## Complete Sudoku Collection - Vol. 1

Everything about Sudoku that doesn't fit in one of the other sections

### Complete Sudoku Collection - Vol. 1

I have just completed a long search that required several weeks of calculations.
I have found all puzzles where the clues are placed in the following pattern of 19:
Code: Select all
`*...*.......*...*...*...*...*...*...*...*...*...*...*...*...*...*...*.......*...*`

The end result is that there are exactly 851 different puzzles following that pattern.

The difficulties as rated by my program are distributed as follows:
Code: Select all
`singles              313  36,78%box-line exclusion    89  10,46%hidden pair           25   2,94%naked pair             4   0,47%x-wing                 3   0,35%turbot fish           97  11,40%swordfish             11   1,29%xy-chain              58   6,82%forcing chain        201  23,62%multi forcing chain   43   5,05%forcing tree           7   0,82%                     851 100,00%`

Almost all of the puzzles are minimal, that is, no clue can be removed maintaining a unique solution. Only 8 are not minimal and can be removed to a (not symmetrical) 18-clue puzzle by removing one clue.

And finally, here is the list, roughly in order of difficulty. The puzzles are normalised so that the first line is always 123456789.

(part 1, puzzles 1-400)
Hidden Text: Show
Code: Select all
`1...5.......1...3...7...6...5...8...9...2...1...3...6...6...8...3...7.......9...51...5.......1...3...7...6...5...8...9...7...1...3...6...6...8...3...2.......9...51...5.......1...3...7...4...5...4...3...9...1...8...7...4...8...6...2.......3...51...5.......1...3...7...4...5...4...3...2...1...8...7...4...8...6...2.......3...51...5.......3...2...6...4...5...4...9...6...1...2...3...8...1...4...3.......9...51...5.......1...4...4...3...6...3...5...7...1...8...7...9...8...3...4.......6...51...5.......3...2...5...4...3...4...9...8...1...2...3...4...8...7...1.......9...51...5.......1...4...4...6...3...9...5...1...3...6...2...6...2...9...7.......3...11...5.......1...4...4...6...3...9...5...1...3...6...2...6...9...9...7.......3...11...5.......1...3...7...6...5...8...9...6...1...3...7...6...8...3...2.......9...51...5.......1...3...7...6...5...4...3...8...1...6...7...6...2...9...8.......3...51...5.......2...6...4...3...6...3...5...8...4...1...5...9...6...3...8.......4...21...5.......3...2...5...4...3...4...6...3...1...9...7...4...9...7...1.......2...51...5.......3...4...5...6...3...4...5...1...8...9...7...4...1...7...3.......8...51...5.......2...6...8...4...3...8...8...6...5...9...1...5...3...9...4.......1...81...5.......1...2...7...3...5...8...9...6...1...2...7...2...8...4...3.......9...51...5.......1...3...7...2...5...4...6...7...1...2...7...9...8...3...9.......6...51...5.......2...3...7...4...3...4...5...8...3...9...7...6...5...9...7.......3...11...5.......2...3...7...4...5...7...4...1...8...3...9...9...5...3...9.......4...11...5.......3...2...9...4...3...4...2...6...5...9...6...4...8...6...9.......2...31...5.......1...3...4...2...6...3...5...1...4...7...5...7...6...5...2.......4...81...5.......1...3...4...2...6...3...5...1...4...7...5...7...9...5...2.......4...81...5.......1...3...7...6...5...9...3...8...1...6...7...6...4...9...8.......3...51...5.......1...3...7...6...5...9...3...8...1...6...7...6...8...9...4.......3...51...5.......1...3...8...4...5...8...9...7...1...6...4...7...8...3...4.......6...51...5.......1...3...7...6...5...8...3...4...1...6...7...6...4...9...4.......3...51...5.......1...3...8...4...5...8...6...7...1...9...4...7...8...3...4.......6...51...5.......3...2...5...4...3...4...9...8...1...9...3...4...8...7...1.......2...51...5.......3...5...4...2...3...2...5...7...4...9...6...6...3...9...5.......4...11...5.......3...6...4...2...3...7...5...2...4...6...5...6...9...7...8.......4...11...5.......3...6...4...2...7...2...5...9...7...1...3...2...5...6...4.......7...11...5.......3...6...4...2...8...7...5...8...4...6...9...6...9...3...5.......4...11...5.......1...4...9...6...3...9...5...1...3...6...2...6...9...4...7.......3...11...5.......1...2...9...3...5...8...6...7...1...2...9...2...9...7...3.......6...51...5.......1...6...9...3...8...3...5...1...8...7...2...8...9...3...2.......8...11...5.......2...4...4...3...8...3...5...2...6...9...5...9...8...3...4.......1...21...5.......3...2...6...3...5...8...9...3...1...2...6...2...1...3...7.......9...51...5.......3...6...4...2...3...2...5...9...4...8...9...2...8...6...5.......4...11...5.......3...5...4...2...3...2...5...6...4...7...9...2...8...8...5.......4...11...5.......2...3...6...1...5...7...6...4...5...3...9...9...8...3...2.......1...61...5.......1...3...7...2...5...8...6...7...1...9...7...9...8...3...9.......6...51...5.......1...3...7...2...5...8...6...7...1...6...7...9...8...3...9.......6...51...5.......1...5...7...3...4...8...5...1...2...3...9...2...8...3...9.......4...11...5.......1...6...4...3...8...3...5...1...4...7...5...6...8...3...9.......4...21...5.......2...3...6...2...7...3...5...2...7...6...9...4...5...3...9.......7...11...5.......3...2...5...4...6...4...3...8...5...2...9...8...1...4...9.......1...31...5.......3...6...4...2...3...2...5...8...4...6...7...6...3...7...5.......4...81...5.......3...6...9...4...7...4...5...1...7...6...9...6...5...3...2.......7...11...5.......1...2...7...6...8...3...5...1...4...9...6...9...1...6...2.......7...51...5.......3...2...5...4...9...4...3...8...5...2...6...8...1...4...9.......1...31...5.......3...6...4...2...3...1...5...9...4...6...2...8...9...6...5.......4...11...5.......3...6...4...2...3...2...5...1...4...6...7...6...3...7...5.......4...81...5.......1...4...7...2...3...4...5...1...3...6...9...2...8...4...7.......3...11...5.......1...4...7...2...3...4...5...1...3...6...9...2...9...4...7.......3...11...5.......3...6...4...2...3...1...5...8...4...6...2...8...9...6...5.......4...11...5.......3...6...4...2...7...1...5...9...7...6...3...2...5...6...4.......7...11...5.......1...3...4...6...6...3...9...4...1...6...9...7...8...3...4.......9...51...5.......1...3...7...2...5...1...9...7...1...2...7...4...8...3...4.......9...51...5.......1...3...7...6...5...2...9...8...1...6...7...6...4...3...8.......9...51...5.......1...6...4...2...3...8...6...3...5...2...9...2...6...7...4.......6...11...5.......2...3...8...2...7...3...5...6...7...8...4...6...5...3...4.......7...11...5.......1...3...7...6...5...8...3...2...1...6...7...6...9...9...4.......3...51...5.......1...4...6...3...7...3...5...9...7...8...2...1...5...3...4.......7...81...5.......1...6...9...4...3...9...5...1...3...6...2...6...9...4...7.......3...11...5.......3...6...7...4...3...9...4...1...2...6...7...6...5...7...2.......4...11...5.......1...6...7...4...5...4...3...9...8...6...7...6...1...7...9.......3...51...5.......1...6...8...4...5...4...3...9...7...8...2...4...5...6...2.......3...11...5.......2...3...4...6...8...9...3...4...5...8...6...8...2...6...3.......1...81...5.......3...1...4...6...3...8...2...3...7...7...6...9...3...6...1.......2...51...5.......3...2...7...4...6...4...3...8...5...2...7...9...1...4...7.......1...31...5.......3...6...5...2...3...9...7...3...1...5...4...9...4...6...1.......7...51...5.......3...6...5...2...3...9...7...3...1...5...4...9...8...6...1.......7...51...5.......1...2...7...3...5...2...9...4...1...3...7...2...6...4...3.......9...51...5.......2...3...5...6...7...1...8...4...7...3...6...9...2...6...3.......7...51...5.......2...6...4...3...8...1...5...2...8...6...7...9...5...6...7.......8...11...5.......1...6...4...2...3...2...5...9...4...6...7...6...1...7...5.......4...81...5.......1...6...4...3...3...8...5...2...4...6...7...6...1...7...5.......4...21...5.......1...2...4...6...9...4...8...1...5...2...6...5...1...6...7.......4...81...5.......1...3...4...2...3...4...9...6...5...2...6...2...9...6...7.......9...11...5.......1...3...7...2...5...8...9...7...1...6...7...4...8...3...4.......9...51...5.......3...4...6...2...5...4...7...9...1...2...6...8...1...3...2.......7...51...5.......1...3...4...6...6...3...5...1...7...9...5...7...2...3...9.......4...11...5.......1...3...4...6...8...7...5...1...4...6...5...6...8...3...9.......4...21...5.......1...3...9...6...4...2...8...1...5...3...6...5...1...6...3.......7...81...5.......1...6...4...2...3...2...5...8...4...6...7...6...1...7...5.......4...81...5.......1...6...4...3...8...3...5...1...4...8...5...6...9...3...7.......4...21...5.......1...6...8...4...5...4...3...2...7...8...2...4...5...6...2.......3...11...5.......2...4...6...3...8...3...5...8...1...9...6...4...9...3...5.......6...81...5.......2...6...4...3...8...1...5...2...8...6...7...1...5...6...7.......8...11...5.......3...2...4...6...5...2...7...4...1...8...9...2...1...3...8.......7...51...5.......3...2...7...4...8...1...3...2...5...9...7...9...1...4...7.......1...31...5.......3...2...7...4...8...1...3...6...5...9...7...9...1...4...7.......1...31...5.......3...4...7...6...9...1...3...4...5...8...6...8...1...6...4.......1...31...5.......3...6...4...2...3...7...5...1...4...6...7...6...9...7...5.......4...11...5.......3...6...4...2...7...8...5...2...4...6...5...6...8...3...7.......4...11...5.......3...6...7...4...3...4...5...8...2...6...7...6...3...7...5.......9...81...5.......1...2...7...6...5...8...3...7...1...6...7...2...8...6...9.......3...51...5.......1...3...4...2...8...4...9...6...5...2...6...2...9...7...3.......9...11...5.......1...3...7...4...5...8...6...7...1...9...7...2...8...9...3.......6...51...5.......1...4...4...3...9...3...2...8...1...5...7...7...8...3...4.......9...5`
Hidden Text: Show
Code: Select all
`1...5.......1...4...6...3...7...3...5...6...7...8...9...1...5...3...4.......7...81...5.......2...6...9...3...8...9...5...1...8...6...7...2...5...6...7.......8...11...5.......3...4...6...2...5...4...7...8...1...2...6...8...1...3...2.......7...51...5.......3...6...4...2...3...1...5...9...4...6...9...8...9...6...5.......4...11...5.......3...6...9...4...8...4...5...3...8...6...9...6...9...3...2.......8...51...5.......1...3...4...6...8...2...5...1...4...6...5...6...8...3...9.......4...21...5.......1...5...4...3...8...9...5...1...7...3...4...2...8...3...4.......7...11...5.......1...6...7...3...6...3...7...8...1...5...9...4...8...3...2.......7...51...5.......1...6...7...3...6...3...7...8...1...5...9...4...8...3...8.......7...51...5.......1...6...9...2...3...9...5...1...3...6...7...6...8...7...4.......3...11...5.......2...4...4...3...9...3...8...2...5...9...7...5...8...3...4.......7...11...5.......3...4...9...3...4...8...8...6...7...1...9...1...6...3...2.......4...81...5.......3...6...9...2...7...2...5...4...7...6...9...6...5...3...4.......7...81...5.......1...3...9...6...7...4...2...1...5...3...6...5...1...6...3.......7...81...5.......2...4...4...3...9...3...2...8...5...9...6...5...8...3...4.......6...11...5.......2...4...6...3...7...3...5...6...7...8...1...2...5...3...4.......7...81...5.......2...4...6...3...7...3...5...6...7...8...9...2...5...3...4.......7...81...5.......3...6...5...2...7...3...5...9...1...6...9...6...4...3...5.......1...71...5.......1...2...7...4...5...9...8...7...1...3...7...2...3...9...2.......8...51...5.......1...4...6...3...7...3...5...2...7...8...6...1...5...3...4.......7...81...5.......3...4...6...2...5...4...7...9...1...2...6...7...1...3...2.......8...51...5.......1...4...6...3...7...3...5...2...7...8...2...1...5...3...4.......7...81...5.......1...6...8...2...3...4...5...1...3...6...7...6...8...9...7.......3...11...5.......3...4...6...2...5...4...7...9...1...2...6...8...1...3...2.......8...51...5.......3...4...6...2...8...2...5...8...1...9...6...2...9...4...5.......6...81...5.......3...6...4...2...3...7...5...8...4...6...5...6...9...8...2.......4...11...5.......1...6...4...3...8...3...5...1...4...2...5...6...8...3...9.......4...21...5.......2...5...4...3...9...3...5...2...4...7...9...7...2...6...5.......4...11...5.......3...2...5...4...9...4...3...6...5...2...6...8...1...4...9.......1...31...5.......3...4...7...2...3...4...9...8...5...7...6...6...9...4...2.......9...31...5.......3...6...4...2...3...7...5...9...4...6...5...6...9...8...2.......4...11...5.......1...2...7...3...5...4...9...7...1...3...7...2...8...4...2.......9...51...5.......1...3...4...6...8...2...5...9...4...6...7...6...1...3...5.......4...71...5.......1...6...4...3...8...2...5...7...4...6...7...6...1...7...5.......4...81...5.......2...6...9...3...8...9...5...3...8...6...7...2...5...6...7.......8...11...5.......3...2...4...6...5...2...7...4...1...8...9...2...1...3...4.......7...51...5.......3...2...6...4...5...7...6...9...1...2...9...2...1...3...8.......6...51...5.......3...4...7...2...3...4...9...1...5...7...6...6...9...4...2.......9...31...5.......1...2...7...6...5...2...3...7...1...6...7...9...8...6...9.......3...51...5.......1...3...7...6...5...3...3...2...1...6...7...6...8...9...4.......3...51...5.......1...6...4...3...8...2...5...3...4...6...7...6...1...7...5.......4...21...5.......1...6...7...3...6...3...7...8...1...5...9...2...8...3...2.......7...51...5.......3...2...7...4...8...1...3...8...5...9...7...9...1...4...7.......1...31...5.......3...6...4...2...7...8...5...3...4...6...5...6...8...3...7.......4...11...5.......1...2...7...6...5...8...3...2...1...6...7...6...4...9...7.......3...51...5.......1...2...8...4...5...8...8...9...1...3...7...2...8...7...2.......3...51...5.......1...3...4...2...9...4...8...3...5...2...6...2...8...7...3.......8...11...5.......1...3...7...4...5...8...6...7...1...6...7...2...8...9...3.......6...51...5.......1...6...4...3...9...8...5...2...4...6...7...6...1...3...5.......4...71...5.......1...6...7...3...6...3...7...4...1...5...9...2...8...3...2.......7...51...5.......2...3...6...4...5...4...8...9...1...1...6...9...1...4...3.......8...51...5.......2...3...6...4...5...4...8...9...1...1...6...9...1...4...7.......8...51...5.......1...2...6...4...5...4...3...7...1...9...7...4...9...7...2.......3...51...5.......1...2...7...6...8...4...3...1...8...9...6...9...1...6...2.......7...31...5.......1...6...4...2...3...8...6...7...5...2...9...2...6...7...4.......6...11...5.......2...6...4...3...3...7...4...2...5...6...7...9...2...6...5.......4...11...5.......1...2...4...3...7...2...5...1...8...7...5...2...6...9...3.......4...11...5.......1...3...4...6...5...1...7...8...5...3...4...2...8...3...9.......7...11...5.......2...6...7...4...8...4...5...9...8...7...3...2...5...3...7.......8...11...5.......1...2...8...6...4...3...7...6...1...2...6...2...8...9...1.......7...51...5.......1...2...8...6...8...3...9...6...1...2...6...2...8...7...1.......9...51...5.......2...6...4...3...8...1...5...3...4...6...7...6.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Hidden Text: Show
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Last edited by Nick70 on Sun Dec 18, 2005 12:03 pm, edited 1 time in total.
Nick70

Posts: 156
Joined: 16 June 2005

(part 2, puzzles 401-851)

Code: Select all
`1...5.......1...3...7...6...5...8...9...3...1...6...4...2...8...3...7.......9...51...5.......2...6...4...3...8...3...7...2...5...9...4...5...2...3...4.......7...81...5.......2...6...9...3...5...3...7...8...5...6...2...4...6...3...2.......7...11...5.......1...6...4...2...7...3...5...2...8...6...7...6...3...3...7.......4...11...5.......1...6...4...2...7...3...5...9...8...6...7...6...3...3...7.......4...11...5.......1...6...4...2...7...3...9...2...8...6...7...6...3...3...7.......4...11...5.......2...5...9...3...4...3...5...4...2...6...1...7...6...3...1.......2...81...5.......2...6...9...3...5...3...7...8...5...6...2...4...6...3...2.......9...11...5.......1...6...8...3...3...9...5...7...4...6...7...6...1...7...5.......4...81...5.......1...6...8...4...3...4...5...7...2...6...7...6...1...7...5.......2...81...5.......2...6...9...3...6...3...5...4...1...6...5...2...9...3...4.......1...81...5.......1...4...4...3...9...3...5...2...1...8...7...9...8...3...4.......6...51...5.......1...6...4...3...6...4...2...8...1...3...7...6...8...7...1.......2...51...5.......2...6...7...4...3...4...2...9...5...6...7...6...5...9...7.......2...31...5.......2...6...7...4...3...4...2...9...5...6...7...6...5...9...7.......2...81...5.......3...6...8...4...4...1...3...6...5...8...9...9...1...6...7.......1...31...5.......1...3...4...2...7...4...5...8...1...3...6...2...8...3...2.......4...51...5.......2...3...4...6...3...1...8...2...5...9...6...9...8...6...3.......8...11...5.......1...4...7...6...5...8...3...6...1...9...7...6...9...9...4.......3...51...5.......3...4...5...2...4...2...3...1...5...7...9...7...6...3...9.......4...11...5.......1...4...4...6...5...2...8...9...1...7...3...7...8...9...4.......2...51...5.......1...4...4...6...5...9...8...3...1...2...6...2...8...9...4.......7...51...5.......1...4...8...2...5...4...9...1...5...6...7...6...1...4...7.......9...81...5.......3...2...5...6...3...8...8...3...5...5...6...4...9...6...2.......7...11...5.......2...3...5...2...9...7...5...8...1...3...6...6...8...3...9.......2...51...5.......2...3...9...4...4...7...3...1...5...8...7...2...8...7...3.......7...11...5.......1...6...6...3...4...8...5...9...4...3...7...7...8...3...9.......4...11...5.......1...3...4...2...5...2...8...4...5...3...6...6...8...3...4.......9...11...5.......1...3...4...2...5...2...6...4...5...3...7...7...8...3...9.......6...11...5.......7...4...4...6...8...3...5...7...8...6...9...6...3...3...2.......8...51...5.......7...4...6...3...3...4...5...7...2...6...5...4...9...9...1.......2...81...5.......1...6...7...4...3...4...5...1...3...8...2...2...8...6...7.......3...11...5.......2...6...4...3...3...1...2...8...1...7...4...7...1...6...4.......2...51...5.......3...2...8...4...4...1...3...8...5...9...7...5...1...7...2.......1...31...5.......1...3...4...6...8...9...5...7...4...6...9...6...1...3...5.......4...71...5.......1...6...4...3...6...3...8...4...1...7...2...1...5...3...4.......2...81...5.......1...3...8...4...4...3...5...4...8...2...9...6...1...3...9.......1...51...5.......1...4...4...6...8...3...5...1...7...6...5...8...2...6...9.......7...11...5.......1...3...7...2...5...8...6...7...1...2...9...1...8...3...9.......6...51...5.......1...3...8...4...4...3...5...4...8...7...9...6...1...3...7.......1...51...5.......1...3...4...6...8...9...5...1...4...6...5...6...8...3...2.......4...21...5.......2...6...4...3...4...9...5...2...1...6...7...2...1...6...7.......4...51...5.......1...2...4...6...8...4...9...6...1...2...6...2...4...7...1.......9...51...5.......3...6...4...3...3...2...5...3...4...9...5...9...2...6...1.......4...81...5.......1...6...7...4...3...9...5...1...3...6...9...8...2...6...7.......3...11...5.......2...6...8...4...4...3...9...2...1...6...7...2...1...6...1.......9...51...5.......1...2...9...4...8...2...4...7...1...6...7...2...8...6...8.......1...41...5.......1...2...4...6...8...2...6...4...5...3...7...2...1...9...4.......7...41...5.......2...3...9...4...8...9...5...8...1...6...2...8...1...4...5.......6...81...5.......2...6...4...3...4...9...5...2...1...6...9...2...1...6...8.......4...51...5.......3...2...4...6...7...1...5...7...4...2...9...9...2...6...5.......4...11...5.......1...2...8...4...8...2...6...8...3...7...1...2...8...7...1.......3...61...5.......1...3...7...4...5...4...6...7...1...8...9...1...2...3...9.......6...51...5.......1...6...7...2...3...4...5...1...3...6...4...6...8...8...7.......3...11...5.......1...3...8...4...5...3...7...4...1...9...4...2...6...3...9.......7...51...5.......2...5...9...3...8...3...5...8...2...6...1...4...8...3...1.......2...61...5.......7...2...4...6...3...2...5...7...4...9...5...2...8...6...4.......1...71...5.......3...6...4...2...3...1...5...8...4...9...7...8...9...6...5.......4...11...5.......3...2...4...6...5...3...7...4...1...6...4...2...1...6...9.......7...51...5.......1...2...4...3...9...2...5...1...7...6...5...2...8...7...9.......4...11...5.......1...2...6...4...5...4...3...7...1...2...7...4...2...7...9.......3...51...5.......2...3...7...2...3...2...5...8...3...9...7...6.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Nick70

Posts: 156
Joined: 16 June 2005

Very nice
How did you do it ?

Could you perform your analysis [or show me] on a 17 clue [non-symmetric,sorry] pattern ?

Based on 17 clue patterns......
Gfroyle wrote:There are 20717 different clue-patterns with the most popular pattern occurring 36 times - here is one with this pattern.

Code: Select all
` 0 8 0  0 0 0  0 0 9  0 1 2  0 0 0  0 0 0  0 0 0  6 0 0  3 0 0  0 7 0  0 0 0  2 8 0  9 0 0  4 0 0  0 0 0  0 0 0  3 0 0  0 0 0  3 0 0  0 0 0  4 0 0  5 0 0  0 8 0  0 0 0  0 0 0  0 1 0  0 0 0 `

See if we can get more than 36 !

Maybe Gordon has done this already ?

Regards

.
coloin

Posts: 1946
Joined: 05 May 2005

Actually, I have done some thinking on how to do an exhaustive search on a pattern.

I have not written it yet, but I have a couple of thoughts on how to do it:

First of all: Let new symbols come in ascending order. I.e., if you read the clues in a specific order, the first occurence of 1 should be before 2 etc., and if only 8 symbols occur in the clues, let 9 be the missing symbol.

Secondly, use the benifit from knowing the pattern to fill in the remaining grids in an apparently best order: Fill in those cells that are expected to have fewest possibilities first. You can use an expected number of possibilities in a cell based on the pattern on which cells are allready filled in on the same row, same column, and in the same box in or outside the row/column. More exactly:

Code: Select all
`XBB DDD DDDCAA ... ...CAA ... ...E.. ... ...E.. ... ...E.. ... ...E.. ... ...E.. ... ...E.. ... ...`

Suppose the number of cells already filled in are A (range from 0 to 4), B (0-2), C (0-6), D (0-2), E (0-6) on the cells with the same names above. What is the expected number on possible values for X? With no assumption except that the filled-in cells follow the rules of Sudoku (i.e. the A's and B's differ, the A's and C's differ, the B's and D's differ and the C's and E's differ), the expected possibilities are:
Code: Select all
`A B C D E expected number of values for X0 0 0 0 0 9.00 0 0 0 1 8.00 0 0 0 2 7.00 0 0 0 3 6.00 0 0 0 4 5.00 0 0 0 5 4.00 0 0 0 6 3.00 0 0 1 0 8.00 0 0 1 1 7.111111110 0 0 1 2 6.222222220 0 0 1 3 5.333333330 0 0 1 4 4.444444440 0 0 1 5 3.555555560 0 0 1 6 2.666666670 0 0 2 0 7.00 0 0 2 1 6.222222220 0 0 2 2 5.444444440 0 0 2 3 4.666666670 0 0 2 4 3.888888890 0 0 2 5 3.111111110 0 0 2 6 2.333333330 0 0 3 0 6.00 0 0 3 1 5.333333330 0 0 3 2 4.666666670 0 0 3 3 4.00 0 0 3 4 3.333333330 0 0 3 5 2.666666670 0 0 3 6 2.00 0 0 4 0 5.00 0 0 4 1 4.444444440 0 0 4 2 3.888888890 0 0 4 3 3.333333330 0 0 4 4 2.777777780 0 0 4 5 2.222222220 0 0 4 6 1.666666670 0 0 5 0 4.00 0 0 5 1 3.555555560 0 0 5 2 3.111111110 0 0 5 3 2.666666670 0 0 5 4 2.222222220 0 0 5 5 1.777777780 0 0 5 6 1.333333330 0 0 6 0 3.00 0 0 6 1 2.666666670 0 0 6 2 2.333333330 0 0 6 3 2.00 0 0 6 4 1.666666670 0 0 6 5 1.333333330 0 0 6 6 1.00 0 1 0 0 8.00 0 1 0 1 7.00 0 1 0 2 6.00 0 1 0 3 5.00 0 1 0 4 4.00 0 1 0 5 3.00 0 1 0 6 2.00 0 1 1 0 7.111111110 0 1 1 1 6.222222220 0 1 1 2 5.333333330 0 1 1 3 4.444444440 0 1 1 4 3.555555560 0 1 1 5 2.666666670 0 1 1 6 1.777777780 0 1 2 0 6.222222220 0 1 2 1 5.444444440 0 1 2 2 4.666666670 0 1 2 3 3.888888890 0 1 2 4 3.111111110 0 1 2 5 2.333333330 0 1 2 6 1.555555560 0 1 3 0 5.333333330 0 1 3 1 4.666666670 0 1 3 2 4.00 0 1 3 3 3.333333330 0 1 3 4 2.666666670 0 1 3 5 2.00 0 1 3 6 1.333333330 0 1 4 0 4.444444440 0 1 4 1 3.888888890 0 1 4 2 3.333333330 0 1 4 3 2.777777780 0 1 4 4 2.222222220 0 1 4 5 1.666666670 0 1 4 6 1.111111110 0 1 5 0 3.555555560 0 1 5 1 3.111111110 0 1 5 2 2.666666670 0 1 5 3 2.222222220 0 1 5 4 1.777777780 0 1 5 5 1.333333330 0 1 5 6 0.888888890 0 1 6 0 2.666666670 0 1 6 1 2.333333330 0 1 6 2 2.00 0 1 6 3 1.666666670 0 1 6 4 1.333333330 0 1 6 5 1.00 0 1 6 6 0.666666670 0 2 0 0 7.00 0 2 0 1 6.00 0 2 0 2 5.00 0 2 0 3 4.00 0 2 0 4 3.00 0 2 0 5 2.00 0 2 0 6 1.00 0 2 1 0 6.222222220 0 2 1 1 5.333333330 0 2 1 2 4.444444440 0 2 1 3 3.555555560 0 2 1 4 2.666666670 0 2 1 5 1.777777780 0 2 1 6 0.888888890 0 2 2 0 5.444444440 0 2 2 1 4.666666670 0 2 2 2 3.888888890 0 2 2 3 3.111111110 0 2 2 4 2.333333330 0 2 2 5 1.555555560 0 2 2 6 0.777777780 0 2 3 0 4.666666670 0 2 3 1 4.00 0 2 3 2 3.333333330 0 2 3 3 2.666666670 0 2 3 4 2.00 0 2 3 5 1.333333330 0 2 3 6 0.666666670 0 2 4 0 3.888888890 0 2 4 1 3.333333330 0 2 4 2 2.777777780 0 2 4 3 2.222222220 0 2 4 4 1.666666670 0 2 4 5 1.111111110 0 2 4 6 0.555555560 0 2 5 0 3.111111110 0 2 5 1 2.666666670 0 2 5 2 2.222222220 0 2 5 3 1.777777780 0 2 5 4 1.333333330 0 2 5 5 0.888888890 0 2 5 6 0.444444440 0 2 6 0 2.333333330 0 2 6 1 2.00 0 2 6 2 1.666666670 0 2 6 3 1.333333330 0 2 6 4 1.00 0 2 6 5 0.666666670 0 2 6 6 0.333333330 1 0 0 0 8.00 1 0 0 1 7.111111110 1 0 0 2 6.222222220 1 0 0 3 5.333333330 1 0 0 4 4.444444440 1 0 0 5 3.555555560 1 0 0 6 2.666666670 1 0 1 0 7.00 1 0 1 1 6.222222220 1 0 1 2 5.444444440 1 0 1 3 4.666666670 1 0 1 4 3.888888890 1 0 1 5 3.111111110 1 0 1 6 2.333333330 1 0 2 0 6.00 1 0 2 1 5.333333330 1 0 2 2 4.666666670 1 0 2 3 4.00 1 0 2 4 3.333333330 1 0 2 5 2.666666670 1 0 2 6 2.00 1 0 3 0 5.00 1 0 3 1 4.444444440 1 0 3 2 3.888888890 1 0 3 3 3.333333330 1 0 3 4 2.777777780 1 0 3 5 2.222222220 1 0 3 6 1.666666670 1 0 4 0 4.00 1 0 4 1 3.555555560 1 0 4 2 3.111111110 1 0 4 3 2.666666670 1 0 4 4 2.222222220 1 0 4 5 1.777777780 1 0 4 6 1.333333330 1 0 5 0 3.00 1 0 5 1 2.666666670 1 0 5 2 2.333333330 1 0 5 3 2.00 1 0 5 4 1.666666670 1 0 5 5 1.333333330 1 0 5 6 1.00 1 0 6 0 2.00 1 0 6 1 1.777777780 1 0 6 2 1.555555560 1 0 6 3 1.333333330 1 0 6 4 1.111111110 1 0 6 5 0.888888890 1 0 6 6 0.666666670 1 1 0 0 7.00 1 1 0 1 6.1250 1 1 0 2 5.250 1 1 0 3 4.3750 1 1 0 4 3.50 1 1 0 5 2.6250 1 1 0 6 1.750 1 1 1 0 6.1250 1 1 1 1 5.3593750 1 1 1 2 4.593750 1 1 1 3 3.8281250 1 1 1 4 3.06250 1 1 1 5 2.2968750 1 1 1 6 1.531250 1 1 2 0 5.250 1 1 2 1 4.593750 1 1 2 2 3.93750 1 1 2 3 3.281250 1 1 2 4 2.6250 1 1 2 5 1.968750 1 1 2 6 1.31250 1 1 3 0 4.3750 1 1 3 1 3.8281250 1 1 3 2 3.281250 1 1 3 3 2.7343750 1 1 3 4 2.18750 1 1 3 5 1.6406250 1 1 3 6 1.093750 1 1 4 0 3.50 1 1 4 1 3.06250 1 1 4 2 2.6250 1 1 4 3 2.18750 1 1 4 4 1.750 1 1 4 5 1.31250 1 1 4 6 0.8750 1 1 5 0 2.6250 1 1 5 1 2.2968750 1 1 5 2 1.968750 1 1 5 3 1.6406250 1 1 5 4 1.31250 1 1 5 5 0.9843750 1 1 5 6 0.656250 1 1 6 0 1.750 1 1 6 1 1.531250 1 1 6 2 1.31250 1 1 6 3 1.093750 1 1 6 4 0.8750 1 1 6 5 0.656250 1 1 6 6 0.43750 1 2 0 0 6.00 1 2 0 1 5.142857140 1 2 0 2 4.285714290 1 2 0 3 3.428571430 1 2 0 4 2.571428570 1 2 0 5 1.714285710 1 2 0 6 0.857142860 1 2 1 0 5.250 1 2 1 1 4.50 1 2 1 2 3.750 1 2 1 3 3.00 1 2 1 4 2.250 1 2 1 5 1.50 1 2 1 6 0.750 1 2 2 0 4.50 1 2 2 1 3.857142860 1 2 2 2 3.214285710 1 2 2 3 2.571428570 1 2 2 4 1.928571430 1 2 2 5 1.285714290 1 2 2 6 0.642857140 1 2 3 0 3.750 1 2 3 1 3.214285710 1 2 3 2 2.678571430 1 2 3 3 2.142857140 1 2 3 4 1.607142860 1 2 3 5 1.071428570 1 2 3 6 0.535714290 1 2 4 0 3.00 1 2 4 1 2.571428570 1 2 4 2 2.142857140 1 2 4 3 1.714285710 1 2 4 4 1.285714290 1 2 4 5 0.857142860 1 2 4 6 0.428571430 1 2 5 0 2.250 1 2 5 1 1.928571430 1 2 5 2 1.607142860 1 2 5 3 1.285714290 1 2 5 4 0.964285710 1 2 5 5 0.642857140 1 2 5 6 0.321428570 1 2 6 0 1.50 1 2 6 1 1.285714290 1 2 6 2 1.071428570 1 2 6 3 0.857142860 1 2 6 4 0.642857140 1 2 6 5 0.428571430 1 2 6 6 0.214285710 2 0 0 0 7.00 2 0 0 1 6.222222220 2 0 0 2 5.444444440 2 0 0 3 4.666666670 2 0 0 4 3.888888890 2 0 0 5 3.111111110 2 0 0 6 2.333333330 2 0 1 0 6.00 2 0 1 1 5.333333330 2 0 1 2 4.666666670 2 0 1 3 4.00 2 0 1 4 3.333333330 2 0 1 5 2.666666670 2 0 1 6 2.00 2 0 2 0 5.00 2 0 2 1 4.444444440 2 0 2 2 3.888888890 2 0 2 3 3.333333330 2 0 2 4 2.777777780 2 0 2 5 2.222222220 2 0 2 6 1.666666670 2 0 3 0 4.00 2 0 3 1 3.555555560 2 0 3 2 3.111111110 2 0 3 3 2.666666670 2 0 3 4 2.222222220 2 0 3 5 1.777777780 2 0 3 6 1.333333330 2 0 4 0 3.00 2 0 4 1 2.666666670 2 0 4 2 2.333333330 2 0 4 3 2.00 2 0 4 4 1.666666670 2 0 4 5 1.333333330 2 0 4 6 1.00 2 0 5 0 2.00 2 0 5 1 1.777777780 2 0 5 2 1.555555560 2 0 5 3 1.333333330 2 0 5 4 1.111111110 2 0 5 5 0.888888890 2 0 5 6 0.666666670 2 0 6 0 1.00 2 0 6 1 0.888888890 2 0 6 2 0.777777780 2 0 6 3 0.666666670 2 0 6 4 0.555555560 2 0 6 5 0.444444440 2 0 6 6 0.333333330 2 1 0 0 6.00 2 1 0 1 5.250 2 1 0 2 4.50 2 1 0 3 3.750 2 1 0 4 3.00 2 1 0 5 2.250 2 1 0 6 1.50 2 1 1 0 5.142857140 2 1 1 1 4.50 2 1 1 2 3.857142860 2 1 1 3 3.214285710 2 1 1 4 2.571428570 2 1 1 5 1.928571430 2 1 1 6 1.285714290 2 1 2 0 4.285714290 2 1 2 1 3.750 2 1 2 2 3.214285710 2 1 2 3 2.678571430 2 1 2 4 2.142857140 2 1 2 5 1.607142860 2 1 2 6 1.071428570 2 1 3 0 3.428571430 2 1 3 1 3.00 2 1 3 2 2.571428570 2 1 3 3 2.142857140 2 1 3 4 1.714285710 2 1 3 5 1.285714290 2 1 3 6 0.857142860 2 1 4 0 2.571428570 2 1 4 1 2.250 2 1 4 2 1.928571430 2 1 4 3 1.607142860 2 1 4 4 1.285714290 2 1 4 5 0.964285710 2 1 4 6 0.642857140 2 1 5 0 1.714285710 2 1 5 1 1.50 2 1 5 2 1.285714290 2 1 5 3 1.071428570 2 1 5 4 0.857142860 2 1 5 5 0.642857140 2 1 5 6 0.428571430 2 1 6 0 0.857142860 2 1 6 1 0.750 2 1 6 2 0.642857140 2 1 6 3 0.535714290 2 1 6 4 0.428571430 2 1 6 5 0.321428570 2 1 6 6 0.214285710 2 2 0 0 5.00 2 2 0 1 4.285714290 2 2 0 2 3.571428570 2 2 0 3 2.857142860 2 2 0 4 2.142857140 2 2 0 5 1.428571430 2 2 0 6 0.714285710 2 2 1 0 4.285714290 2 2 1 1 3.673469390 2 2 1 2 3.061224490 2 2 1 3 2.448979590 2 2 1 4 1.836734690 2 2 1 5 1.22448980 2 2 1 6 0.61224490 2 2 2 0 3.571428570 2 2 2 1 3.061224490 2 2 2 2 2.551020410 2 2 2 3 2.040816330 2 2 2 4 1.530612240 2 2 2 5 1.020408160 2 2 2 6 0.510204080 2 2 3 0 2.857142860 2 2 3 1 2.448979590 2 2 3 2 2.040816330 2 2 3 3 1.632653060 2 2 3 4 1.22448980 2 2 3 5 0.816326530 2 2 3 6 0.408163270 2 2 4 0 2.142857140 2 2 4 1 1.836734690 2 2 4 2 1.530612240 2 2 4 3 1.22448980 2 2 4 4 0.918367350 2 2 4 5 0.61224490 2 2 4 6 0.306122450 2 2 5 0 1.428571430 2 2 5 1 1.22448980 2 2 5 2 1.020408160 2 2 5 3 0.816326530 2 2 5 4 0.61224490 2 2 5 5 0.408163270 2 2 5 6 0.204081630 2 2 6 0 0.714285710 2 2 6 1 0.61224490 2 2 6 2 0.510204080 2 2 6 3 0.408163270 2 2 6 4 0.306122450 2 2 6 5 0.204081630 2 2 6 6 0.102040821 0 0 0 0 8.01 0 0 0 1 7.111111111 0 0 0 2 6.222222221 0 0 0 3 5.333333331 0 0 0 4 4.444444441 0 0 0 5 3.555555561 0 0 0 6 2.666666671 0 0 1 0 7.111111111 0 0 1 1 6.320987651 0 0 1 2 5.53086421 0 0 1 3 4.740740741 0 0 1 4 3.950617281 0 0 1 5 3.160493831 0 0 1 6 2.370370371 0 0 2 0 6.222222221 0 0 2 1 5.53086421 0 0 2 2 4.839506171 0 0 2 3 4.148148151 0 0 2 4 3.456790121 0 0 2 5 2.76543211 0 0 2 6 2.074074071 0 0 3 0 5.333333331 0 0 3 1 4.740740741 0 0 3 2 4.148148151 0 0 3 3 3.555555561 0 0 3 4 2.962962961 0 0 3 5 2.370370371 0 0 3 6 1.777777781 0 0 4 0 4.444444441 0 0 4 1 3.950617281 0 0 4 2 3.456790121 0 0 4 3 2.962962961 0 0 4 4 2.46913581 0 0 4 5 1.975308641 0 0 4 6 1.481481481 0 0 5 0 3.555555561 0 0 5 1 3.160493831 0 0 5 2 2.76543211 0 0 5 3 2.370370371 0 0 5 4 1.975308641 0 0 5 5 1.580246911 0 0 5 6 1.185185191 0 0 6 0 2.666666671 0 0 6 1 2.370370371 0 0 6 2 2.074074071 0 0 6 3 1.777777781 0 0 6 4 1.481481481 0 0 6 5 1.185185191 0 0 6 6 0.888888891 0 1 0 0 7.01 0 1 0 1 6.1251 0 1 0 2 5.251 0 1 0 3 4.3751 0 1 0 4 3.51 0 1 0 5 2.6251 0 1 0 6 1.751 0 1 1 0 6.222222221 0 1 1 1 5.444444441 0 1 1 2 4.666666671 0 1 1 3 3.888888891 0 1 1 4 3.111111111 0 1 1 5 2.333333331 0 1 1 6 1.555555561 0 1 2 0 5.444444441 0 1 2 1 4.763888891 0 1 2 2 4.083333331 0 1 2 3 3.402777781 0 1 2 4 2.722222221 0 1 2 5 2.041666671 0 1 2 6 1.361111111 0 1 3 0 4.666666671 0 1 3 1 4.083333331 0 1 3 2 3.51 0 1 3 3 2.916666671 0 1 3 4 2.333333331 0 1 3 5 1.751 0 1 3 6 1.166666671 0 1 4 0 3.888888891 0 1 4 1 3.402777781 0 1 4 2 2.916666671 0 1 4 3 2.430555561 0 1 4 4 1.944444441 0 1 4 5 1.458333331 0 1 4 6 0.972222221 0 1 5 0 3.111111111 0 1 5 1 2.722222221 0 1 5 2 2.333333331 0 1 5 3 1.944444441 0 1 5 4 1.555555561 0 1 5 5 1.166666671 0 1 5 6 0.777777781 0 1 6 0 2.333333331 0 1 6 1 2.041666671 0 1 6 2 1.751 0 1 6 3 1.458333331 0 1 6 4 1.166666671 0 1 6 5 0.8751 0 1 6 6 0.583333331 0 2 0 0 6.01 0 2 0 1 5.142857141 0 2 0 2 4.285714291 0 2 0 3 3.428571431 0 2 0 4 2.571428571 0 2 0 5 1.714285711 0 2 0 6 0.857142861 0 2 1 0 5.333333331 0 2 1 1 4.571428571 0 2 1 2 3.809523811 0 2 1 3 3.047619051 0 2 1 4 2.285714291 0 2 1 5 1.523809521 0 2 1 6 0.761904761 0 2 2 0 4.666666671 0 2 2 1 4.01 0 2 2 2 3.333333331 0 2 2 3 2.666666671 0 2 2 4 2.01 0 2 2 5 1.333333331 0 2 2 6 0.666666671 0 2 3 0 4.01 0 2 3 1 3.428571431 0 2 3 2 2.857142861 0 2 3 3 2.285714291 0 2 3 4 1.714285711 0 2 3 5 1.142857141 0 2 3 6 0.571428571 0 2 4 0 3.333333331 0 2 4 1 2.857142861 0 2 4 2 2.380952381 0 2 4 3 1.90476191 0 2 4 4 1.428571431 0 2 4 5 0.952380951 0 2 4 6 0.476190481 0 2 5 0 2.666666671 0 2 5 1 2.285714291 0 2 5 2 1.90476191 0 2 5 3 1.523809521 0 2 5 4 1.142857141 0 2 5 5 0.761904761 0 2 5 6 0.380952381 0 2 6 0 2.01 0 2 6 1 1.714285711 0 2 6 2 1.428571431 0 2 6 3 1.142857141 0 2 6 4 0.857142861 0 2 6 5 0.571428571 0 2 6 6 0.285714291 1 0 0 0 7.01 1 0 0 1 6.222222221 1 0 0 2 5.444444441 1 0 0 3 4.666666671 1 0 0 4 3.888888891 1 0 0 5 3.111111111 1 0 0 6 2.333333331 1 0 1 0 6.1251 1 0 1 1 5.444444441 1 0 1 2 4.763888891 1 0 1 3 4.083333331 1 0 1 4 3.402777781 1 0 1 5 2.722222221 1 0 1 6 2.041666671 1 0 2 0 5.251 1 0 2 1 4.666666671 1 0 2 2 4.083333331 1 0 2 3 3.51 1 0 2 4 2.916666671 1 0 2 5 2.333333331 1 0 2 6 1.751 1 0 3 0 4.3751 1 0 3 1 3.888888891 1 0 3 2 3.402777781 1 0 3 3 2.916666671 1 0 3 4 2.430555561 1 0 3 5 1.944444441 1 0 3 6 1.458333331 1 0 4 0 3.51 1 0 4 1 3.111111111 1 0 4 2 2.722222221 1 0 4 3 2.333333331 1 0 4 4 1.944444441 1 0 4 5 1.555555561 1 0 4 6 1.166666671 1 0 5 0 2.6251 1 0 5 1 2.333333331 1 0 5 2 2.041666671 1 0 5 3 1.751 1 0 5 4 1.458333331 1 0 5 5 1.166666671 1 0 5 6 0.8751 1 0 6 0 1.751 1 0 6 1 1.555555561 1 0 6 2 1.361111111 1 0 6 3 1.166666671 1 0 6 4 0.972222221 1 0 6 5 0.777777781 1 0 6 6 0.583333331 1 1 0 0 6.01 1 1 0 1 5.251 1 1 0 2 4.51 1 1 0 3 3.751 1 1 0 4 3.01 1 1 0 5 2.251 1 1 0 6 1.51 1 1 1 0 5.251 1 1 1 1 4.593751 1 1 1 2 3.93751 1 1 1 3 3.281251 1 1 1 4 2.6251 1 1 1 5 1.968751 1 1 1 6 1.31251 1 1 2 0 4.51 1 1 2 1 3.93751 1 1 2 2 3.3751 1 1 2 3 2.81251 1 1 2 4 2.251 1 1 2 5 1.68751 1 1 2 6 1.1251 1 1 3 0 3.751 1 1 3 1 3.281251 1 1 3 2 2.81251 1 1 3 3 2.343751 1 1 3 4 1.8751 1 1 3 5 1.406251 1 1 3 6 0.93751 1 1 4 0 3.01 1 1 4 1 2.6251 1 1 4 2 2.251 1 1 4 3 1.8751 1 1 4 4 1.51 1 1 4 5 1.1251 1 1 4 6 0.751 1 1 5 0 2.251 1 1 5 1 1.968751 1 1 5 2 1.68751 1 1 5 3 1.406251 1 1 5 4 1.1251 1 1 5 5 0.843751 1 1 5 6 0.56251 1 1 6 0 1.51 1 1 6 1 1.31251 1 1 6 2 1.1251 1 1 6 3 0.93751 1 1 6 4 0.751 1 1 6 5 0.56251 1 1 6 6 0.3751 1 2 0 0 5.01 1 2 0 1 4.285714291 1 2 0 2 3.571428571 1 2 0 3 2.857142861 1 2 0 4 2.142857141 1 2 0 5 1.428571431 1 2 0 6 0.714285711 1 2 1 0 4.3751 1 2 1 1 3.751 1 2 1 2 3.1251 1 2 1 3 2.51 1 2 1 4 1.8751 1 2 1 5 1.251 1 2 1 6 0.6251 1 2 2 0 3.751 1 2 2 1 3.214285711 1 2 2 2 2.678571431 1 2 2 3 2.142857141 1 2 2 4 1.607142861 1 2 2 5 1.071428571 1 2 2 6 0.535714291 1 2 3 0 3.1251 1 2 3 1 2.678571431 1 2 3 2 2.232142861 1 2 3 3 1.785714291 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0.3753 1 2 2 0 2.253 1 2 2 1 1.928571433 1 2 2 2 1.607142863 1 2 2 3 1.285714293 1 2 2 4 0.964285713 1 2 2 5 0.642857143 1 2 2 6 0.321428573 1 2 3 0 1.8753 1 2 3 1 1.607142863 1 2 3 2 1.339285713 1 2 3 3 1.071428573 1 2 3 4 0.803571433 1 2 3 5 0.535714293 1 2 3 6 0.267857143 1 2 4 0 1.53 1 2 4 1 1.285714293 1 2 4 2 1.071428573 1 2 4 3 0.857142863 1 2 4 4 0.642857143 1 2 4 5 0.428571433 1 2 4 6 0.214285713 1 2 5 0 1.1253 1 2 5 1 0.964285713 1 2 5 2 0.803571433 1 2 5 3 0.642857143 1 2 5 4 0.482142863 1 2 5 5 0.321428573 1 2 5 6 0.160714293 1 2 6 0 0.753 1 2 6 1 0.642857143 1 2 6 2 0.535714293 1 2 6 3 0.428571433 1 2 6 4 0.321428573 1 2 6 5 0.214285713 1 2 6 6 0.107142863 2 0 0 0 4.03 2 0 0 1 3.555555563 2 0 0 2 3.111111113 2 0 0 3 2.666666673 2 0 0 4 2.222222223 2 0 0 5 1.777777783 2 0 0 6 1.333333333 2 0 1 0 3.428571433 2 0 1 1 3.047619053 2 0 1 2 2.666666673 2 0 1 3 2.285714293 2 0 1 4 1.90476193 2 0 1 5 1.523809523 2 0 1 6 1.142857143 2 0 2 0 2.857142863 2 0 2 1 2.539682543 2 0 2 2 2.222222223 2 0 2 3 1.90476193 2 0 2 4 1.587301593 2 0 2 5 1.269841273 2 0 2 6 0.952380953 2 0 3 0 2.285714293 2 0 3 1 2.031746033 2 0 3 2 1.777777783 2 0 3 3 1.523809523 2 0 3 4 1.269841273 2 0 3 5 1.015873023 2 0 3 6 0.761904763 2 0 4 0 1.714285713 2 0 4 1 1.523809523 2 0 4 2 1.333333333 2 0 4 3 1.142857143 2 0 4 4 0.952380953 2 0 4 5 0.761904763 2 0 4 6 0.571428573 2 0 5 0 1.142857143 2 0 5 1 1.015873023 2 0 5 2 0.888888893 2 0 5 3 0.761904763 2 0 5 4 0.634920633 2 0 5 5 0.507936513 2 0 5 6 0.380952383 2 0 6 0 0.571428573 2 0 6 1 0.507936513 2 0 6 2 0.444444443 2 0 6 3 0.380952383 2 0 6 4 0.317460323 2 0 6 5 0.253968253 2 0 6 6 0.190476193 2 1 0 0 3.03 2 1 0 1 2.6253 2 1 0 2 2.253 2 1 0 3 1.8753 2 1 0 4 1.53 2 1 0 5 1.1253 2 1 0 6 0.753 2 1 1 0 2.571428573 2 1 1 1 2.253 2 1 1 2 1.928571433 2 1 1 3 1.607142863 2 1 1 4 1.285714293 2 1 1 5 0.964285713 2 1 1 6 0.642857143 2 1 2 0 2.142857143 2 1 2 1 1.8753 2 1 2 2 1.607142863 2 1 2 3 1.339285713 2 1 2 4 1.071428573 2 1 2 5 0.803571433 2 1 2 6 0.535714293 2 1 3 0 1.714285713 2 1 3 1 1.53 2 1 3 2 1.285714293 2 1 3 3 1.071428573 2 1 3 4 0.857142863 2 1 3 5 0.642857143 2 1 3 6 0.428571433 2 1 4 0 1.285714293 2 1 4 1 1.1253 2 1 4 2 0.964285713 2 1 4 3 0.803571433 2 1 4 4 0.642857143 2 1 4 5 0.482142863 2 1 4 6 0.321428573 2 1 5 0 0.857142863 2 1 5 1 0.753 2 1 5 2 0.642857143 2 1 5 3 0.535714293 2 1 5 4 0.428571433 2 1 5 5 0.321428573 2 1 5 6 0.214285713 2 1 6 0 0.428571433 2 1 6 1 0.3753 2 1 6 2 0.321428573 2 1 6 3 0.267857143 2 1 6 4 0.214285713 2 1 6 5 0.160714293 2 1 6 6 0.107142863 2 2 0 0 2.03 2 2 0 1 1.714285713 2 2 0 2 1.428571433 2 2 0 3 1.142857143 2 2 0 4 0.857142863 2 2 0 5 0.571428573 2 2 0 6 0.285714293 2 2 1 0 1.714285713 2 2 1 1 1.469387763 2 2 1 2 1.22448983 2 2 1 3 0.979591843 2 2 1 4 0.734693883 2 2 1 5 0.489795923 2 2 1 6 0.244897963 2 2 2 0 1.428571433 2 2 2 1 1.22448983 2 2 2 2 1.020408163 2 2 2 3 0.816326533 2 2 2 4 0.61224493 2 2 2 5 0.408163273 2 2 2 6 0.204081633 2 2 3 0 1.142857143 2 2 3 1 0.979591843 2 2 3 2 0.816326533 2 2 3 3 0.653061223 2 2 3 4 0.489795923 2 2 3 5 0.326530613 2 2 3 6 0.163265313 2 2 4 0 0.857142863 2 2 4 1 0.734693883 2 2 4 2 0.61224493 2 2 4 3 0.489795923 2 2 4 4 0.367346943 2 2 4 5 0.244897963 2 2 4 6 0.122448983 2 2 5 0 0.571428573 2 2 5 1 0.489795923 2 2 5 2 0.408163273 2 2 5 3 0.326530613 2 2 5 4 0.244897963 2 2 5 5 0.163265313 2 2 5 6 0.081632653 2 2 6 0 0.285714293 2 2 6 1 0.244897963 2 2 6 2 0.204081633 2 2 6 3 0.163265313 2 2 6 4 0.122448983 2 2 6 5 0.081632653 2 2 6 6 0.040816334 0 0 0 0 5.04 0 0 0 1 4.444444444 0 0 0 2 3.888888894 0 0 0 3 3.333333334 0 0 0 4 2.777777784 0 0 0 5 2.222222224 0 0 0 6 1.666666674 0 0 1 0 4.444444444 0 0 1 1 3.950617284 0 0 1 2 3.456790124 0 0 1 3 2.962962964 0 0 1 4 2.46913584 0 0 1 5 1.975308644 0 0 1 6 1.481481484 0 0 2 0 3.888888894 0 0 2 1 3.456790124 0 0 2 2 3.024691364 0 0 2 3 2.592592594 0 0 2 4 2.160493834 0 0 2 5 1.728395064 0 0 2 6 1.29629634 0 0 3 0 3.333333334 0 0 3 1 2.962962964 0 0 3 2 2.592592594 0 0 3 3 2.222222224 0 0 3 4 1.851851854 0 0 3 5 1.481481484 0 0 3 6 1.111111114 0 0 4 0 2.777777784 0 0 4 1 2.46913584 0 0 4 2 2.160493834 0 0 4 3 1.851851854 0 0 4 4 1.543209884 0 0 4 5 1.23456794 0 0 4 6 0.925925934 0 0 5 0 2.222222224 0 0 5 1 1.975308644 0 0 5 2 1.728395064 0 0 5 3 1.481481484 0 0 5 4 1.23456794 0 0 5 5 0.987654324 0 0 5 6 0.740740744 0 0 6 0 1.666666674 0 0 6 1 1.481481484 0 0 6 2 1.29629634 0 0 6 3 1.111111114 0 0 6 4 0.925925934 0 0 6 5 0.740740744 0 0 6 6 0.555555564 0 1 0 0 4.04 0 1 0 1 3.54 0 1 0 2 3.04 0 1 0 3 2.54 0 1 0 4 2.04 0 1 0 5 1.54 0 1 0 6 1.04 0 1 1 0 3.555555564 0 1 1 1 3.111111114 0 1 1 2 2.666666674 0 1 1 3 2.222222224 0 1 1 4 1.777777784 0 1 1 5 1.333333334 0 1 1 6 0.888888894 0 1 2 0 3.111111114 0 1 2 1 2.722222224 0 1 2 2 2.333333334 0 1 2 3 1.944444444 0 1 2 4 1.555555564 0 1 2 5 1.166666674 0 1 2 6 0.777777784 0 1 3 0 2.666666674 0 1 3 1 2.333333334 0 1 3 2 2.04 0 1 3 3 1.666666674 0 1 3 4 1.333333334 0 1 3 5 1.04 0 1 3 6 0.666666674 0 1 4 0 2.222222224 0 1 4 1 1.944444444 0 1 4 2 1.666666674 0 1 4 3 1.388888894 0 1 4 4 1.111111114 0 1 4 5 0.833333334 0 1 4 6 0.555555564 0 1 5 0 1.777777784 0 1 5 1 1.555555564 0 1 5 2 1.333333334 0 1 5 3 1.111111114 0 1 5 4 0.888888894 0 1 5 5 0.666666674 0 1 5 6 0.444444444 0 1 6 0 1.333333334 0 1 6 1 1.166666674 0 1 6 2 1.04 0 1 6 3 0.833333334 0 1 6 4 0.666666674 0 1 6 5 0.54 0 1 6 6 0.333333334 0 2 0 0 3.04 0 2 0 1 2.571428574 0 2 0 2 2.142857144 0 2 0 3 1.714285714 0 2 0 4 1.285714294 0 2 0 5 0.857142864 0 2 0 6 0.428571434 0 2 1 0 2.666666674 0 2 1 1 2.285714294 0 2 1 2 1.90476194 0 2 1 3 1.523809524 0 2 1 4 1.142857144 0 2 1 5 0.761904764 0 2 1 6 0.380952384 0 2 2 0 2.333333334 0 2 2 1 2.04 0 2 2 2 1.666666674 0 2 2 3 1.333333334 0 2 2 4 1.04 0 2 2 5 0.666666674 0 2 2 6 0.333333334 0 2 3 0 2.04 0 2 3 1 1.714285714 0 2 3 2 1.428571434 0 2 3 3 1.142857144 0 2 3 4 0.857142864 0 2 3 5 0.571428574 0 2 3 6 0.285714294 0 2 4 0 1.666666674 0 2 4 1 1.428571434 0 2 4 2 1.190476194 0 2 4 3 0.952380954 0 2 4 4 0.714285714 0 2 4 5 0.476190484 0 2 4 6 0.238095244 0 2 5 0 1.333333334 0 2 5 1 1.142857144 0 2 5 2 0.952380954 0 2 5 3 0.761904764 0 2 5 4 0.571428574 0 2 5 5 0.380952384 0 2 5 6 0.190476194 0 2 6 0 1.04 0 2 6 1 0.857142864 0 2 6 2 0.714285714 0 2 6 3 0.571428574 0 2 6 4 0.428571434 0 2 6 5 0.285714294 0 2 6 6 0.142857144 1 0 0 0 4.04 1 0 0 1 3.555555564 1 0 0 2 3.111111114 1 0 0 3 2.666666674 1 0 0 4 2.222222224 1 0 0 5 1.777777784 1 0 0 6 1.333333334 1 0 1 0 3.54 1 0 1 1 3.111111114 1 0 1 2 2.722222224 1 0 1 3 2.333333334 1 0 1 4 1.944444444 1 0 1 5 1.555555564 1 0 1 6 1.166666674 1 0 2 0 3.04 1 0 2 1 2.666666674 1 0 2 2 2.333333334 1 0 2 3 2.04 1 0 2 4 1.666666674 1 0 2 5 1.333333334 1 0 2 6 1.04 1 0 3 0 2.54 1 0 3 1 2.222222224 1 0 3 2 1.944444444 1 0 3 3 1.666666674 1 0 3 4 1.388888894 1 0 3 5 1.111111114 1 0 3 6 0.833333334 1 0 4 0 2.04 1 0 4 1 1.777777784 1 0 4 2 1.555555564 1 0 4 3 1.333333334 1 0 4 4 1.111111114 1 0 4 5 0.888888894 1 0 4 6 0.666666674 1 0 5 0 1.54 1 0 5 1 1.333333334 1 0 5 2 1.166666674 1 0 5 3 1.04 1 0 5 4 0.833333334 1 0 5 5 0.666666674 1 0 5 6 0.54 1 0 6 0 1.04 1 0 6 1 0.888888894 1 0 6 2 0.777777784 1 0 6 3 0.666666674 1 0 6 4 0.555555564 1 0 6 5 0.444444444 1 0 6 6 0.333333334 1 1 0 0 3.04 1 1 0 1 2.6254 1 1 0 2 2.254 1 1 0 3 1.8754 1 1 0 4 1.54 1 1 0 5 1.1254 1 1 0 6 0.754 1 1 1 0 2.6254 1 1 1 1 2.2968754 1 1 1 2 1.968754 1 1 1 3 1.6406254 1 1 1 4 1.31254 1 1 1 5 0.9843754 1 1 1 6 0.656254 1 1 2 0 2.254 1 1 2 1 1.968754 1 1 2 2 1.68754 1 1 2 3 1.406254 1 1 2 4 1.1254 1 1 2 5 0.843754 1 1 2 6 0.56254 1 1 3 0 1.8754 1 1 3 1 1.6406254 1 1 3 2 1.406254 1 1 3 3 1.1718754 1 1 3 4 0.93754 1 1 3 5 0.7031254 1 1 3 6 0.468754 1 1 4 0 1.54 1 1 4 1 1.31254 1 1 4 2 1.1254 1 1 4 3 0.93754 1 1 4 4 0.754 1 1 4 5 0.56254 1 1 4 6 0.3754 1 1 5 0 1.1254 1 1 5 1 0.9843754 1 1 5 2 0.843754 1 1 5 3 0.7031254 1 1 5 4 0.56254 1 1 5 5 0.4218754 1 1 5 6 0.281254 1 1 6 0 0.754 1 1 6 1 0.656254 1 1 6 2 0.56254 1 1 6 3 0.468754 1 1 6 4 0.3754 1 1 6 5 0.281254 1 1 6 6 0.18754 1 2 0 0 2.04 1 2 0 1 1.714285714 1 2 0 2 1.428571434 1 2 0 3 1.142857144 1 2 0 4 0.857142864 1 2 0 5 0.571428574 1 2 0 6 0.285714294 1 2 1 0 1.754 1 2 1 1 1.54 1 2 1 2 1.254 1 2 1 3 1.04 1 2 1 4 0.754 1 2 1 5 0.54 1 2 1 6 0.254 1 2 2 0 1.54 1 2 2 1 1.285714294 1 2 2 2 1.071428574 1 2 2 3 0.857142864 1 2 2 4 0.642857144 1 2 2 5 0.428571434 1 2 2 6 0.214285714 1 2 3 0 1.254 1 2 3 1 1.071428574 1 2 3 2 0.892857144 1 2 3 3 0.714285714 1 2 3 4 0.535714294 1 2 3 5 0.357142864 1 2 3 6 0.178571434 1 2 4 0 1.04 1 2 4 1 0.857142864 1 2 4 2 0.714285714 1 2 4 3 0.571428574 1 2 4 4 0.428571434 1 2 4 5 0.285714294 1 2 4 6 0.142857144 1 2 5 0 0.754 1 2 5 1 0.642857144 1 2 5 2 0.535714294 1 2 5 3 0.428571434 1 2 5 4 0.321428574 1 2 5 5 0.214285714 1 2 5 6 0.107142864 1 2 6 0 0.54 1 2 6 1 0.428571434 1 2 6 2 0.357142864 1 2 6 3 0.285714294 1 2 6 4 0.214285714 1 2 6 5 0.142857144 1 2 6 6 0.071428574 2 0 0 0 3.04 2 0 0 1 2.666666674 2 0 0 2 2.333333334 2 0 0 3 2.04 2 0 0 4 1.666666674 2 0 0 5 1.333333334 2 0 0 6 1.04 2 0 1 0 2.571428574 2 0 1 1 2.285714294 2 0 1 2 2.04 2 0 1 3 1.714285714 2 0 1 4 1.428571434 2 0 1 5 1.142857144 2 0 1 6 0.857142864 2 0 2 0 2.142857144 2 0 2 1 1.90476194 2 0 2 2 1.666666674 2 0 2 3 1.428571434 2 0 2 4 1.190476194 2 0 2 5 0.952380954 2 0 2 6 0.714285714 2 0 3 0 1.714285714 2 0 3 1 1.523809524 2 0 3 2 1.333333334 2 0 3 3 1.142857144 2 0 3 4 0.952380954 2 0 3 5 0.761904764 2 0 3 6 0.571428574 2 0 4 0 1.285714294 2 0 4 1 1.142857144 2 0 4 2 1.04 2 0 4 3 0.857142864 2 0 4 4 0.714285714 2 0 4 5 0.571428574 2 0 4 6 0.428571434 2 0 5 0 0.857142864 2 0 5 1 0.761904764 2 0 5 2 0.666666674 2 0 5 3 0.571428574 2 0 5 4 0.476190484 2 0 5 5 0.380952384 2 0 5 6 0.285714294 2 0 6 0 0.428571434 2 0 6 1 0.380952384 2 0 6 2 0.333333334 2 0 6 3 0.285714294 2 0 6 4 0.238095244 2 0 6 5 0.190476194 2 0 6 6 0.142857144 2 1 0 0 2.04 2 1 0 1 1.754 2 1 0 2 1.54 2 1 0 3 1.254 2 1 0 4 1.04 2 1 0 5 0.754 2 1 0 6 0.54 2 1 1 0 1.714285714 2 1 1 1 1.54 2 1 1 2 1.285714294 2 1 1 3 1.071428574 2 1 1 4 0.857142864 2 1 1 5 0.642857144 2 1 1 6 0.428571434 2 1 2 0 1.428571434 2 1 2 1 1.254 2 1 2 2 1.071428574 2 1 2 3 0.892857144 2 1 2 4 0.714285714 2 1 2 5 0.535714294 2 1 2 6 0.357142864 2 1 3 0 1.142857144 2 1 3 1 1.04 2 1 3 2 0.857142864 2 1 3 3 0.714285714 2 1 3 4 0.571428574 2 1 3 5 0.428571434 2 1 3 6 0.285714294 2 1 4 0 0.857142864 2 1 4 1 0.754 2 1 4 2 0.642857144 2 1 4 3 0.535714294 2 1 4 4 0.428571434 2 1 4 5 0.321428574 2 1 4 6 0.214285714 2 1 5 0 0.571428574 2 1 5 1 0.54 2 1 5 2 0.428571434 2 1 5 3 0.357142864 2 1 5 4 0.285714294 2 1 5 5 0.214285714 2 1 5 6 0.142857144 2 1 6 0 0.285714294 2 1 6 1 0.254 2 1 6 2 0.214285714 2 1 6 3 0.178571434 2 1 6 4 0.142857144 2 1 6 5 0.107142864 2 1 6 6 0.071428574 2 2 0 0 1.04 2 2 0 1 0.857142864 2 2 0 2 0.714285714 2 2 0 3 0.571428574 2 2 0 4 0.428571434 2 2 0 5 0.285714294 2 2 0 6 0.142857144 2 2 1 0 0.857142864 2 2 1 1 0.734693884 2 2 1 2 0.61224494 2 2 1 3 0.489795924 2 2 1 4 0.367346944 2 2 1 5 0.244897964 2 2 1 6 0.122448984 2 2 2 0 0.714285714 2 2 2 1 0.61224494 2 2 2 2 0.510204084 2 2 2 3 0.408163274 2 2 2 4 0.306122454 2 2 2 5 0.204081634 2 2 2 6 0.102040824 2 2 3 0 0.571428574 2 2 3 1 0.489795924 2 2 3 2 0.408163274 2 2 3 3 0.326530614 2 2 3 4 0.244897964 2 2 3 5 0.163265314 2 2 3 6 0.081632654 2 2 4 0 0.428571434 2 2 4 1 0.367346944 2 2 4 2 0.306122454 2 2 4 3 0.244897964 2 2 4 4 0.183673474 2 2 4 5 0.122448984 2 2 4 6 0.061224494 2 2 5 0 0.285714294 2 2 5 1 0.244897964 2 2 5 2 0.204081634 2 2 5 3 0.163265314 2 2 5 4 0.122448984 2 2 5 5 0.081632654 2 2 5 6 0.040816334 2 2 6 0 0.142857144 2 2 6 1 0.122448984 2 2 6 2 0.102040824 2 2 6 3 0.081632654 2 2 6 4 0.061224494 2 2 6 5 0.040816334 2 2 6 6 0.02040816`
kjellfp

Posts: 140
Joined: 04 October 2005

I presume it would be faster to search for 17s with the X pattern.

Code: Select all
`x.. ... ..x.x. ... .x...x ... x..... x.x ...... .x. ...... x.x .....x ... x...x. ... .x.x.. ... ..x`

Conventional wisdom says there won't be any.
Moschopulus

Posts: 256
Joined: 16 July 2005

I might try that X thing some time, however my program won't brute force the whole thing yet, i would try out some finished grids. I only have 2,500 at the moment and so i probably wouldn't find any. When i have 1,000,000 finished puzzles i will try the X

Are there any more interesting shapes you'd like me to try.

When my school finishes for christmas i will try these:

Code: Select all
`[b][u]he House[/u][/b]|---|-x-|---||---|xxx|---||-x-|xxx|-x-||-x-|---|-x-||-x-|x-x|-x-||-x-|---|-x-||-x-|---|-x-||-x-|-x-|-x-||-x-|-x-|-x-|[i]25 clues[/i][b][u]The Face[/u][/b]|---|---|---||xxx|---|xxx|---|---|---||---|-x-|---||x--|xxx|--x||-x-|---|-x-||--x|---|x---||---|xxx|---||---|---|---|[i]19 clues[/i][b][u]S-D-K[/u][/b]|-xx|x--|x-x||x--|xx-|x-x||x--|x-x|x-x||x--|x-x|xx-||-x-|x-x|xx-||--x|x-x|x-x||--x|x-x|x-x||--x|xx-|x-x||xx-|x--|x-x|[i]45 clues[/i][/i][/b]`
Pi

Posts: 389
Joined: 27 May 2005

I have done an exhaustive search on the X-pattern.

Three 17s were found, but because of the mysterious shape of this pattern, I have been forced by the government not to say anything

Seriously: No 17 was found.
kjellfp

Posts: 140
Joined: 04 October 2005

I don't beieve that you'll find any in the house or face patterns.

kjellfp: What was the closest you came to a unique solution?
Lardarse

Posts: 106
Joined: 01 July 2005

Lardarse wrote:I don't believe that you'll find any in the house or face patterns.

Me neither. The house will have multiple solutions because there are 2 columns per stack void of clues. The face has the same problem with rows 7 and 9.

The S-D-K patten has so many clues, it will take forever to find all possible puzzles.

Here's one to get you started:

Code: Select all
`. 7 3|8 . .|5 . 29 . .|7 3 .|4 . 62 . .|6 . 9|7 . 1-----+-----+-----4 . .|2 . 1|8 5 .. 5 .|4 . 7|3 6 .. . 9|3 . 5|2 . 4-----+-----+-----. . 4|1 . 8|9 . 5. . 7|5 2 .|1 . 35 2 .|9 . .|6 . 8`

Ruud.
Ruud

Posts: 664
Joined: 28 October 2005

Lardarse wrote:kjellfp: What was the closest you came to a unique solution?

Don't know. Didn't count solutions.
kjellfp

Posts: 140
Joined: 04 October 2005

The reason we want to count the number of Gordon's 17 patterns is to determine the extent that he has completed the 17 clue search.

A way of counting all the essentially different grids that will solve in this most common 17 clue pattern might be
Code: Select all
`+---+---+---+|483|...|..9||612|...|...||759|A..|B..|+---+---+---+|.C.|...|FG.||9..|D..|...||...|E..|...|+---+---+---+|H..|...|L..||I..|.J.|...||...|.K.|...|+---+---+---+`

The maximum options for each clue are
A=6,B=5,C=5,D=7,E=7,F=7,G=7,H=5,I=4,J=8,K=8,L=6.

multiplying = 2,765,952,000

So who can program those iterations to solve a puzzle of this pattern ?
Code: Select all
`0 8 0  0 0 0  0 0 9  0 1 2  0 0 0  0 0 0  0 0 0  6 0 0  3 0 0  0 7 0  0 0 0  2 8 0  9 0 0  4 0 0  0 0 0  0 0 0  3 0 0  0 0 0  3 0 0  0 0 0  4 0 0  5 0 0  0 8 0  0 0 0  0 0 0  0 1 0  0 0 0  `
coloin

Posts: 1946
Joined: 05 May 2005

I have written a code now for doing an exhastive search on the number of 17s of a given pattern. I just tried it for a test on the X-shape. Also, the X-shape has symmetries that makes the search go faster. There is no symmetry in the pattern you mention.

I can try to start a search on the pattern overnight to see if there are more than 36 17s.
kjellfp

Posts: 140
Joined: 04 October 2005

kjellfp wrote:I have written a code now for doing an exhastive search on the number of 17s of a given pattern..

Does your program fill in the pattern in all possible ways, and then check each one to see if it has a unique completion?

Now we know that in order to have a unique completion the 17 clues must use either 8 or 9 numbers between them. But there are Stirling2(17,8) ways of partitioning the 17 positions into 8 parts, and Stirling2(17,9) ways of partitioning them into 9 parts - that is 20415995028 and 9528822303 respectively, for a total of almost 30 billion.

Of course a lot of those ways are not legal - two cells in the same row or column or block cannot be assigned the same colour, but even so the numbers are in the billions.

Or do you have a cleverer way than this?

Cheers

Gordon
gfroyle

Posts: 214
Joined: 21 June 2005

I only search in those grids where
- At least eight different symbols occur.
- The first appearance of a symbol comes in ascending order, i.e. the first cell in the pattern must be 1, the second either 1 or 2, the third either 1, 2 or 3 (the latter only if the second symbol is 2) etc.
- If only eight symbols occur, the missing symbol is 9.
- The symbols placed follow the rules of Sudoku.

Also, the remaining cells are filled in a precalculated order such that I always try the remaining cell with lowest expected number of possibilities. The expected number of possibilities only depends on the pattern, not the symbols already filled in.
kjellfp

Posts: 140
Joined: 04 October 2005

It is good to see Gordon's input.... I take it from it that he has not yet done this calculation. I suspect that Gordon will be right with the 36 though.

I know how we are interested in optimizing things. I think this will be quicker if it can be programmed - and perhaps used for other patterns if quick enough.

This is the original grid
Code: Select all
`+---+---+---+|.8.|...|..9||.12|...|...||...|6..|3..|+---+---+---+|.7.|...|28.||9..|4..|...||...|3..|...|+---+---+---+|3..|...|4..||5..|.8.|...||...|.1.|...|+---+---+---+`

Reduce [N] Bertram by 9! and 6^6 with
Code: Select all
`+---+---+---+|483|...|..9||612|..9|...||759|...|...|+---+---+---+|...|.9.|...||9..|...|...||...|...|.9.|+---+---+---+|.9.|...|...||...|...|9..||...|9..|...|+---+---+---+`

Code: Select all
`+---+---+---+ |483|...|..9| |612|..9|...| |759|A..|B..| +---+---+---+ |.C.|.9.|FG.| |9..|D..|...| |...|E..|.9.| +---+---+---+ |H9.|...|L..| |I..|.J.|9..| |...|9K.|...| +---+---+---+ `

The options to fill in the 12 clues [labelled A-K][17 minus 5] [5 are included in the reduction] are actually reduced from my previous posting.

Code: Select all
`pattern.*......*.**.........*..*...*....**.*..*........*.....*.....*..*...*........*....clue 8      9 12         A  B   C    FG 9  D        E     H     L  I   J        Kmaskline..similar to its use in suexmult020000002022000000000100100010000110200100000000100000100000100100010000000010000clue options to iterate.8......9.12.........1..1...2....11.9..1........1.....1.....1..1...1........1.....8......9.12.........2..2...3....22.9..2........2.....2.....2..2...2........2.....8......9.12.........3..3...4....33.9..3........3.....3.....3..3...3........3.....8......9.12.........4..4...6....44.9..4........4.....5.....4..5...4........4.....8......9.12.........6..6...7....55.9..5........5.....8.....5..8...5........5.....8......9.12.........8..8........66.9..6........6...........6......6........6.....8......9.12.....................77.9..7........7...........7......7........7.....8......9.12.....................88.9..8........8...........8......8........8....maximum possible iterations for each clue 1      1 11         6  6   5    88 1  8        8     5     8  5   8        8    maximum actual iterations  for each clue, given a preceeding clue 1      1 11         6  5   5    65 1  7        6     5     6  4   7        7    `

Code: Select all
`A can be 1,2,3,4,6,8B can be 1,2,3,4,6,8        C can be 2,3,4,6,7 D can be 1,2,3,4,5,6,7,8E can be 1,2,3,4,5,6,7,8F can be 1,2,3,4,5,6,7,8   G can be 1,2,3,4,5,6,7,8   H can be 1,2,3,5,8I can be 1,2,3,5,8             J can be 1,2,3,4,5,6,7,8K can be 1,2,3,4,5,6,7,8L can be 1,2,3,4,5,6,7,8,   I realize it might be easier to roll through with these options 8^7*6^2*5^3    =  9,437,184,000Sudoku constraints apply to these clues:ABADEBFLCFGHIHLIJJKwhich will reduce the grids to solve to less than 7^3*6^4*5^4*4 =    1,111,320,000`

EDIT
this can be reduced furthur
The set of clues {ABCDEFGHIJK} only one of 3,4,5,6,7 can be omitted - if two of these clue numbers are not used the puzzle cannot be solved.

Construct a file with
Code: Select all
`.8......9.12.........A..B...C....FG.9..D........E.....H.....L..I...J........K....`

An example
Code: Select all
`.8......9.12.........6..3...7....28.9..4........3.....3.....4..5...8........1....`

suexmult file.txt 12 1
Code: Select all
`020000002022000000000100100010000110200100000000100000100000100100010000000010000.8......9.12.........6..3...7....28.9..4........3.....3.....4..5...8........1....`
this is the original solution of course
Last edited by coloin on Wed Dec 21, 2005 11:44 am, edited 5 times in total.
coloin

Posts: 1946
Joined: 05 May 2005

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