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

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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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