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dukuso

Joined: 14 Jul 2005
Posts: 454
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Location: germany

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PostPosted: Tue Jul 26, 2005 12:37 pm    Post subject: Reply with quote

here is the collection of puzzles which I found so far, which
require more than forced2 chains, where forced1 refers to
the 4*81 basic constraints. Bifurcations where one fork
is a forced1-chain would be considered forced2.
All other puzzles posted here
(if I found them) were solvable by considering forced2 chains
only, without backtracking.



....3....93..6.8..56......4..2.16...85.47....6...29..37.....21.................59
..26......9....4...1...9..7....46..5..4.9..8....71.3.48...31...3..98.......4...32
3...6...5.2.....4...7...2.....6.7...9...8...6...9.1.....2...7...4.....1.6...5...9
8.2.....4.9......7..5..139..8..17......5.2..1.....8.36..71.....4...7....32...5...
..3.5.4..7...6.....5.8...6.5....3..4.1..7..8.2..4....7.4...8.5.....4...9..6.1.2..
.2..........6....3.74.8.........3..2.8..4..1.6..5.........1.78.5....9..........4.
....1.78.5....9..........4..26.........6....3.74.8.........3..2.8..4..1.6..5.....
..12...6...9..8.4..5..4.9..73..8......5.3.1......6..34..3.2..9..2.8..5...9...14..
....7..9......8..4.42..1.7...4.....88..2.5..95.....7...7.6..13.2..8......6..3....



solver output:

1 solutions , 1(2) guesses , 3982 placements time=0/91sec.
1 solutions , 1(2) guesses , 5643 placements time=0/91sec.
1 solutions , 1(2) guesses , 4850 placements time=0/91sec.
1 solutions , 1(2) guesses , 8098 placements time=0/91sec.
1 solutions , 1(2) guesses , 6895 placements time=0/91sec.
1 solutions , 3(6) guesses , 10525 placements time=0/91sec.
1 solutions , 2(4) guesses , 5344 placements time=5/91sec.
1 solutions , 1(2) guesses , 6097 placements time=5/91sec.
1 solutions , 1(2) guesses , 4807 placements time=5/91sec.


my other solver says:

1 solutions 242 nodes 396 node2 1203 node3 3 guesses
1 solutions 186 nodes 202 node2 1110 node3 1 guesses
1 solutions 280 nodes 364 node2 2353 node3 2 guesses
1 solutions 271 nodes 790 node2 2961 node3 5 guesses
1 solutions 405 nodes 356 node2 1623 node3 2 guesses
1 solutions 436 nodes 556 node2 2188 node3 3 guesses
1 solutions 390 nodes 602 node2 2037 node3 3 guesses
1 solutions 249 nodes 268 node2 1007 node3 1 guesses
1 solutions 244 nodes 110 node2 343 node3 1 guesses


it depends on the ordering of the constraints, so an equivalent
transformation of the sudoku gives a different result once
backtracking ("guesses") is involved.


Guenter.
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Nick70

Joined: 08 Jun 2005
Posts: 160
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PostPosted: Tue Jul 26, 2005 2:01 pm    Post subject: Reply with quote

Are you sure you posted the right puzzles?
Especially the first one, which is easy.

Code:
....3....93..6.8..56......4..2.16...85.47....6...29..37.....21.................59
diff 01 [single sector candidate]

..26......9....4...1...9..7....46..5..4.9..8....71.3.48...31...3..98.......4...32
diff 13 [forcing chain] (chain score  505)

3...6...5.2.....4...7...2.....6.7...9...8...6...9.1.....2...7...4.....1.6...5...9
diff 15 [guessing] ( 1 lucky guesses to solution) (first easy iteration:  6)

8.2.....4.9......7..5..139..8..17......5.2..1.....8.36..71.....4...7....32...5...
diff 14 [multi forcing chain] (chain score  856) (first easy iteration:  2)

..3.5.4..7...6.....5.8...6.5....3..4.1..7..8.2..4....7.4...8.5.....4...9..6.1.2..
diff 15 [guessing] ( 2 lucky guesses to solution)

.2..........6....3.74.8.........3..2.8..4..1.6..5.........1.78.5....9..........4.
diff 11 [xy-wing] (score  42, total 1, empty cells at first 27)

....1.78.5....9..........4..26.........6....3.74.8.........3..2.8..4..1.6..5.....
diff 11 [xy-wing] (score  42, total 1, empty cells at first 27) (first easy iteration:  4)

..12...6...9..8.4..5..4.9..73..8......5.3.1......6..34..3.2..9..2.8..5...9...14..
diff 15 [guessing] ( 1 lucky guesses to solution)

....7..9......8..4.42..1.7...4.....88..2.5..95.....7...7.6..13.2..8......6..3....
diff 15 [guessing] ( 2 lucky guesses to solution)
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dukuso

Joined: 14 Jul 2005
Posts: 454
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Location: germany

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PostPosted: Tue Jul 26, 2005 3:05 pm    Post subject: Reply with quote

yes, I'm sure I posted the right puzzles.
I'm not sure how to interpret your comments.
Do you think I have a bug in my program ?
Is there a forced2-chain to solve puzzle 1 ?

I can add some clues, so this is the critical position:

... .3. ...
93. .6. 8..
56. ... ..4

3.2 .16 ...
85. 473 ...
6.. .29 ..3

7.. ... 21.
... ... ...
... ... .59
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Nick70

Joined: 08 Jun 2005
Posts: 160
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PostPosted: Tue Jul 26, 2005 5:56 pm    Post subject: Reply with quote

dukuso wrote:
Do you think I have a bug in my program ?


Maybe, since it is missing one of the most basic logic rules.

There are many single sector candidate eliminations possible. For example:

8 is limited to column 4 in box 5
2 is limited to row 1 in box 1
5 is limited to column 4 in box 5

and so on.

Even Simple Sudoku suggest to use a naked pair before the single candidate rule, I guess this is by design but it seems a bit odd.
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angusj
Site Admin
Joined: 18 Jun 2005
Posts: 409
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PostPosted: Wed Jul 27, 2005 12:20 am    Post subject: Reply with quote

Nick70 wrote:
Even Simple Sudoku suggest to use a naked pair before the single candidate rule, I guess this is by design but it seems a bit odd.

Yes, it's by design because I generally find it easier to spot Naked Pairs than what you call single sector candidates (or what I've less helpfully called Eliminating Candidates).
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dukuso

Joined: 14 Jul 2005
Posts: 454
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Location: germany

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PostPosted: Wed Jul 27, 2005 5:24 am    Post subject: Reply with quote

>dukuso wrote:
>>Do you think I have a bug in my program ?
>
>Maybe, since it is missing one of the most basic logic rules.

I think it works as described and this "basic" rule is missing by design.
This could be a weakness, I'm not sure.Maybe I can change this.

>There are many single sector candidate eliminations possible.
>For example:
>
>8 is limited to column 4 in box 5
>5 is limited to column 4 in box 5

but which row ?

>2 is limited to row 1 in box 1

gives no forced placement yet

>and so on.
>
>Even Simple Sudoku suggest to use a naked pair before the
>single candidate rule, I guess this is by design but it seems
>a bit odd.


Can you send/post your hardest sudokus ?
(preferrably in one big file to sterten( at)aol.com)





-------------

I changed it now.
My old rule went like this:

We have the obvious 324 constraints : cell, symbol in row,
symbol in column, symbol in block with 81 each.
These make the forced(1) - placements.
Forced(2) includes forced(1) and bifurcation with (at least) one
dead end (when filling in forced(1)-placements)

Now I made it:
Forced(2) includes forced(1) and k-furcations with (at least) k-1
dead ends (when filling in forced(1)-placements)

A k-furcation is a constraint which can be met in k ways.
Or a binary column with sum=k in exact-cover-speak.

That means now, that I not necessarily always choose a
binary column with minimum sum as is typical for exact-cover-solver.
This could make it slower for small n.

Now with this new forced(2)-rule, I can find no 9*9 sudoku-grid
which requires backtracking.

here is one 16*16 which still requires guessing:


BC-1--6GD-E--F----------3--FC-1BE-6-9A----8-G----5--2-------697----------B-G-C5-5-3-F-72-----1--2-A-5---4--E-8----B9-E-3FC--2D--3----65-G-9-FB---E58B--F--D--7---2D-C-8----4----A--6-----E7-----6--B--9A-D---4F---8-G--B-A4----1G-4-3--E61C----5--E----5---3--89


there could still be bugs in that version ....
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dukuso

Joined: 14 Jul 2005
Posts: 454
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Location: germany

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PostPosted: Wed Jul 27, 2005 7:35 am    Post subject: Reply with quote

here is my updated list of hard 9*9 sudokus.
The 1st sudoku forces my new program (with the k-furkations rule)
to backtrack.
The others force my previous program (with the bifurcations rule) to backtrack.



6...4...3.1.....7...5...8.....5.2...3...9...2...1.3.....8...9...7.....5.2...3...4
....1.78.5....9..........4..26.........6....3.74.8.........3..2.8..4..1.6..5.....
....3....93..6.8..56......4..2.16...85.47....6...29..37.....21.................59
....3....93..6.8..56......43.2.16...85.473...6...29..37.....21.................59
....7..9......8..4.42..1.7...4.....88..2.5..95.....7...7.6..13.2..8......6..3....
..12...6...9..8.4..5..4.9..73..8......5.3.1......6..34..3.2..9..2.8..5...9...14..
..26......9....4...1...9..7....46..5..4.9..8....71.3.48...31...3..98.......4...32
..3.5.4..7...6.....5.8...6.5....3..4.1..7..8.2..4....7.4...8.5.....4...9..6.1.2..
.2..........6....3.74.8.........3..2.8..4..1.6..5.........1.78.5....9..........4.
3...6...5.2.....4...7...2.....6.7...9...8...6...9.1.....2...7...4.....1.6...5...9
4...1...8.5.....2...6...9.....9.2...8...5...3...1.8.....9...6...2.....5.1...7...4
6...7...9.1.....2...5...4.....1.2...9...8...6...6.9.....1...2...3.....4.7...5...8
8.2.....4.9......7..5..139..8..17......5.2..1.....8.36..71.....4...7....32...5...
9...7...4.1.....5...8...2.....8.9...7...4...6...2.7.....3...1...2.....8.6...9...7
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Nick70

Joined: 08 Jun 2005
Posts: 160
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PostPosted: Wed Jul 27, 2005 8:21 am    Post subject: Reply with quote

dukuso wrote:
I think it works as described and this "basic" rule is missing by design.


Well, if you are attempting to rate the difficulty of puzzles, and your program considers super-hard puzzles that everyone else considers easy, I think that is definitely a bug Smile

dukuso wrote:
>8 is limited to column 4 in box 5
>5 is limited to column 4 in box 5

but which row ?


Who knows? But the candidate can be removed from the other cells of box 5.

dukuso wrote:
Can you send/post your hardest sudokus ?
(preferrably in one big file to sterten( at)aol.com)


I can just post them here.
Out of ~70000 puzzles I've generated so far (my generator is slower than yours, but I'm doing a complete search of puzzles with a fixed initial pattern) only ~100 require my solver to use T&E.

Code:
31.6.......2.......5..3.89......5....8..1..7....4......47.8..3.......9.......7.62
31.6.......2.......5..9.86......5....6..1..9....4......94.6..7.......3.......7.12
31.6.......2.......6..7.59......5....9..1..7....4......78.9..4.......3.......7.12
31.6.......2.......6..8.37......5....3..1..6....4......75.3..9.......6.......7.42
31.6.......2.......7..3.89......5....8..1..7....4......97.8..3.......4.......7.62
31.6.......2.......8..9.76......5....6..1..9....4......98.6..1.......4.......7.82
31.6.......4.......7..3.95......5....6..1..3....4......98.5..6.......7.......7.42
31.6.......4.......9..8.15......5....2..1..3....4......86.3..7.......4.......7.92
31.6.......4.......9..8.57......5....3..1..8....4......87.9..3.......1.......7.62
31.6.......5.......2..7.84......5....7..1..2....4......46.9..8.......4.......7.12
31.6.......5.......2..9.56......5....6..1..8....4......38.6..9.......4.......7.12
31.6.......5.......8..3.47......5....2..1..3....4......37.2..1.......5.......7.62
31.6.......5.......8..9.75......5....3..1..6....4......58.6..3.......4.......7.12
31.6.......5.......9..7.18......5....8..1..7....4......76.8..9.......3.......7.12
31.6.......5.......9..7.82......5....8..1..7....4......74.9..3.......4.......7.12
31.6.......7.......9..4.28......5....8..1..3....4......45.8..9.......5.......7.62
31.6.......9.......7..2.48......5....2..1..6....4......56.8..9.......1.......7.32
32.6.......1.......9..8.74......5....7..1..3....4......85.3..6.......9.......7.12
32.6.......4.......5..8.17......5....7..1..9....4......37.5..4.......6.......7.82
32.6.......4.......7..9.81......5....9..1..3....4......15.3..9.......5.......7.62
32.6.......5.......6..7.41......5....7..1..6....4......18.6..7.......3.......7.52
32.6.......5.......6..7.49......5....7..1..6....4......98.6..7.......3.......7.52
32.6.......5.......6..8.71......5....8..1..3....4......16.3..8.......9.......7.62
32.6.......5.......7..8.16......5....8..1..9....4......67.9..8.......5.......7.32
32.6.......5.......7..9.18......5....9..1..6....4......36.8..9.......7.......7.12
32.6.......5.......9..7.16......5....7..1..9....4......68.9..7.......3.......7.52
32.6.......6.......4..7.81......5....9..1..7....4......85.4..9.......3.......7.42
32.6.......7.......1..4.59......5....9..1..7....4......78.9..4.......6.......7.82
32.6.......7.......1..8.37......5....7..1..2....4......86.2..9.......4.......7.12
32.6.......7.......1..8.56......5....3..1..8....4......85.6..1.......7.......7.52
32.6.......7.......1..9.58......5....9..1..2....4......48.3..9.......6.......7.12
32.6.......7.......4..3.18......5....6..1..3....4......38.4..6.......5.......7.92
32.6.......7.......4..8.59......5....3..1..7....4......98.3..1.......6.......7.42
32.6.......8.......6..9.71......5....9..1..3....4......85.3..9.......4.......7.62
32.6.......9.......1..8.45......5....8..1..2....4......75.3..8.......9.......7.62
32.6.......9.......6..4.58......5....8..1..2....4......17.5..3.......9.......7.62
32.6.......9.......6..8.57......5....8..1..2....4......37.4..1.......9.......7.62
32.6.......9.......8..3.67......5....6..1..3....4......17.6..9.......4.......7.82
34.6.......2.......6..7.18......5....7..1..6....4......85.6..7.......4.......7.32
34.6.......2.......6..7.81......5....7..1..6....4......15.6..7.......4.......7.32
34.6.......2.......6..9.17......5....3..1..8....4......98.3..6.......7.......7.42
34.6.......2.......6..9.83......5....8..1..7....4......75.8..1.......4.......7.62
34.6.......2.......7..3.51......5....3..1..7....4......28.5..6.......1.......7.32
34.6.......5.......2..8.53......5....9..1..7....4......78.3..1.......6.......7.42
34.6.......5.......7..8.53......5....8..1..9....4......38.9..7.......6.......7.42
34.6.......7.......2..8.57......5....7..1..2....4......36.2..1.......9.......7.82
34.6.......7.......2..9.57......5....7..1..2....4......68.2..1.......3.......7.92
35.6.......2.......6..5.48......5....3..1..6....4......18.3..5.......7.......7.92
35.6.......2.......9..5.48......5....6..1..9....4......18.6..5.......7.......7.32
35.6.......4.......1..7.29......5....7..1..3....4......68.9..1.......4.......7.52
35.6.......4.......1..7.29......5....7..1..3....4......68.9..7.......4.......7.52
35.6.......4.......2..7.89......5....7..1..2....4......36.9..1.......5.......7.82
35.6.......4.......8..3.57......5....3..1..8....4......16.8..3.......7.......7.42
35.6.......6.......1..4.29......5....7..1..2....4......48.9..6.......5.......7.12
35.6.......6.......1..4.98......5....2..1..7....4......48.2..6.......5.......7.12
35.6.......6.......9..4.17......5....7..1..2....4......48.9..6.......5.......7.12
35.6.......6.......9..4.17......5....7..1..8....4......48.2..6.......5.......7.12
35.6.......6.......9..4.17......5....7..1..9....4......48.2..6.......5.......7.12
35.6.......7.......1..2.89......5....6..1..2....4......94.8..5.......6.......7.32
35.6.......7.......1..2.94......5....3..1..8....4......48.9..1.......7.......7.32
35.6.......7.......1..8.34......5....2..1..8....4......46.2..1.......7.......7.52
35.6.......7.......9..3.18......5....6..1..9....4......18.9..6.......5.......7.32
35.6.......9.......6..8.71......5....8..1..3....4......16.3..7.......4.......7.82
37.6.......2.......1..9.85......5....9..1..3....4......35.6..9.......4.......7.82
37.6.......2.......6..8.14......5....2..1..3....4......85.3..6.......7.......7.92
37.6.......4.......1..3.62......5....2..1..3....4......65.2..8.......4.......7.12
37.6.......4.......5..2.61......5....2..1..3....4......18.3..7.......4.......7.92
37.6.......4.......5..8.19......5....9..1..3....4......85.3..7.......6.......7.42
37.6.......4.......9..2.41......5....2..1..9....4......18.9..6.......5.......7.32
37.6.......5.......2..8.69......5....6..1..8....4......98.2..6.......3.......7.12
37.6.......5.......6..2.19......5....2..1..6....4......38.6..1.......5.......7.32
37.6.......5.......8..9.42......5....2..1..5....4......46.8..9.......7.......7.82
37.6.......5.......9..2.48......5....2..1..9....4......16.9..7.......8.......7.32
37.6.......9.......2..8.16......5....9..1..8....4......58.6..9.......3.......7.42
37.6.......9.......2..8.65......5....6..1..8....4......98.2..4.......3.......7.12
37.6.......9.......6..2.18......5....2..1..9....4......16.9..7.......5.......7.42
37.6.......9.......8..2.46......5....3..1..8....4......45.8..1.......9.......7.32
38.6.......2.......7..3.51......5....9..1..6....4......18.6..3.......4.......7.92
38.6.......4.......1..7.52......5....7..1..9....4......58.9..7.......4.......7.52
38.6.......4.......1..9.72......5....3..1..6....4......98.6..3.......5.......7.42
38.6.......4.......2..9.15......5....7..1..6....4......98.6..7.......4.......7.32
38.6.......4.......6..9.17......5....9..1..3....4......16.3..9.......5.......7.82
38.6.......4.......6..9.17......5....9..1..6....4......17.6..9.......5.......7.82
38.6.......5.......1..7.89......5....9..1..7....4......76.9..8.......3.......7.12
38.6.......5.......6..2.71......5....2..1..8....4......16.8..7.......9.......7.42
38.6.......5.......9..7.42......5....2..1..9....4......48.9..1.......3.......7.62
38.6.......6.......2..7.41......5....9..1..7....4......48.2..5.......3.......7.92
38.6.......6.......9..8.75......5....4..1..3....4......35.9..8.......4.......7.62
38.6.......7.......5..9.86......5....6..1..9....4......94.5..1.......6.......7.32
38.6.......9.......4..7.12......5....7..1..8....4......15.8..9.......3.......7.42
39.6.......2.......1..3.87......5....3..1..6....4......64.9..3.......6.......7.52
39.6.......2.......1..8.75......5....7..1..8....4......38.5..7.......6.......7.92
39.6.......2.......4..3.85......5....6..1..9....4......15.6..3.......7.......7.82
39.6.......2.......5..3.18......5....3..1..6....4......85.6..1.......4.......7.32
39.6.......5.......6..2.81......5....2..1..3....4......17.3..4.......5.......7.62
39.6.......7.......6..4.82......5....8..1..6....4......46.8..1.......3.......7.92
39.6.......7.......6..8.52......5....2..1..6....4......85.6..1.......4.......7.32
39.6.......7.......6..8.52......5....2..1..6....4......85.9..1.......4.......7.32
39.6.......7.......6..9.12......5....2..1..6....4......85.6..9.......4.......7.32
31.6.......2.......5..9.78......5....9..1..6....4......75.6..3.......4.......7.92
31.6.......4.......5..9.28......5....7..1..3....4......38.5..9.......4.......7.62
31.6.......4.......7..3.95......5....6..1..3....4......98.5..1.......7.......7.42
31.6.......5.......9..7.18......5....8..1..7....4......76.8..1.......3.......7.92
31.6.......7.......9..2.85......5....3..1..9....4......84.9..1.......6.......7.32
31.6.......7.......9..8.52......5....2..1..9....4......35.9..1.......4.......7.62
32.6.......4.......6..8.17......5....7..1..8....4......85.9..1.......4.......7.52
32.6.......6.......1..8.95......5....9..1..2....4......58.3..1.......6.......7.42
32.6.......9.......8..7.15......5....7..1..3....4......15.8..7.......6.......7.82
34.6.......2.......6..7.89......5....7..1..6....4......95.6..7.......4.......7.32
34.6.......5.......8..7.12......5....7..1..3....4......16.2..4.......9.......7.82
35.6.......6.......7..4.98......5....2..1..7....4......48.2..6.......5.......7.12
37.6.......4.......1..8.52......5....2..1..8....4......47.5..9.......8.......7.62
37.6.......9.......8..2.71......5....2..1..8....4......16.8..7.......4.......7.32
38.6.......2.......9..7.41......5....7..1..9....4......45.8..3.......5.......7.82
38.6.......4.......2..8.45......5....9..1..6....4......15.6..9.......3.......7.82
38.6.......5.......9..7.61......5....2..1..7....4......67.2..8.......9.......7.32
38.6.......9.......2..3.51......5....3..1..6....4......17.5..8.......9.......7.32
39.6.......5.......2..7.46......5....7..1..9....4......86.9..4.......3.......7.12
39.6.......6.......4..2.81......5....7..1..2....4......85.4..7.......3.......7.42
39.6.......6.......4..8.52......5....2..1..9....4......18.6..4.......9.......7.32
39.6.......7.......1..4.28......5....8..1..9....4......46.3..1.......5.......7.62
32.6.......6.......4..9.53......5....3..1..7....4......98.3..1.......6.......7.42
32.6.......8.......6..9.17......5....9..1..3....4......85.3..9.......4.......7.62
37.6.......4.......1..8.52......5....2..1..8....4......47.5..3.......8.......7.62
37.6.......5.......1..8.46......5....6..1..8....4......28.9..7.......3.......7.52
38.6.......4.......1..9.37......5....9..1..8....4......35.8..6.......4.......7.12
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dukuso

Joined: 14 Jul 2005
Posts: 454
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PostPosted: Wed Jul 27, 2005 12:41 pm    Post subject: Reply with quote

thanks for the 125 !
Now I have 2 (42) which require backtracking with algo2 (algo1).
Yes, my hardness measure is not so good for humans to determine
how hard a problem will be for them to solve.
But for computers-solvers it could be useful. It's just the level of lookahead required.
I'm wondering which level we need for 16*16,25*25,... sudokus.
Well, I just tried 25*25 and it is already rather slow.
I didn't succeed to generate a 25*25 sudoku with my program.


here are the 42: (first 2 are "hardest")

38.6.......9.......2..3.51......5....3..1..6....4......17.5..8.......9.......7.32
6...4...3.1.....7...5...8.....5.2...3...9...2...1.3.....8...9...7.....5.2...3...4
....1.78.5....9..........4..26.........6....3.74.8.........3..2.8..4..1.6..5.....
....3....93..6.8..56......4..2.16...85.47....6...29..37.....21.................59
....3....93..6.8..56......43.2.16...85.473...6...29..37.....21.................59
....7..9......8..4.42..1.7...4.....88..2.5..95.....7...7.6..13.2..8......6..3....
..12...6...9..8.4..5..4.9..73..8......5.3.1......6..34..3.2..9..2.8..5...9...14..
..26......9....4...1...9..7....46..5..4.9..8....71.3.48...31...3..98.......4...32
..3.5.4..7...6.....5.8...6.5....3..4.1..7..8.2..4....7.4...8.5.....4...9..6.1.2..
.2..........6....3.74.8.........3..2.8..4..1.6..5.........1.78.5....9..........4.
3...6...5.2.....4...7...2.....6.7...9...8...6...9.1.....2...7...4.....1.6...5...9
4...1...8.5.....2...6...9.....9.2...8...5...3...1.8.....9...6...2.....5.1...7...4
6...7...9.1.....2...5...4.....1.2...9...8...6...6.9.....1...2...3.....4.7...5...8
8.2.....4.9......7..5..139..8..17......5.2..1.....8.36..71.....4...7....32...5...
9...7...4.1.....5...8...2.....8.9...7...4...6...2.7.....3...1...2.....8.6...9...7
31.6.......2.......5..9.86......5....6..1..9....4......94.6..7.......3.......7.12
31.6.......2.......6..7.59......5....9..1..7....4......78.9..4.......3.......7.12
31.6.......2.......6..8.37......5....3..1..6....4......75.3..9.......6.......7.42
31.6.......2.......7..3.89......5....8..1..7....4......97.8..3.......4.......7.62
31.6.......5.......2..9.56......5....6..1..8....4......38.6..9.......4.......7.12
31.6.......5.......8..3.47......5....2..1..3....4......37.2..1.......5.......7.62
31.6.......5.......9..7.82......5....8..1..7....4......74.9..3.......4.......7.12
32.6.......5.......6..8.71......5....8..1..3....4......16.3..8.......9.......7.62
32.6.......7.......1..8.37......5....7..1..2....4......86.2..9.......4.......7.12
34.6.......2.......6..9.83......5....8..1..7....4......75.8..1.......4.......7.62
34.6.......7.......2..8.57......5....7..1..2....4......36.2..1.......9.......7.82
37.6.......4.......1..3.62......5....2..1..3....4......65.2..8.......4.......7.12
37.6.......5.......2..8.69......5....6..1..8....4......98.2..6.......3.......7.12
37.6.......5.......6..2.19......5....2..1..6....4......38.6..1.......5.......7.32
38.6.......2.......7..3.51......5....9..1..6....4......18.6..3.......4.......7.92
38.6.......9.......4..7.12......5....7..1..8....4......15.8..9.......3.......7.42
39.6.......2.......1..8.75......5....7..1..8....4......38.5..7.......6.......7.92
39.6.......7.......6..4.82......5....8..1..6....4......46.8..1.......3.......7.92
39.6.......7.......6..9.12......5....2..1..6....4......85.6..9.......4.......7.32
32.6.......9.......8..7.15......5....7..1..3....4......15.8..7.......6.......7.82
34.6.......5.......8..7.12......5....7..1..3....4......16.2..4.......9.......7.82
37.6.......4.......1..8.52......5....2..1..8....4......47.5..9.......8.......7.62
37.6.......9.......8..2.71......5....2..1..8....4......16.8..7.......4.......7.32
38.6.......2.......9..7.41......5....7..1..9....4......45.8..3.......5.......7.82
38.6.......4.......2..8.45......5....9..1..6....4......15.6..9.......3.......7.82
39.6.......6.......4..8.52......5....2..1..9....4......18.6..4.......9.......7.32
37.6.......4.......1..8.52......5....2..1..8....4......47.5..3.......8.......7.62
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MadOverlord

Joined: 01 Jun 2005
Posts: 80
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PostPosted: Tue Aug 09, 2005 12:11 pm    Post subject: Reply with quote

60 deduction passes in Susser, lots of Bingo.
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Sambor

Joined: 07 Nov 2005
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PostPosted: Mon Nov 07, 2005 11:26 am    Post subject: Reply with quote

tilps wrote:
Since we're here
1.6.3 - current hardest

Code:
..3|.5.|4..
7..|.6.|...
.5.|8..|.6.
-----------
5..|..3|..4
.1.|.7.|.8.
2..|4..|..7
-----------
.4.|..8|.5.
...|.4.|..9
..6|.1.|2..


Hmm, I have tried this but didn't get far. So I tried to check it with various solvers, and they all claim that there is no solution. So is it correct? Is your solver doing something no one else do? Just wondering...
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dukuso

Joined: 14 Jul 2005
Posts: 454
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PostPosted: Mon Nov 07, 2005 5:33 pm    Post subject: Reply with quote

Sambor wrote:
tilps wrote:
Since we're here
1.6.3 - current hardest

Code:
..3|.5.|4..
7..|.6.|...
.5.|8..|.6.
-----------
5..|..3|..4
.1.|.7.|.8.
2..|4..|..7
-----------
.4.|..8|.5.
...|.4.|..9
..6|.1.|2..


Hmm, I have tried this but didn't get far. So I tried to check it with various solvers, and they all claim that there is no solution. So is it correct? Is your solver doing something no one else do? Just wondering...


exactly one solution. You tried the wrong solvers
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Ruud
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Joined: 17 Sep 2005
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PostPosted: Mon Nov 07, 2005 7:13 pm    Post subject: Reply with quote

Quote:
exactly one solution

Correct. Worthy candidate for the top871 though...
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dukuso

Joined: 14 Jul 2005
Posts: 454
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PostPosted: Tue Nov 08, 2005 8:28 am    Post subject: Reply with quote

Ruud wrote:
Quote:
exactly one solution

Correct. Worthy candidate for the top871 though...



rating is 385, it's #723 in top862
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gsf

Joined: 18 Aug 2005
Posts: 484
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PostPosted: Tue Nov 08, 2005 12:04 pm    Post subject: Reply with quote

dukuso wrote:
thanks for the 125 !
here are the 42: (first 2 are "hardest")


the 125 had some equivalent dups and these may have filtered into the 42
here are the first and dup occurrences, preceded by the canonical solution
Code:

123456789456789132789231546247318695361925478598647213674892351835164927912573864
....1.78.5....9..........4..26.........6....3.74.8.........3..2.8..4..1.6..5.....
.2..........6....3.74.8.........3..2.8..4..1.6..5.........1.78.5....9..........4.
123456789456789231789132465238915674574268913961374852312697548695841327847523196
38.6.......2.......9..7.41......5....7..1..9....4......45.8..3.......5.......7.82
38.6.......4.......2..8.45......5....9..1..6....4......15.6..9.......3.......7.82
123457689456189237789236415215764893374598162698312574567843921842971356931625748
31.6.......2.......5..9.86......5....6..1..9....4......94.6..7.......3.......7.12
31.6.......2.......6..7.59......5....9..1..7....4......78.9..4.......3.......7.12
123457689456189237789263154295874316314526978867391542572618493638945721941732865
31.6.......2.......7..3.89......5....8..1..7....4......97.8..3.......4.......7.62
37.6.......5.......2..8.69......5....6..1..8....4......98.2..6.......3.......7.12
123457689456189237789623415234716958517894326698532741371948562862375194945261873
32.6.......5.......6..8.71......5....8..1..3....4......16.3..8.......9.......7.62
37.6.......9.......8..2.71......5....2..1..8....4......16.8..7.......4.......7.32
123457689456189327789263145275641938638972514914538276362894751547316892891725463
31.6.......5.......8..3.47......5....2..1..3....4......37.2..1.......5.......7.62
37.6.......4.......1..3.62......5....2..1..3....4......65.2..8.......4.......7.12
123457689456189327789263451278635914391842576564971832612598743847316295935724168
39.6.......2.......1..8.75......5....7..1..8....4......38.5..7.......6.......7.92
39.6.......7.......6..4.82......5....8..1..6....4......46.8..1.......3.......7.92
123457689456189372789263154238791546574638921691542837347816295815924763962375418
31.6.......5.......2..9.56......5....6..1..8....4......38.6..9.......4.......7.12
31.6.......5.......9..7.82......5....8..1..7....4......74.9..3.......4.......7.12
123457689456189723789362154248916375395874261617523498532648917874291536961735842
....3....93..6.8..56......4..2.16...85.47....6...29..37.....21.................59
....3....93..6.8..56......43.2.16...85.473...6...29..37.....21.................59


also, this one (one of the dups) only needs the basic FN constraints and box claims to solve:
Code:
....3....93..6.8..56......4..2.16...85.47...6...29..37.....21.................59
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