The New Sudoku Players' Forum

[qiuyanzhe]

I remember the 17-clue puzzle pack is somewhere in this forum. But it seems hard to find.
Also, is there already a database of 16-clue puzzles with 2 solutions, or how to make it quickly using the 17-clue database?

[champagne]

I remember the 17-clue puzzle pack is somewhere in this forum. But it seems hard to find.
Also, is there already a database of 16-clue puzzles with 2 solutions, or how to make it quickly using the 17-clue database?

I have several morphs of the 49158 17 clues, but not currently available for download.
I'll put in my google drive the morph used to check redundancy, but this morph is in my canonical max lexical form.

regarding the list of 16 clues with 2 solutions, the logical exhaustive search would be to try all 17 with one clue discarded.

here an example of an output in my current work.

Code: Select all

.23..........8.1..7.9.........3...9..........6...1....51..6..........97.....4..3.
123456789456789123789132465241375698375698214698214357517963842834521976962847531

.23..........8.1..7.9.........3...9..........6...1....51..6.......9...7.....4..3.
123456789456789123789132465241375698375698214698214357517863942834921576962547831


These 2 solution grids have the same first 2 bands and differ in band 3 by an unavoidable set of 6 cells.
We can bet that killing the "9" would give a 16 with 2 solutions

EDIT the list of the 49158 is available here
https://drive.google.com/file/d/1StS_Sm_Eh9ZJTapOsrRJccM6UP6PmQ3B/view

[m_b_metcalf]

regarding the list of 16 clues with 2 solutions, the logical exhaustive search would be to try all 17 with one clue discarded.

Which is just what I was doing. Here is a list of all the 16-clue 'puzzles' that have fewer than five solutions. The first column is the original 17-clue puzzle, the second is the number of solutions, the third and fourth are the r/c coordinates of the clue that can be removed to obtain the 16 clues in question. No 17-clue puzzle appears twice.

HTH

Mike

Code: Select all

                                                                                 #sln r  c
....1...47......2.3........58....2.....7...3..1............48.16.23..............  2  4  1
....1.4..7......6....8......41.5...........73......5..2..7.6....6....1.....3.....  4  6  7
....1.4..8......6....5......41.5...........83......7..2..8.6....6....1.....3.....  4  6  7
....1.4..8......6....9......41.5...........83......7..2..8.6....6....1.....3.....  4  6  7
....5..28.31...............6..3.47..8......4....1.....2...8.....4....3.....6.....  4  4  1
....5..32617..................1.46..2......4....7......4....1..3...2.......8.....  4  2  1
....6.3.24.1..................4.5.7..2....5.....1.....5......4..3..2....8..6.....  4  9  1
....61.9..23.................73......4....5..6......1....8..3.71...7..........2..  4  5  2
....8..3..6.4......1............96.17...3.5........4.....6..2..8......4.3........  4  5  7
....8..327.1...............63..2....4.....7.....6........7.45...2.....4....1.....  4  4  1
....8..327.1...............63..2....4.....7.....9........7.45...2.....4....1.....  4  4  1
...2.1.7.34................5...3......2....1.......8......6.3.5.615...........4..  4  8  2
...3.1..86......7....4.....2...46......5..3..7.........3....4......7..2..1.......  4  4  6
...54..6..2.3.....8.........7....3.2....61............6.4....5....2..4..1........  4  1  4
...54..6..2.3.....8.........8....3.2....61............6.4....7....2..4..1........  4  1  4
...6..2..3...4....5...........2.1..98......5....4......2...74......5..3..1.......  4  7  6
...6.73..2.1.....5..........3....8..7...2........1......5....1..7.8.....4..3.....  2  9  1
...7.8.5.3.1................7.....842...3..........5......6.3.2.8.2...........1..  4  4  9
...7.8.9.3.1................7.....842...3..........5......6.3.2.8.2...........1..  4  4  9
..1.5..62.38..................3.74..2......7....8......7....3..6...2.......1.....  4  1  3
..3..5.816.47.................2..7...8.....4..1...........1...52.....4..7........  2  1  3
.1.....7....8....2...5.......7...41.5..3.2............8.......5....1.6......4.2..  2  8  7
.1..7.........32........56.2....5......3...8........1.5.....4.3..781.............  2  3  8
.1.4...72...6.8............6.3...5......2..3.8...........3..6...2..7....1........  4  1  4
.2.....6.....3.4..7..5......8.6.2.........3.1.........3.4.5.......4...2.1........  4  3  4
.2.....6.....3.4..7..8......7.6.2.........3.1.........3.4.5.......4...2.1........  4  3  4
.2.....6.....3.4..7..8......9.6.2.........3.1.........3.4.5.......4...2.1........  4  3  4
.2..3.4.....5...7.3.........8..24..........51.........5.76..........72..1........  4  1  5
.2..3.4.....6...7.5.........8..24..........61.........6.73..........72..1........  4  1  5
.2..3.4.....6...8.5.........5..24..........61.........6.87..........82..1........  4  1  5
.2.78........6.5.1.........5.3..4......3...8.1.............53...8.....7.2........  4  2  5
.3..25.........71..6...........6...57.....6..1..4.....4......8..5......2...1.....  2  7  8
.4.6.........3..2..1.......3......6....4..5..2.............74.18...2.......5..6..  4  9  4
.4.6.........3..2..1.......3......6....4..8..2.............74.17...2.......5..6..  4  9  4
.5.4...72...6.8............6.3...4......2..3.8...........3..6...2..7....1........  4  1  4
.6.....35...2.1.............4..5..8.2.8...7..1...........8..2...5..3....4........  4  4  2
.6.....52...3.1....4..........7..1...2..5....8........1.....8..3..4.........2..4.  2  4  4
.6.....83...5.1...4........5.2...4......3..2.1...........2..5...3..8....7........  4  3  1
.6.....83...5.1...4........5.2...7......3..2.1...........2..5...3..8....6........  4  3  1
.6....7.5...4.1....3........5..7......8....1.2............5.3..1......2.4..3.....  2  5  3
.6..53.........8.1.2..........42..3.8.....2..1..7......3.....5.7...........1.....  2  4  4
.6.5.........3..2..1.......3..4...5....6..7..2.............46.18...2..........5..  4  4  4
.6.5.3.........2.1.4.......1...7....2.....4.....4...3.7..8......3.....5.....1....  2  7  4
.7.5.........3..2..1.......3..6...5....7..8..2.............47.19...2..........5..  4  4  4
.756............81...3.....2..5..7......4....1........4...1........8..3..3....5..  2  4  1
1.....2.87...35...............8...35647.....................71..5.2...........6..  4  5  2
2......3.....1.7...3..4.......6...825..3......41......8..2...........1......7....  2  5  1
2..1.3...7......65.............563..4.7.......8..........72.....6....1.....4.....  4  6  2
3.....2.6....71...4........51.....8..7..4.......6..4..6..2............1..8.......  2  4  1
3.7.2....2.....5.1..........4.5.6...6......7....1.........7..3..5....6.....8.....  4  2  1
3.7.2....4.....5.1..........4.5.6...6......7....1.........7..3..5....6.....8.....  4  2  1
3.8.2....4.....6.1..........5.6.7...7......8....1.........8..3..6....7.....2.....  4  2  1
3.96..5......71..4............5..2...7..9.....1............4.1.2..9.....5........  2  1  4
36......7....1.8..4...........3....4.5.....7..1.......2.74..........815..........  2  1  2
4.1.....8...2...7.3...........7.2...5.....4...3.6......7.....6.....4.3......1....  4  4  6
4.1.....8...7...6.3...........6.2...2.....4...3.5......6.....5.....4.3......1....  4  4  6
5......37...2.1...............6..2..7...3.....8........26...4......7..6.41.......  4  9  1
5.....7.....1......6.......3...75..........812.........1.6..4...8.....2.....2.5..  2  7  7
6......2..8..4...........1.2..5.........6.8.......74....72.1....4....3.....6.....  4  6  6
6.45............1..3.......7.....5.6....81...2...........6..2...8..2.....1.....3.  2  1  3
65..83..........71.........7.42.........4.3..1...........7...4..3....8..5........  4  1  1
69..83..........71.........7.42.........4.3..1...........7...4..3....8..5........  4  1  1
7...6..58...4...3.2..1.....35..8..........1......5.......2..7...4........1.......  4  1  5
8......4.3..7.........4.2..51..62..........83.4........2....6..7...........3.....  2  4  1
8..4.3...1......27.............273..6.1.........5........18.....7....4.....6.....  4  6  4


[qiuyanzhe]

the list of the 49158 is available here
https://drive.google.com/file/d/1StS_Sm ... PmQ3B/view

Here is a list of all the 16-clue 'puzzles' that have fewer than five solutions.

Thanks for your help!!

[JPF]

Actually, out of those 65 puzzles, only 4 are essentialy different.
Here there are with the number of solutions:

Code: Select all

.....5.816.47.................2..7...8.....4..1...........1...52.....4..7........    2 
1.....2.87...35...............8...356.7.....................71..5.2...........6..    4 
....1.4..8......6....5......41.5...........83.........2..8.6....6....1.....3.....    4 
....1.4..7......6....8......41.5...........73.........2..7.6....6....1.....3.....    4 


edit : btw, the 16-clues puzzle having 2 solutions was given by Gordon Royle, years ago here.

JPF

[m_b_metcalf]

Actually, out of those 65 puzzles, only 4 are essentialy different.

Wow, what a memory, thanks. For convenience, here they are in minlex form:

Code: Select all

..............1.23.45.6............1..65.....2.......7......5...2....4..1....7...     2           
................12..3.45........64...1.......62.7........2....6..4...5...8.......     4           
................12..3.45........64...1.......62.7........2....6..4...5...3.......     4           
................12..3.45...............6.3..745......1...17.......2.......6...5..     4     

Regards,

Mike

P.S. Note: only the second one has 8 distinct digits.