Sudoku Programmers

Re: Minimum clues for a samurai?

m_b_metcalf — Thu Feb 14, 2013 2:29 pm

Author: m_b_metcalf

Posted: Thu Feb 14, 2013 2:29 pm

m_b_metcalf wrote:

P.S. Upon reflection, I suppose that one could imagine 4 outside puzzles each with 16 clues and a central one with 5.

This isn't quite that, but here's a very hard one with 16 clues only in three of the 'ears' (and 17 in the fourth) and with 13 in the middle. (It unfortunately needs a clue at r3c1 or r3c3 of the bottom right puzzle. A clue at r3c2 makes it trivial.)

Regards,

Mike Metcalf

Code:

. . . 8 7 . . . . . . . . . . 9 3 . . . .
. 9 . . . . . 3 . . . . . 5 . . . . . 6 .
. . . 4 . . . . . . . . . . . 8 . . . . .
4 . . 1 . . . . 8 . . . 8 . . 7 . . . . 9
. . . . . 3 7 2 . . . . . . . . . 6 3 4 .
. . . . . . 6 . . . . . . . . . . . 1 . .
7 . . . 4 . . . . 5 7 . . . . . 8 . . . .
. . . 9 . 2 . . . . . . . . . 5 . 4 . 7 .
. . . . . . . . . 6 . . . . . . . . . . .
. . . . . . 6 . . 3 . . . . 5 . . . . . .
. . . . . . . . . . . 8 . 4 . . . . . . .
. . . . . . . . . . . . 2 . . . . . . . .
. . . 1 3 . . . . . 6 . . . . 9 7 . . . .
. 2 . . . . . . . 1 . 4 . . . . . . . 5 .
. . . 8 . . . . . . . . . . 8 2 . . . . .
8 . . 7 . . . . 1 . . . 2 . . 8 . . . . 9
. . . . . 6 3 4 . . . . . . . . . 5 7 6 .
. . . . . . 9 . . . . . . . . . . . 4 . .
3 . . . 8 . . . . . . . 7 . . . 2 . . . .
. . . 2 . 4 . 7 . . . . . . . 3 . 6 . 8 .
. . . . . . . . . . . . . . . . . . . . .

Re: Minimum clues for a samurai?

m_b_metcalf — Wed Feb 24, 2010 10:31 am

Author: m_b_metcalf

Posted: Wed Feb 24, 2010 10:31 am

garthd wrote:

It appears that the minimum number of clues for a standard 9x9 sudoku that still results in a single valid solution is 17 clues (on the assumption that no one has - as yet - found a valid 16 clue puzzle with a single solution). Does anyone have views on the minimum number of clues for a samurai puzzle?

Just for fun, I made a stab at a small number of clues. The result is 4 x 14 + 20 (=76). It's based on a 17-clue puzzle from Gordon Royle's collection and is rotationally symmetric.

[Edit: the clue 3 in row 10 is redundant, making a 75-clue puzzle.]

Regards,

Mike Metcalf

Code:

. 2 . . . . . . . . . . . . . . . . . 8 .
. 8 1 . . . . . . . . . . . . . . . 7 2 .
. . . 4 . . 5 . . . . . . . 3 . . 9 . . .
. . . 9 . . . . . . . . . . . . . 6 . . .
. . . . . . . 2 8 . . . 2 8 . . . . . . .
7 . . 5 . 6 . . . . . . . . . 4 . 3 . . 5
5 . . . . . . . . 8 . 2 . . . . . . . . 3
3 . . . . . . . . 5 . 1 . . . . . . . . 6
. . . . 1 . . . . . 9 4 . . . . 7 . . . .
. . . . . . 4 . . . . . . 3 5 . . . . . .
. . . . . . . . 6 . . . 1 . . . . . . . .
. . . . . . 1 3 . . . . . . 7 . . . . . .
. . . . 2 . . . . 9 1 . . . . . 1 . . . .
8 . . . . . . . . 2 . 3 . . . . . . . . 3
1 . . . . . . . . 4 . 8 . . . . . . . . 5
3 . . 1 . 5 . . . . . . . . . 6 . 5 . . 7
. . . . . . . 4 9 . . . 8 2 . . . . . . .
. . . 8 . . . . . . . . . . . . . 9 . . .
. . . 6 . . 1 . . . . . . . 5 . . 4 . . .
. 9 2 . . . . . . . . . . . . . . . 1 8 .
. 4 . . . . . . . . . . . . . . . . . 2 .

Code:

.2........81.........4..5.....9............287..5.6...5........3............1.... tl
.......8.......72...3..9........6...28..........4.3..5........3........6....7.... tr
...8.2......5.1.......94...4......35..6...1..13......7...91.......2.3......4.8... m
....2....8........1........3..1.5..........49...8........6..1...92.......4....... bl
....1............3........5...6.5..782............9.....5..4.........18........2. br

Re: Minimum clues for a samurai?

m_b_metcalf — Tue Feb 23, 2010 2:00 pm

Author: m_b_metcalf

Posted: Tue Feb 23, 2010 2:00 pm

garthd wrote:

Since this discussion I haven't really thought about it.

Regards,

Mike Metcalf

P.S. Upon reflection, I suppose that one could imagine 4 outside puzzles each with 16 clues and a central one with 5.

P.P.S. I now see that the puzzle I posted there with only 5 clues in the central box is not minimal. Here is a minimal version:

Code:

. . . . . . . . . . . . . . . . . . . . .
. . . . . . . . 1 . . . . . . 1 . . . 8 4
. . . 1 2 3 4 . 5 . . . . . 9 . . . 2 . .
. 1 . . . 5 . . 7 . . . . . 5 . . 2 . . 9
. . . . . . . 2 . . . . . . 7 . . . . 4 .
. . 8 . 7 4 3 . 6 . . . . 3 . . . 4 5 . 2
. 3 . . 4 8 . . . . . . . . . . . 6 . . .
. 4 . 6 . 7 . . . . . . . . . . 2 3 . 7 5
9 . 1 . . . . . . . . . . . . 8 . 5 1 . .
. . . . . . . . . 3 7 . . . . . . . . . .
. . . . . . . . . . . 6 . . . . . . . . .
. . . . . . . . . . 2 4 . . . . . . . . .
. . . . . . . . . . . . . . . 1 . . 7 . 9
. 5 . . . 7 . . . . . . . . . 2 8 . . 5 .
. 8 9 1 4 . . . . . . . . . . . . . . . 3
. 1 . . . 6 . 9 . . . . 1 . . . 4 6 . . 7
. . . 7 9 . . 3 . . . . . . . . . . . . .
. . . . . . . . . . . . . 8 9 3 1 . . . 4
. . 1 8 6 . . . . . . . . 4 . . 5 3 . . .
. . 3 . 2 4 8 5 . . . . . 9 3 . . 4 . . 2
. . . . . . 2 . . . . . . . . . . . . . .

Code:

.................1...1234.5.1...5..7.......2...8.743.6.3..48....4.6.7...9.1......
............1...84..9...2....5..2..9..7....4..3...45.2.....6.......23.75...8.51..
..............................37.........6.......24..............................
..........5...7....8914.....1...6.9....79..3............186......3.2485.......2..
...1..7.9...28..5.........31...46..7..........8931...4.4..53....93..4..2.........

Minimum clues for a samurai?

garthd — Tue Feb 23, 2010 11:25 am

Author: garthd

Posted: Tue Feb 23, 2010 11:25 am

It appears that the minimum number of clues for a standard 9x9 sudoku that still results in a single valid solution is 17 clues (on the assumption that no one has - as yet - found a valid 16 clue puzzle with a single solution). Does anyone have views on the minimum number of clues for a samurai puzzle?