Minimum number of clues in the centre of an X-samurai

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Re: Minimum number of clues in the centre of an X-samurai

Postby tarek » Fri Jan 18, 2019 8:11 am

Great. I didn't have time to access my Gattai solver. All resources are now on single grid variants :D

tarek
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Re: Minimum number of clues in the centre of an X-samurai

Postby m_b_metcalf » Fri Jan 18, 2019 8:59 am

Mathimagics wrote:
m_b_metcalf wrote:tarek, thanks for confirming that result. Did you also check my claim that the puzzle is minimal (I have my doubts)?

Confirmed as minimal (with my DLX solver). 8-)

Thanks. I've now discovered the bug/feature that led me to think otherwise.

Mike
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Empty central grid

Postby Mathimagics » Sat Jan 19, 2019 4:17 am

Here is a minimal Samurai SudokuP puzzle with an empty central grid:

Code: Select all
.................................................................................
8.....64..1.....32..9....8.......2.......1......7....6167........4........2......
.62.45...8.........3..9.....93.....8..........................1......7.3...4..8.2
........5.......3....6.9...6.4..2.....7....1.59..............9...23......4......6
4.........79........5.82.....4.....7.2.............4..1......98.....814........6.

Note: line 1 is the central grid, obviously. The 4 x corner grid puzzles start with the top-left and proceed clockwise.

Puzzle (grid view): Show
Code: Select all
8 . . . . . 6 4 .       . 6 2 . 4 5 . . .
. 1 . . . . . 3 2       8 . . . . . . . .
. . 9 . . . . 8 .       . 3 . . 9 . . . .
. . . . . . 2 . .       . 9 3 . . . . . 8
. . . . . 1 . . .       . . . . . . . . .
. . . 7 . . . . 6       . . . . . . . . .
1 6 7 . . . . . . . . . . . . . . . . . 1
. . 4 . . . . . . . . . . . . . . . 7 . 3
. . 2 . . . . . . . . . . . . 4 . . 8 . 2
            . . . . . . . . .           
            . . . . . . . . .
            . . . . . . . . .
4 . . . . . . . . . . . . . . . . . . . 5
. 7 9 . . . . . . . . . . . . . . . . 3 .
. . 5 . 8 2 . . . . . . . . . 6 . 9 . . .
. . 4 . . . . . 7       6 . 4 . . 2 . . .
. 2 . . . . . . .       . . 7 . . . . 1 .
. . . . . . 4 . .       5 9 . . . . . . .
1 . . . . . . 9 8       . . . . . . . 9 .
. . . . . 8 1 4 .       . . 2 3 . . . . .
. . . . . . . 6 .       . 4 . . . . . . 6

Solution: Show
Code: Select all
8 7 3 5 1 2 6 4 9       1 6 2 8 4 5 9 3 7
5 1 6 8 4 9 7 3 2       8 4 9 1 3 7 5 2 6
2 4 9 6 3 7 5 8 1       7 3 5 2 9 6 1 8 4
7 3 1 9 8 6 2 5 4       6 9 3 5 1 4 2 7 8
6 2 8 4 5 1 9 7 3       4 7 8 9 6 2 3 1 5
4 9 5 7 2 3 8 1 6       5 2 1 3 7 8 6 4 9
1 6 7 3 9 8 4 2 5 1 9 7 3 8 6 7 2 9 4 5 1
3 8 4 2 6 5 1 9 7 3 8 6 2 5 4 6 8 1 7 9 3
9 5 2 1 7 4 3 6 8 4 5 2 9 1 7 4 5 3 8 6 2
            5 4 9 6 1 8 7 3 2
            7 1 3 9 2 5 6 4 8
            2 8 6 7 4 3 5 9 1
4 8 2 6 7 3 9 5 1 2 7 4 8 6 3 4 7 1 9 2 5
6 7 9 4 5 1 8 3 2 5 6 1 4 7 9 8 2 5 6 3 1
3 1 5 9 8 2 6 7 4 8 3 9 1 2 5 6 3 9 8 7 4
8 6 4 5 2 9 3 1 7       6 3 4 1 5 2 7 8 9
9 2 3 7 1 4 5 8 6       2 8 7 9 6 4 5 1 3
7 5 1 8 3 6 4 2 9       5 9 1 7 8 3 4 6 2
1 3 6 2 4 5 7 9 8       3 1 6 5 4 8 2 9 7
2 9 7 3 6 8 1 4 5       7 5 2 3 9 6 1 4 8
5 4 8 1 9 7 2 6 3       9 4 8 2 1 7 3 5 6
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