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| ChPicard
| | Joined: 12 Mar 2008 | | Posts: 82 | | : | | Location: Montreal, Canada |
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 Posted: Mon Nov 02, 2009 7:15 am Post subject: Conditions for a valid 17 given sudoku |
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Conditions for a valid 17 given sudoku
| coloin wrote: |
But many of these will be invalid.
eg
must have at least 1 clue in every double row of 18 clues
must have at least 3 clues in a band of 27 clues ?
must have at least 8 clues in 2 bands [2 x 27 clues]
must have no more than 9 clues in a band
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must have 0 or 1 number missing
Never seen in Royle's database (49151 different puzzles):
5 times (or more) the same number
3 empty boxes
5 givens in the same row, column
6 givens in the same box
2 (or less), 10 (or more) givens in the same band or stack
Could you confirm and complete?
Thank you
JPS |
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| coloin
| | Joined: 05 May 2005 | | Posts: 97 | | : | |
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| Posted: Tue Nov 03, 2009 8:16 pm Post subject: |
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Well - even too much for my programmining skills !
gsf's program can count the clue freq and clues in a box - that could be done easily. The other conditions im sure gsf could confirm.
Does it help us do a {-3+3} ? it might but it would be darn complex.
I also havnt seen a 17-puzzle which had these [equivalent] clues.
| Code: | +---+---+---+
|1..|...|...|
|...|1..|...|
|...|...|1..|
+---+---+---+
|...|...|...|
|...|...|...|
|...|...|...|
+---+---+---+
|...|...|...|
|...|...|...|
|...|...|...|
+---+---+---+ |
I perhaps could confirm this one
I also havnt seen a 17-puzzle which didnt have these [equivalent] clues.
| Code: | +---+---+---+
|1..|...|...|
|...|2..|...|
|...|...|...|
+---+---+---+
|.3.|...|...|
|...|.4.|...|
|...|...|...|
+---+---+---+
|...|...|...|
|...|...|...|
|...|...|..5|
+---+---+---+ |
There are puzzles with,6,7 and 8 clues.
There are only 2 of the 17-puzzles have the 9-clue arranged as such
| Code: | +---+---+---+
|1..|...|...|
|...|2..|...|
|...|...|3..|
+---+---+---+
|.4.|...|...|
|...|.5.|...|
|...|...|.6.|
+---+---+---+
|..7|...|...|
|...|..8|...|
|...|...|..9|
+---+---+---+ |
But this doesnt really help us do a {-3+3} either.
C |
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| daj95376
| | Joined: 05 Feb 2006 | | Posts: 349 | | : | |
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| Posted: Thu Nov 05, 2009 1:43 am Post subject: |
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Useless Tidbit #1
Of the 48826 17's that I downloaded and converted to MinLex format, all contain coloin's pattern:
| Code: | +-----------------------+
| 1 2 3 | 4 5 6 | 7 8 9 |
| 4 5 . | . 8 9 | . . . |
| . . . | . . . | . . . |
|-------+-------+-------|
| 2 . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
|-------+-------+-------|
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-----------------------+
|
Maybe someone will eventually find a "17" whose MinLex format matches:
| Code: | +-----------------------+
| 1 2 3 | 4 5 6 | 7 8 9 |
| 4 5 . | 8 9 . | . . . |
| . . . | . . . | . . . |
|-------+-------+-------|
| 2 . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
|-------+-------+-------|
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-----------------------+
|
Useless Tidbit #2
There were 2853 duplicates after converting to MinLex format. |
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