3..C8..1.9...86..4.............B..92..8D.....E....2.......A.3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5.........G8..34..27.9.1.4....65...C.......A...6....65..C7....A......423.1..859......8.....64.B2
.A.29.BC.....3.16..B.....D..A.2........573..C8..1.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9..F64.B2
.A.29.BC.....3.16..B.....D..A.2........573..C8..1.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9..G64.B2
.A72..BC.....3.16..B....9D..A.2........5.3..C8..1.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9..F64.B2
.A72..BC.....3.16..B....9D..A.2........5.3..C8..1.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9..G64.B2
.A729.BC.....3.16..B3....D..A.2........5.3..C8..1.9...86..4.....7.......B..9...8D.....E....2.........3..5...FB7..4.3...D...71...9B1...A2.......74.6.....1.......5.........E8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.....64.B2
.A729.BC.G...3.16..B3....D..A.2........5.3..C8..1.9...86..4.............B..9...8D.....E....2.........3..5...FB7..4.3...D...71...9B1...A2.......74.6.....1.......5.........E8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.....64.B2
.A729.BC.G...3.16..B3....D..A.2........5.3..C8..1.9...86..4.....7.......B..9...8D.....E....2.........3..5...FB7..4.3...D...71...9B1...A2.......74.6.....1.......5.........E8..34..27.9.1.4....65...C......2A...6....65..C7....A......4.3.1..859......8.....64.B2
.A729.BC.....3.16..B3....D..A.2........5.3..C8..1.9...86..4.....7.......B..9...8D.....E....2.........3..5...FB7..4.3...D...71...9B1...A2.......74.6.....1.......5.........G8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.....64.B2
.A729.BC.G...3.16..B3....D..A.2........5.3..C8..1.9...86..4.............B..9...8D.....E....2.........3..5...FB7..4.3...D...71...9B1...A2.......74.6.....1.......5.........G8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.....64.B2
.A729.BC.G...3.16..B3....D..A.2........5.3..C8..1.9...86..4.....7.......B..9...8D.....E....2.........3..5...FB7..4.3...D...71...9B1...A2.......74.6.....1.......5.........G8..34..27.9.1.4....65...C......2A...6....65..C7....A......4.3.1..859......8.....64.B2
.A729.BC.....3.16..B3....D..A.2........5.3..C8..1.9...86..4.....7.......B..9...8D.....E....2.........3..5...GB7..4.3...D...71...9B1...A2.......74.6.....1.......5.........E8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.....64.B2
.A729.BC.G...3.16..B3....D..A.2........5.3..C8..1.9...86..4...........6.B..92..8D.....E....2............5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5.........G8..34.827.9.1.4....65...C......2A...6.....5..C7....A......423.1..859......8.....64.B2
.A72..BC.G...3.16..B....9D..A.2...D....5.3..C8..1.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9...64.B2
.A72..BC.G...3.16..B....9D..A.2........5.3..C8..1.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423D1..859......8.9...64.B2
.A729.BC.....3.16.CB.....D..A.2........5.3..C8..1.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9..F64.B2
.A729.BC.....3.16..B....9D..A.2........5.3..C8..1.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9..F64.B2
.A729.BC.....3.16..B.....D.1A.2........5.3..C8..1.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9..F64.B2
.A729.BC.....3.16..B.....D..A.2........5.3.BC8..1.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9..F64.B2
.A729.BC.....3.16..B.....D..A.2........5.3..C8.91.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9..F64.B2
.A729.BC.....3.16..B.....D..A.2........5.3..C8..139...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9..F64.B2
.A729.BC.....3.16..B.....D..A.2........5.3..C8..1.9.E.86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9..F64.B2
.A729.BC.....3.16..B.....D..A.2........5.3..C8..1.9...86..4C....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9..F64.B2
.A729.BC.....3.16..B.....D..A.2........5.3..C8..1.9...86..4....B7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9..F64.B2
.A729.BC.....3.16..B.....D..A.2........5.3..C8..1.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74C6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9..F64.B2
.A729.BC.....3.16..B.....D..A.2........5.3..C8..1.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5.....7....8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9..F64.B2
.A729.BC.....3.16..B3....D..A.2........5.3..C8..1.9...86..4.....7.....5.B..9...8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9..F64.B2
.A729.BC.....3.16.CB.....D..A.2........5.3..C8..1.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9..G64.B2
.A729.BC.....3.16..B....9D..A.2........5.3..C8..1.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9..G64.B2
.A729.BC.....3.16..B.....D.1A.2........5.3..C8..1.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9..G64.B2
.A729.BC.....3.16..B.....D..A.2........5.3.BC8..1.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9..G64.B2
.A729.BC.....3.16..B.....D..A.2........5.3..C8.91.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9..G64.B2
.A729.BC.....3.16..B.....D..A.2........5.3..C8..139...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9..G64.B2
.A729.BC.....3.16..B.....D..A.2........5.3..C8..1.9.E.86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9..G64.B2
.A729.BC.....3.16..B.....D..A.2........5.3..C8..1.9...86..4C....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9..G64.B2
.A729.BC.....3.16..B.....D..A.2........5.3..C8..1.9...86..4....B7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9..G64.B2
.A729.BC.....3.16..B.....D..A.2........5.3..C8..1.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74C6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9..G64.B2
.A729.BC.....3.16..B.....D..A.2........5.3..C8..1.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5.....7....8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9..G64.B2
.A729.BC.....3.16..B3....D..A.2........5.3..C8..1.9...86..4.....7.....5.B..9...8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9..G64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3..C8..1.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74C6.....1.......5.........A8..34..27.9.1.4....65...C.......A...6....65..C7....A......423.1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3..C8..1.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74C6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..D7....A......423.1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D.1A.2........5.3..C8..1.9...86..4.............B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A.G....423.1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3.BC8..1.9...86..4.............B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A.G....423.1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3..C8..1.9...86..4C............B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A.G....423.1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3..C8..1.9...86..4....B........B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A.G....423.1..859......8.9...64.B2
.A729.BC.G...3.16..B3....D..A.2........5.3..C8..1.9...86..4.....7.......B..9...8D..........2.........3..5...FB7..4.3...DG..71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9...64.B2
.A729.BC.G...3.16..B3....D..A.2........5.3..C8..1.9...86..4.....7.......B..9...8D.....E....2.........3..5...FB7..4.3...D...71...9B1...A2.......74.6.....1.......5.........G8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.....64.B2
.A729.BC.G...3.16..B3....D..A.2........5.3..C8..1.9...86..4.....7.......B..92..8D..........2.........3..5....B7..4.3...D...71...9B1...A2.......74.6..........1..5.......F..8..34.827.9.1.4....65...C......2A...6....65..C7....A.......23.1..859......8.9...64.B2
.A729.BC.G...3.16..B3....D..A.2........5.3..C8..1.9...86..4.....7.......B..92...D.....E....2.........3..5.D..B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859..G...8.9...64.B.
.A729.BC.G...3.16..B3....D..A.2........5.3..C8..1.9...86..4.....7.......B..9...8D..........2.........3..5...EB7..4.3...DG..71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9...64.B2
.A729.BC.G...3.16..B3....D..A.2........5.3..C8..1.9...86..4.....7.......B..9...8D..........2.........3..5...GB7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A...E..423.1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3..C8..1.9.E.86..4.....7.......B..92..8D..........2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9..G64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3..C8..1.9.F.86..4.....7.......B..92..8D..........2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9..G64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3.BC8..1.9...86..4.............B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.G.....5..........8..34.82..9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3..C8..1.9...86..4C............B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.G.....5..........8..34.82..9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3..C8..1.9...86..4....B........B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.G.....5..........8..34.82..9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9...64.B2
.A729.BC.G...3.16..B3....D..A.2........5.3..C8..1.9...86..4...........6.B..92..8D.....E....2............5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5.........G8..34.827.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.....64.B2
.A729.BC.G...3.16..B3....D..A.2........5.3..C8..1.9...86..4.....7.....6.B..92..8D.....E....2............5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5.........G8..34.827.9.1.4....65...C......2A...6.....5..C7....A......423.1..859......8.....64.B2
.A729.BC.G...3.16..B3....D..A.2........5.3..C8..1.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5.........G8..34..27.9.1.4....65...C...G..2A...6....65..C7....A......42..1..859......8.....64.B2
.A729.BC.....3.16..B.....D.1A.2........5.3..C8..1.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34.827.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9..F64.B2
.A729.BC.....3.16..B.....D..A.2........5.3.BC8..1.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34.827.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9..F64.B2
.A729.BC.....3.16..B.....D..A.2........5.3..C8..139...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34.827.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9..F64.B2
.A729.BC.....3.16..B.....D..A.2........5.3..C8..1.9...86..4C....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34.827.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9..F64.B2
.A729.BC.....3.16..B.....D..A.2........5.3..C8..1.9...86..4....B7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34.827.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9..F64.B2
.A729.BC.....3.16..B3....D..A.2........5.3..C8..1.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5.........G8..34.827.9.1.4....65...C......2A...6....65..C7....A.......23.1..859......8.9..F64.B2
.A729.BC.....3.16..B.....D.1A.2........5.3..C8..1.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34.827.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9..G64.B2
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.A729.BC.....3.16..B.....D..A.2........5.3..C8..1.9...86..4C....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34.827.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9..G64.B2
.A729.BC.....3.16..B.....D..A.2........5.3..C8..1.9...86..4....B7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34.827.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9..G64.B2
.A729.BC.....3.16..B3....D..A.2........5.3..C8..1.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5.........F8..34.827.9.1.4....65...C......2A...6....65..C7....A.......23.1..859......8.9..G64.B2
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.A729.BC.G...3.16..B.....D.1A.2........5.3..C8..1.9...86..4.............B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34.827.9.1.4....65...C......2A...6....65..C7....A.G....423.1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3.BC8..1.9...86..4.............B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34.827.9.1.4....65...C......2A...6....65..C7....A.G....423.1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3..C8..1.9...86..4....B........B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34.827.9.1.4....65...C......2A...6....65..C7....A.G....423.1..859......8.9...64.B2
.A729.BC.G...3.16..B....9D..A.2...D....5.3..C8..1.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D.1A.2...D....5.3..C8..1.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2...D....5.3.BC8..1.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2...D....5.3..C8.91.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2...D....5.3..C8..139...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2...D....5.3..C8..1.9.E.86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2...D....5.3..C8..1.9...86..4C....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2...D....5.3..C8..1.9...86..4....B7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9...64.B2
.A729.BC.G...3.16..B3....D..A.2...D....5.3..C8..1.9...86..4.....7.....5.B..9...8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D.1A.2........5.3..C8..1.9...86..4.....7.......B..92..8D.....E...12.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3.BC8..1.9...86..4.....7.......B..92..8D.....E...12.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3..C8..139...86..4.....7.......B..92..8D.....E...12.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3..C8..1.9...86..4C....7.......B..92..8D.....E...12.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3..C8..1.9...86..4....B7.......B..92..8D.....E...12.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3..C8..1.9...86..4....B7.......B..92..8D.....E....2.......1.3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D.1A.2........5.3..C8..1.9...86..4.....7.......B..92..8D.....E....2.........3..5.D..B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3.BC8..1.9...86..4.....7.......B..92..8D.....E....2.........3..5.D..B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3..C8..139...86..4.....7.......B..92..8D.....E....2.........3..5.D..B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3..C8..1.9...86..4C....7.......B..92..8D.....E....2.........3..5.D..B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3..C8..1.9...86..4....B7.......B..92..8D.....E....2.........3..5.D..B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D.1A.2........5.3..C8..1.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...DG..71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3.BC8..1.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...DG..71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3..C8.91.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...DG..71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3..C8..139...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...DG..71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3..C8..1.9...86..4C....7.......B..92..8D.....E....2.........3..5....B7..4.3...DG..71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3..C8..1.9...86..4....B7.......B..92..8D.....E....2.........3..5....B7..4.3...DG..71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9...64.B2
.A729.BC.G...3.16..B3....D..A.2........5.3..C8..1.9...86..4.....7.....5.B..9...8D.....E....2.........3..5....B7..4.3...DG..71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9...64.B2
.A729.BC.G...3.16..B3....D..A.2........5.3..C8..1.9...86..4.....7.......B..9...8D.....E....2.........3..5....B7..4.3...DG8.71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D.1A.2........5.3..C8..1.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1..D....5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3.BC8..1.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1..D....5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3..C8..139...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1..D....5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3..C8..1.9...86..4C....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1..D....5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3..C8..1.9...86..4....B7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1..D....5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D.1A.2........5.3..C8..1.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..D.......8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3.BC8..1.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..D.......8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3..C8.91.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..D.......8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3..C8..139...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..D.......8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3..C8..1.9...86..4C....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..D.......8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3..C8..1.9...86..4....B7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..D.......8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3..C8..1.9...86..4C....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27D9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9...64.B2
.A729.BC.G...3.16..B3....D..A.2........5.3..C8..1.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27D9...4....65B..C......2A...6....65..C7....A......423.1..859......8.9...64.B2
.A729.BC.G...3.16..B3....D..A.2........5.3..C8..1.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27D9...4....65...C......2A...6....65.BC7....A......423.1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D.1A.2........5.3..C8..1.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A.G....423.1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3.BC8..1.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A.G....423.1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3..C8..1.9...86..4C....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A.G....423.1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3..C8..1.9...86..4....B7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A.G....423.1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D.1A.2........5.3..C8..1.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A...E..423.1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3.BC8..1.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A...E..423.1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3..C8..1.9...86..4C....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A...E..423.1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3..C8..1.9...86..4....B7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A...E..423.1..859......8.9...64.B2
.A729.BC.G...3.16..B....9D..A.2........5.3..C8..1.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423D1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D.1A.2........5.3..C8..1.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423D1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3.BC8..1.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423D1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3..C8.91.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423D1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3..C8..139...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423D1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3..C8..1.9.E.86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423D1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3..C8..1.9...86..4C....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423D1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3..C8..1.9...86..4....B7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423D1..859......8.9...64.B2
.A729.BC.G...3.16..B3....D..A.2........5.3..C8..1.9...86..4.....7.....5.B..9...8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423D1..859......8.9...64.B2
.A729.BC.G...3.16..B.....D.1A.2........5.3..C8..1.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859..D...8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3.BC8..1.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859..D...8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3..C8.91.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859..D...8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3..C8..139...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859..D...8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3..C8..1.9.E.86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859..D...8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3..C8..1.9...86..4C....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859..D...8.9...64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3..C8..1.9...86..4....B7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859..D...8.9...64.B2
.A729.BC.G...3.16..B3....D..A.2........5.3..C8..1.9...86..4.....7.....5.B..9...8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859..D...8.9...64.B2
.A729.BC.G...3.16..B.....D.1A.2........5.3..C8..1.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9..G64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3.BC8..1.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9..G64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3..C8.91.9...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9..G64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3..C8..139...86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9..G64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3..C8..1.9.E.86..4.....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9..G64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3..C8..1.9...86..4C....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9..G64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3..C8..1.9...86..4....B7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9..G64.B2
.A729.BC.G...3.16..B3....D..A.2........5.3..C8..1.9...86..4.....7.....5.B..9...8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5..........8..34..27.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9..G64.B2
.A729.BC.G...3.16..B3....D..A.2........5.3..C8..1.9...86..4.....7.....6.B..92..8D.....E....2............5....B7..4.3...D...71...9B1...A2.......74.6.....1.......5.........G8..34.827.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.....64.B2
.A729.BC.G...3.16..B.....D..A.2........5.3..C8..1.9...86..4C....7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1......F5..........8..34.827.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9...64.B.
.A729.BC.G...3.16..B.....D..A.2........5.3..C8..1.9...86..4....B7.......B..92..8D.....E....2.........3..5....B7..4.3...D...71...9B1...A2.......74.6.....1......F5..........8..34.827.9.1.4....65...C......2A...6....65..C7....A......423.1..859......8.9...64.B.
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Re: Sudoku16 - Minimal Puzzles

Postby Mathimagics » Mon Mar 04, 2019 5:20 am

Hi tarek!

Do I understand the terminology correctly - "singles Backdoor size 3" means adding 3 (particular) clues gives a singles-only puzzle?
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Re: Sudoku16 - Minimal Puzzles

Postby tarek » Mon Mar 04, 2019 7:54 am

Mathimagics wrote:Hi tarek!

Do I understand the terminology correctly - "singles Backdoor size 3" means adding 3 (particular) clues gives a singles-only puzzle?

Correct (sort of). Solving any 2 clues would not be enough is more accurate. There could be many 3 clue combinations that would do the trick though!!!

In a singles only world, you can calculate the chance of (a) lucky guess(es) if you know all these clues combinations. This in theory may help in designing puzzles that need a certain technique to solve but are difficult to bypass by guess + singles

Tarek
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1,000,000+ minimal random 16x16 puzzles

Postby tarek » Fri Mar 08, 2019 5:08 pm

I forgot a 16x16 generator was running and discovered it when it was at 800,000. I let it run until I had 1,000,000+ minimal nearly random 16x16 puzzles. I would like to share this file which is now compressed to 81MB but What is the best way to share it here?

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Re: Sudoku16 - Minimal Puzzles

Postby Mathimagics » Fri Mar 08, 2019 7:46 pm

You could invite people who wish to obtain the data to contact you by PM, and to provide you with an email address to send it to … 8-)
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Re: Sudoku16 - Minimal Puzzles

Postby tarek » Fri Mar 08, 2019 7:56 pm

That's a good idea until the next better idea appears ....

For anyone interested please PM with an email address & will send it via a file transfer service.

Each line has one puzzle of 256 characters. Clues are symbols 1-G. Empty cells are "."
.7z compressed file which expands from 80 MB to 270MB when decompressed

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Re: Sudoku16 - Minimal Puzzles

Postby Mathimagics » Sun Mar 10, 2019 10:53 am

I've been looking at tarek's mega-collection of minimal 16x16 Sudoku's, with a view to verifying their minimality.

This is a lot more complicated than doing the 2000 puzzles I originally generated for this thread - I deftly avoided the BGS (bad guess syndrome) problem in the generation process, by skipping over any puzzles that took too long for dSolver16 to solve.

Faced with someone else's output, however, BGS cannot be avoided. For example, just 14 puzzles into the file, I hit one which takes 25s to solve. Others take as little as 0.01s, a pretty big range! And there are bound to be worse cases.

Of course, this is just verifying that the puzzles are valid, not actually proving them minimal … :?

I'm investigating alternative strategies like those that work for Samurai's - SAT (*), and the "4CS" method. Meanwhile, I am just continuing with dSolver16, filtering the batch using guess limits. The first pass with guess limit of 4K completed in 80 minutes. It verified unique solutions for 801,574 puzzles, and gave up on the other 244,460. A fair result, considering ...

A second pass, with 8K guess limit, solved 55,428 of the 244,460 pending cases in 135 minutes. Puzzles pending is now 189,032.

I've repeated this process a couple of times, doubling the guess limit each time, with similar results - I get about 1/4 of the pending puzzles solved, and the overall time goes up by 50-80% for each pass.

When I have identified a small enough pool of unsolved puzzles, I will remove the guess limit and complete the set. The only information to be gained from this exercise (other than confirming that the puzzles are all valid) is the identification of those puzzles which most trouble dSolver16!

Minimality testing (proper verification of tarek's batch) will have to wait until I come up with a faster solver option …

* tarek's puzzle #14, takes less than 1s with SAT, so that's a positive sign ...
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