Terence Tao, "Machine Assisted Proof"
https://www.youtube.com/watch?v=AayZuuDDKP0

Mostowski Collapse schrieb:
> Don't buy your Pearls in Honk Kong. They are all fake.
>
> So what do you prefer, this Haskell monster:
> https://www.cs.nott.ac.uk/~pszgmh/countdown.pdf

I didn't make all my homework yet.
For example just fiddling around with CLP(FD), I get:

?- maplist(in, Vs, [1\/3..4, 1..2\/4, 1..2\/4,
1..3, 1..3, 1..6]), all_distinct(Vs).
false.

Does Scryer Prolog CLP(Z) have some explanator for that?
What is exactly the conflict that it fails?

Mild Shock schrieb:
>
> Terence Tao, "Machine Assisted Proof"
> https://www.youtube.com/watch?v=AayZuuDDKP0
>
> Mostowski Collapse schrieb:
>> Don't buy your Pearls in Honk Kong. They are all fake.
>>
>> So what do you prefer, this Haskell monster:
>> https://www.cs.nott.ac.uk/~pszgmh/countdown.pdf

Or a more striking example, Peter Norvig's impossible
Sudoku, which he claims took him 1439 seconds
to show that it is unsolvable:

/* Peter Norvig */
problem(9, [[_,_,_,_,_,5,_,8,_],
[_,_,_,6,_,1,_,4,3],
[_,_,_,_,_,_,_,_,_],
[_,1,_,5,_,_,_,_,_],
[_,_,_,1,_,6,_,_,_],
[3,_,_,_,_,_,_,_,5],
[5,3,_,_,_,_,_,6,1],
[_,_,_,_,_,_,_,_,4],
[_,_,_,_,_,_,_,_,_]]).

https://norvig.com/sudoku.html

whereby SWI-Prolog with all_distinct/1 does
it in a blink, even without labeling:

?- problem(9, M), time(sudoku(M)).
% 316,054 inferences, 0.016 CPU in 0.020 seconds
(80% CPU, 20227456 Lips)
false.

Pretty cool!

Mild Shock schrieb:
> I didn't make all my homework yet.
> For example just fiddling around with CLP(FD), I get:
>
> ?- maplist(in, Vs, [1\/3..4, 1..2\/4, 1..2\/4,
>           1..3, 1..3, 1..6]), all_distinct(Vs).
> false.
>
> Does Scryer Prolog CLP(Z) have some explanator for that?
> What is exactly the conflict that it fails?
>
> Mild Shock schrieb:
>>
>> Terence Tao, "Machine Assisted Proof"
>> https://www.youtube.com/watch?v=AayZuuDDKP0
>>
>> Mostowski Collapse schrieb:
>>> Don't buy your Pearls in Honk Kong. They are all fake.
>>>
>>> So what do you prefer, this Haskell monster:
>>> https://www.cs.nott.ac.uk/~pszgmh/countdown.pdf
>

Now I have the feeling there are no difficult 9x9
Sudokus for the computer. At least not for computers
running SWI-Prolog and using CLP(FD) with the global
constraint all_distinct/1.

I was fishing among the 17-clue Sudokus, and the
hardest I could find so far was this one:

/* Gordon Royle #3668 */
problem(11,[[_,_,_,_,_,_,_,_,_],
[_,_,_,_,_,_,_,1,2],
[_,_,3,_,_,4,_,_,_],
[_,_,_,_,_,_,_,_,3],
[_,1,_,2,5,_,_,_,_],
[6,_,_,_,_,_,7,_,_],
[_,_,_,_,2,_,_,_,_],
[_,_,7,_,_,_,4,_,_],
[5,_,_,1,6,_,_,8,_]]).

But SWI-Prolog still does it in around 3 seconds.
SWI-Prolog does other 17-clue Sudokus in less than 100ms.

Are there any 17-clue Sudokus that take more time?

Mild Shock schrieb:
>
> Or a more striking example, Peter Norvig's impossible
> Sudoku, which he claims took him 1439 seconds
> to show that it is unsolvable:
>
> /* Peter Norvig */
> problem(9, [[_,_,_,_,_,5,_,8,_],
>             [_,_,_,6,_,1,_,4,3],
>             [_,_,_,_,_,_,_,_,_],
>             [_,1,_,5,_,_,_,_,_],
>             [_,_,_,1,_,6,_,_,_],
>             [3,_,_,_,_,_,_,_,5],
>             [5,3,_,_,_,_,_,6,1],
>             [_,_,_,_,_,_,_,_,4],
>             [_,_,_,_,_,_,_,_,_]]).
>
> https://norvig.com/sudoku.html
>
> whereby SWI-Prolog with all_distinct/1 does
> it in a blink, even without labeling:
>
> ?- problem(9, M), time(sudoku(M)).
> % 316,054 inferences, 0.016 CPU in 0.020 seconds
>  (80% CPU, 20227456 Lips)
> false.
>
> Pretty cool!
>
> Mild Shock schrieb:
>> I didn't make all my homework yet.
>> For example just fiddling around with CLP(FD), I get:
>>
>> ?- maplist(in, Vs, [1\/3..4, 1..2\/4, 1..2\/4,
>>            1..3, 1..3, 1..6]), all_distinct(Vs).
>> false.
>>
>> Does Scryer Prolog CLP(Z) have some explanator for that?
>> What is exactly the conflict that it fails?
>>
>> Mild Shock schrieb:
>>>
>>> Terence Tao, "Machine Assisted Proof"
>>> https://www.youtube.com/watch?v=AayZuuDDKP0
>>>
>>> Mostowski Collapse schrieb:
>>>> Don't buy your Pearls in Honk Kong. They are all fake.
>>>>
>>>> So what do you prefer, this Haskell monster:
>>>> https://www.cs.nott.ac.uk/~pszgmh/countdown.pdf
>>
>

Is 3 seconds even enough to generate
unique Sudokus? How many trials would be
needed? The uniqueness problem

seems to have no useful reduction,
already the question whether a partial
latin square has a unique solution

is NP complete?

Finding Another Solution
T. Yato & T. Seta - 2002
https://academic.timwylie.com/17CSCI4341/sudoku.pdf

Mild Shock schrieb:
> Now I have the feeling there are no difficult 9x9
> Sudokus for the computer. At least not for computers
> running SWI-Prolog and using CLP(FD) with the global
> constraint all_distinct/1.
>
> I was fishing among the 17-clue Sudokus, and the
> hardest I could find so far was this one:
>
> /* Gordon Royle #3668 */
> problem(11,[[_,_,_,_,_,_,_,_,_],
>             [_,_,_,_,_,_,_,1,2],
>             [_,_,3,_,_,4,_,_,_],
>             [_,_,_,_,_,_,_,_,3],
>             [_,1,_,2,5,_,_,_,_],
>             [6,_,_,_,_,_,7,_,_],
>             [_,_,_,_,2,_,_,_,_],
>             [_,_,7,_,_,_,4,_,_],
>             [5,_,_,1,6,_,_,8,_]]).
>
> But SWI-Prolog still does it in around 3 seconds.
> SWI-Prolog does other 17-clue Sudokus in less than 100ms.
>
> Are there any 17-clue Sudokus that take more time?

On 2024-03-24 17:26:20 +0000, Mild Shock said:

> https://academic.timwylie.com/17CSCI4341/sudoku.pdf

For an expamle about what is reasonable to expect see pages
https://mlevanto.github.io/solver.html
https://mlevanto.github.io/SudokuV.html
https://mlevanto.github.io/Latina.html

The first one is a solver. It also determines whether the
solution is unique.

The other two problem generators. They are a bit slow but
still usable.

Buttons at the bottom are for saving the problem or solution
in different file formats.

--
Mikko