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Options during solving

 
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ChPicard

Joined: 12 Mar 2008
Posts: 82
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Location: Montreal, Canada

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PostPosted: Thu Mar 13, 2008 2:20 pm    Post subject: Options during solving Reply with quote

Hello

Using a sudoku solver, I will appreciate to have the option to choose among the techniques available to eliminate the next candidate, for instance between a XY-wing or a hidden quad or a coloring.

Thank you very much.

I am looking also for a very simple brute force solver in pascal to verify what is going on if I eliminate one given or if I move one given. I would like also make statistics on the position of the givens in the collection of all known 17 given sudokus.

Too much excited by this game.

ChPicard
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coloin

Joined: 05 May 2005
Posts: 97
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PostPosted: Thu Mar 13, 2008 5:29 pm    Post subject: Reply with quote

ChPicard wrote:
I would like also make statistics on the position of the givens in the collection of all known 17 given sudokus.


Interesting if you can do it

Except each 17-puzzle has 9! * 6^8 * 2 isomorphs

If it helps I have "classified" puzzles into catagories which reduce these options significantly.

1. 8 clue values present or 9 cluevalues present


2
Every puzzle has a max value of equivalent clues. Some puzzle have several examples of the max pattern in the puzzle.
Code:
.2.....7.6...1..........68.....9.5...7.8...........1..1.53........7...4.9........        6/9
....4.87..61..................6...312...7....4.........5.1.8...7.....2.....3.....        7/9
.1......9...3..8........6......124..7.3......5........8..6.........4..2....7...5.        7/9
...5.1....9....8...6.......4.1..........7..9........3.8.....1.5...2..4.....36....        8/9
......8.17..2........5.6......7...5..1....3...8.......5......2..4..8....6...3....        6/9
.2.....46...3.1..........7.5.....3......6.8...7..4....1.....5.....9...2.3........        6/9
7..4.....6......9........1..12...8.....6.3......9.....39....7......2...5......4..        7/9
53....1......27............4.7...8.....1.....2.........6.3...5...3.98...........2        7/9
......52..8.4......3...9...5.1...6..2..7........3.....6...1..........7.4.......3.        7/9
3.6.7...........518.........1.4.5...7.....6.....2......2.....4.....8.3.....5.....        7/9
......8.17..2........5.6......7...5..1....3...8.......5......2..3..8....6...4....        7/9
.......71.2.8........4.3...7...6..5....2..3..9........6...7.....8....4......5....        7/9
....14....3....2...7..........9...3.6.1.............8.2.....1.4....5.6.....7.8...        7/9
6.2.5.........4.3..........43...8....1....2........7..5..27...........81...6.....        7/9
.524.........7.1..............8.2...3.....6...9.5.....1.6.3...........897........        7/9
6.2.5.........3.4..........43...8....1....2........7..5..27...........81...6.....        7/9
.923.........8.1...........1.7.4...........658.........6.5.2...4.....7.....9.....        7/9
....75....1..2.....4...3...5.....3.2...8...1.......6.....1..48.2........7........        6/9
64.....3....7.1....9.......2.....8.7.3..6..........5......4..9.7..8.....3........        7/9
......8.16..2........7.5......6...2..1....3...8.......2......7..3..8....5...4....        7/9
.98.1....2......6.............3.2.5..84.........6.........4.8.93..5...........1..        6/9
6.....8.3.4.7.................5.4.7.3..2.....1.6.......2.....5.....8.6......1....        6/9
.8..4....3......1........2...5...4.69..1..8..2...........3.9....6....5.....2.....        7/9
.91.6....4......7.............4.2.5..39.........7.........3.6.92..5...........1..        6/9
52...6.........7.13...........4..8..6......5...........418.........3..2...87.....        6/9
4.....8.5.3..........7......2.....6.....8.4......1.......6.3.7.5..2.....1.4......        6/9
.19....5.4..2..................91.......5..6.7.....3.....3..4.7.61............2..        6/9
.71..8...5......2...............68.14...3..........7.....45..3..16.........2.....        6/9
48.3............71.2.......7.5....6....2..8.............1.76...3.....4......5....        6/9


These were the maximum rook pattern templates I found in these random 17s [accuracy debatable]



Here is the non-attacking rook [chess] pattern with 5 clues
Code:
1oo|ooo|ooo
ooo|ooo|ooo
ooo|ooo|ooo
-----------
ooo|ooo|ooo
ooo|o5o|ooo
ooo|ooo|o6o
-----------
ooo|ooo|ooo
ooo|oo8|ooo
ooo|ooo|oo9

2. Example of maximum rook pattern in puzzle and number of isomorphs with the pattern
Code:

a  5 clues in boxes 15689 [rare]                                               16 isomorphs
b  6 clues - 5 in boxes 15689 and 1 clue in 1 other equivalent box [common]     4 isomorphs
c1 7 clues in boxes 1245689 [common]                                            2 isomorphs
c2 7 clues in boxes 1235689 [common]                                            4 isomorphs
d  8 clues in boxes 12345678 [rare]                                             8 isomorphs
e  9 clues in boxes 123456789 [two puzzles only]                              6^6 isomorphs


So its not an easy one at all !

Good luck

C
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coloin

Joined: 05 May 2005
Posts: 97
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PostPosted: Sat Apr 05, 2008 3:39 pm    Post subject: Reply with quote

A little bit more thought on this one............

Trying to classify these 17s......as I said each indiviual puzzle has 9! * 6^8 * 2 isomorphs.

I also repeat that there are no 17-puzzles without a 5 clue template.

There are 19-clue puzzles without this 5/9 template however:
Code:
+---+---+---+
|.2.|3.4|...|
|97.|...|...|
|...|..1|...|
+---+---+---+
|...|...|4.2|
|...|.75|...|
|...|.6.|..9|
+---+---+---+
|4.1|...|8..|
|8..|...|.6.|
|..5|...|.7.|
+---+---+---+ 19 clues


I have shown some of the reduction in isomorphs using this 5/9,6/9,7/9,8/9 or 9/9 templates - but I missed some !.

Code:
clues                    6^8               *2         9![8 clues]     9![9 clues]
a  5 clues               8 isomorphs        2         24               24
b  6 clues               2 isomorphs        1          6                6
c1 7 clues               1 isomorphs        2          2                2
c2 7 clues               4 isomorphs        1          2                2
d  8 clues               8 isomorphs        2          1                1
e  9 clues             6^8 isomorphs        2          -                1


Not sure if it helps, especially with the 5 and 6 clue templates.

Perhaps best looking at the 17-puzzles with only one of the symmetric 7-clue templates first

C
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