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| ChPicard
| | Joined: 12 Mar 2008 | | Posts: 82 | | : | | Location: Montreal, Canada |
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 Posted: Thu Mar 13, 2008 2:20 pm Post subject: Options during solving |
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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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| Posted: Thu Mar 13, 2008 5:29 pm Post subject: |
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| 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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| Posted: Sat Apr 05, 2008 3:39 pm Post subject: |
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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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