The New Sudoku Players' Forum

[1to9only]

The subject cropped up in other threads:
http://forum.enjoysudoku.com/sudokux-diagonal-sudoku-t34959-75.html#p351633 [jco]
http://forum.enjoysudoku.com/hardest-6x6-t35607-60.html#p351569 [philvo]

These were a small sample (2Rx3C 6x6 sudoku-x) I generated at the time I created Sukaku6Explainer (about 4 years ago!):

Code: Select all

...3.........1............42.6......  5 ED=8.8/8.8/2.9
...........41..........26.......3...  5 ED=8.8/8.8/2.9
..4..1.....3........6....5..........  5 ED=7.7/7.7/2.9
..4.........3...6.........25........  5 ED=7.7/7.7/2.9
...........4.......1.....6.2.5......  5 ED=7.7/7.7/2.9
....1.6....5.....3.........2........  5 ED=7.7/2.9/2.6
.24...........6...5...............1.  5 ED=7.7/1.2/1.2
....5.......32............6...1.....  5 ED=7.6/7.6/2.6
.....6...4.5.................2..3...  5 ED=7.6/2.8/2.8
..5...........42...26.3.............  6 ED=7.6/1.2/1.2
.........4..2.......3.....5.1.......  5 ED=7.2/7.2/2.8
....1.5..3.................43....6..  6 ED=7.2/2.9/2.6
...3.......2.4........5..1..........  5 ED=7.1/7.1/2.9
................6..3.....5..1..4....  5 ED=7.1/7.1/2.8
..6..............5......41...2..5...  6 ED=7.1/1.5/1.5
.........2.4................5...6.1.  5 ED=6.6/2.9/2.6
4........6..3.....1..2........6.....  6 ED=6.6/1.2/1.2
...5....1.3.......4......42.........  6 ED=6.6/1.2/1.2
..2..4...1................6.......3.  5 ED=6.5/6.5/2.9
..................2.1..6.4.......3..  5 ED=6.5/6.5/2.6
.........61....4........425.........  6 ED=6.5/1.2/1.2
.......6.1.4............3.......2...  5 ED=4.4/2.9/2.9
......5..2.....3..4....1..4.........  6 ED=4.4/1.2/1.2
..6....4.......2..............615...  6 ED=4.2/2.0/2.0
...4...6....6...1..........3.5......  6 ED=4.2/1.5/1.5
.23...........6...................14  5 ED=4.2/1.2/1.2
..3...4.........13.....2........6...  6 ED=3.0/1.5/1.5
..3....4........61..........2.......  5 ED=3.0/1.5/1.5
..............5.6..3......2..4.5....  6 ED=3.0/1.2/1.2
.....3...6.......1.........5......4.  5 ED=2.9/2.9/2.9
....31...............2....5....6....  5 ED=2.9/2.9/2.6
.........5..42............3..2...6..  6 ED=2.9/2.9/2.6
6.....................3..5...2.4.3..  6 ED=2.9/1.5/1.5
413.6..............3...............5  6 ED=2.9/1.5/1.5
3........2.....61..............53...  6 ED=2.9/1.5/1.5
....2..................6.1....4..3..  5 ED=2.9/1.5/1.5
......3.........5......4.6....1....5  6 ED=2.9/1.5/1.5
........4.........15.....6.....2...3  6 ED=2.9/1.5/1.5
6.......4.....1.................2.15  6 ED=2.9/1.2/1.2
4......62....3........2.1...........  6 ED=2.9/1.2/1.2
.2.3.......5.4........6....6.....2..  7 ED=2.9/1.2/1.2
....5.6.4.......2............1......  5 ED=2.9/1.2/1.2
.....1.54...3..............2........  5 ED=2.9/1.2/1.2
......6..42..3............1.3.......  6 ED=2.9/1.2/1.2
.........6......4.......5.2........3  5 ED=2.9/1.2/1.2
...........4......1....35....1.2.3..  7 ED=2.9/1.2/1.2
............2.....4......5.......6.3  5 ED=2.9/1.2/1.2
....2.1..........5......3.5.......6.  6 ED=2.6/1.2/1.2
62.................54.....1.........  5 ED=1.5/1.2/1.2
..2......46..........1..........6.3.  6 ED=1.5/1.2/1.2


SE6 requires some form of chaining to solve about 40% of the generated puzzles.

[philvo]

Thanks for this Interesting series.
For my solver, the hardest ones are in descending order : 2, 4, 5, 6 (rated 21) then 1, 3, 10, 12, 13 … (rated 20).
phil

[1to9only]

I've searched all the 5-clues 6x6 sudoku-x - the highest rating is ED=9.1

Code: Select all

.1.2...................3..4....5....  5 ED=9.1/9.1/2.9
.1......2........3.............4.5..  5 ED=9.1/9.1/2.9
..1.2.............3........4......5.  5 ED=9.1/9.1/2.9
..1...2.........3.......4..5........  5 ED=9.1/9.1/2.9
...1.......2.3............4..5......  5 ED=9.1/9.1/2.9
....1....2..3...................4.5.  5 ED=9.1/9.1/2.9
......1..2............3.4.......5...  5 ED=9.1/9.1/2.9
........1..2.......3.........4...5..  5 ED=9.1/9.1/2.9


Other 5-clues 6x6 sudoku-x: Show

Code: Select all

12......3...4....................5..  5 ED=9.0/9.0/2.9
.12....................3...4......5.  5 ED=9.0/9.0/2.9
12..3...4.........5.................  5 ED=8.9/8.9/2.9
1.2.3.............4.....5...........  5 ED=8.9/8.9/2.9
12.3.4.................5............  5 ED=8.8/8.8/2.9
1.2.34............5.................  5 ED=8.8/8.8/2.9
.1.2..3.....45......................  5 ED=8.7/8.7/2.9
.1....2..3..45......................  5 ED=8.7/8.7/2.9
.1......2....3.............4.....5..  5 ED=8.6/8.6/2.9
..1...2.....3..............4.....5..  5 ED=8.6/8.6/2.9
1.......2...3..........4..5.........  5 ED=8.5/8.5/2.9
.12.....3.......4................5..  5 ED=8.5/8.5/2.9
1.2..............3....4...5.........  5 ED=8.4/8.4/2.9
1.......2..3...........4..5.........  5 ED=8.4/8.4/2.9
12.3........4....................5..  5 ED=8.3/8.3/2.9
12.3.............4...5..............  5 ED=8.3/8.3/2.9
12..3..4..............5.............  5 ED=8.2/8.2/2.9
12...............3...............4.5  5 ED=8.2/8.2/2.9
.12..........3..4.................5.  5 ED=8.1/8.1/2.9
.1.................2..3..........45.  5 ED=8.1/8.1/2.9
.1..........23......4............5..  5 ED=8.0/8.0/2.9
..1............2......34..........5.  5 ED=8.0/8.0/2.9
12................3..4...........5..  5 ED=7.9/7.9/2.9
1.2.........3.4...........5.........  5 ED=7.9/7.9/2.9
12.3...4...............5............  5 ED=7.8/7.8/2.9
12.3...................45...........  5 ED=7.8/7.8/2.9
12.3....................4........5..  5 ED=7.7/7.7/2.9
12.3....................4..........5  5 ED=7.7/7.7/2.9
12.3........4.....................5.  5 ED=7.6/7.6/2.9
12.3..................4....5........  5 ED=7.6/7.6/2.9
1...2.3....4.....5..................  5 ED=7.5/7.5/2.9
1...2.3..............4.....5........  5 ED=7.5/7.5/2.9
12......3..........4.........5......  5 ED=7.3/7.3/2.8
.1...............2..........34...5..  5 ED=7.3/7.3/2.8
12..3............4.............5....  5 ED=7.2/7.2/2.9
12......3......4.5..................  5 ED=7.2/7.2/2.9
12.3.............4................5.  5 ED=7.1/7.1/2.9
12.3..........................4...5.  5 ED=7.1/7.1/2.9
1........2...3..4...........5.......  5 ED=7.0/6.5/2.6
1........2............34.5..........  5 ED=7.0/6.5/2.6
1.......2........3...........45.....  5 ED=6.8/2.9/2.9
1..........2...........3..4...5.....  5 ED=6.8/2.9/2.9
12.3...................4.........5..  5 ED=6.6/6.6/2.9
12.....3..............4........5....  5 ED=6.6/6.6/2.9
12......3...............4..........5  5 ED=6.5/6.5/2.9
12...............3....4....5........  5 ED=6.5/6.5/2.9
1.2..3..........4.......5...........  5 ED=6.2/2.9/2.6
1..2.3.......4...............5......  5 ED=6.2/2.9/2.6
.1.................2.......3....45..  5 ED=4.5/4.5/2.9
..12....3.......4.................5.  5 ED=4.5/4.5/2.9
1..........2.........3..4........5..  5 ED=4.4/4.4/2.9
.1.......2.....3.........4........5.  5 ED=4.4/4.4/2.9
1...2............34................5  5 ED=4.2/4.2/2.9
1................23............4...5  5 ED=4.2/4.2/2.9
1.....2..3......45..................  5 ED=3.6/3.6/2.6
.1.2...3........45..................  5 ED=3.6/3.6/2.6
1..2.........3..........4........5..  5 ED=3.4/3.4/2.6
1...2...............34...........5..  5 ED=3.4/3.4/2.6
1.2............3.4.............5....  5 ED=3.2/2.9/2.6
1.2.................3....4.......5..  5 ED=3.2/2.9/2.6
1...2................3.........4.5..  5 ED=3.0/3.0/2.9
.1.2...........3..............4...5.  5 ED=3.0/3.0/2.9
12.3..4................5............  5 ED=2.9/2.9/2.9
12.3.................4........5.....  5 ED=2.9/2.9/2.9
1..............2.....3.....4...5....  5 ED=2.8/2.8/2.8
.1.......2.....3.....4........5.....  5 ED=2.8/2.8/2.8
12.............3....4......5........  5 ED=2.6/2.6/2.6
12.............3....4............5..  5 ED=2.6/2.6/2.6
1.....2............3.....4.........5  5 ED=2.5/1.5/1.5
1.........2.3............4.....5....  5 ED=2.5/1.5/1.5
1.2............3.4.................5  5 ED=2.0/2.0/2.0
1.2..................3...4.....5....  5 ED=2.0/2.0/2.0
1..2...........3.......4....5.......  5 ED=1.7/1.2/1.2
1....2.......3.......4.......5......  5 ED=1.7/1.2/1.2
12.3................4..5............  5 ED=1.5/1.5/1.5
12.3................4..............5  5 ED=1.5/1.5/1.5
1..2..........3..4.....5............  5 ED=1.2/1.2/1.2
1.............2..3....4....5........  5 ED=1.2/1.2/1.2


[philvo]

I am not familiar with ED rating. But my solver confirms that these 8 X-sudokus are very hard ! (rated 21).
In the second list, puzzles 2, 3, 4, 5, 6, 7, 8, 9, 10, 12 … are also rated 21.
It's amazing how difficult 6x6 X-sudokus can be. And with 5 givens, it is sure they are minimal !
I have also a “normalizer”. For the first list, it indicates that puzzles 1, 2, 3, 6 are equivalent to ....1....2..3...................4.5.
and puzzles 4, 5, 7, 8 equivalent to ........1..2.......3.........4...5..
phil

[1to9only]

I've searched all the 5-clues 6x6 sudoku-x - the highest rating is ED=9.1

ED=9.1 is likely the highest rating possible for 6x6 sudoku-x. (ED=8.4 for 6.6 sudoku)

I've also searched for 6-clues 6x6 sudoku-x puzzles, with givens 1-6 (no repeated digit) - the highest rated found is ED=8.8

6-clues 6x6 sudoku-x, 1-6 (no repeated digit): Show

Code: Select all

.1......2...3....4.........5......6.  6 ED=8.8/8.8/2.9
.1......2.........3....4...5......6.  6 ED=8.8/8.8/2.9
                                                       <- no ED=8.5-8.7 puzzles found!
.12.3...........4..........5......6.  6 ED=8.4/8.4/2.9
.1.23........4............5....6....  6 ED=8.4/8.4/2.9
.12.....3...........4..5..6.........  6 ED=8.3/8.3/2.9
.1.2.........3.4...............5.6..  6 ED=8.3/8.3/2.9
1...2....3..4...........5...6.......  6 ED=8.2/8.2/2.9
1...2.................3.4...5...6...  6 ED=8.2/8.2/2.9
1..2........34.5.................6..  6 ED=8.0/8.0/2.6
..1..2........3.45..............6...  6 ED=8.0/8.0/2.6
1..23.................4.5.......6...  6 ED=7.9/7.9/2.9
1...2....3..4...........5......6....  6 ED=7.9/7.9/2.9
12.3.............45..6..............  6 ED=7.8/7.8/2.9
12..34......5..........6............  6 ED=7.8/7.8/2.9
12.3..............4..5...........6..  6 ED=7.7/7.7/2.9
12..3...4.......5..............6....  6 ED=7.7/7.7/2.9
12.34.......5.....................6.  6 ED=7.6/7.6/2.9
12.3.4.................56...........  6 ED=7.6/7.6/2.9
12..3.......4....5....6.............  6 ED=7.5/7.5/2.9
12...................34....56.......  6 ED=7.5/7.5/2.9
1.....2........3.....45..........6..  6 ED=7.3/7.3/2.9
1.................2..3.45.6.........  6 ED=7.3/7.3/2.9
1.234.............5..............6..  6 ED=7.2/7.2/2.9
1.2.3.......4..........5...6........  6 ED=7.2/7.2/2.9
12.3.4...........5.................6  6 ED=7.1/7.1/2.9
12.3..4...........5...........6.....  6 ED=7.1/7.1/2.9
1..2..3..............4.5.........6..  6 ED=7.0/7.0/2.9
.1.....2.3...........45....6........  6 ED=7.0/7.0/2.9
1.2..3.........4......5.6...........  6 ED=6.9/6.9/2.8
1..2.3........4....5.........6......  6 ED=6.9/6.9/2.8
1.23............4....5.6............  6 ED=6.8/6.6/2.8
..12.3.......4....5.6...............  6 ED=6.8/6.6/2.8
1....2..3.............4.....5....6..  6 ED=6.7/6.7/2.8
1....2...3.........4.....5......6...  6 ED=6.7/6.7/2.8
12.3....4...5......................6  6 ED=6.6/6.6/2.9
12.3..............4...5.6...........  6 ED=6.6/6.6/2.9
12.3.4...........5.......6..........  6 ED=6.5/6.5/2.9
12.3.4..................5..........6  6 ED=6.5/6.5/2.9
12...............3...45....6........  6 ED=6.2/6.2/2.9
..1.........2.3....4........56......  6 ED=6.2/6.2/2.9
12...3..4.............5........6....  6 ED=4.5/2.9/2.8
1...23...4.........5..............6.  6 ED=4.5/2.9/2.8
12...............3...45..6..........  6 ED=4.4/4.4/2.9
1..2.......3.........4..5........6..  6 ED=4.4/4.4/2.9
12.3....4.........5................6  6 ED=4.2/4.2/2.9
12.3.............45............6....  6 ED=4.2/4.2/2.9
12...................3..4......5.6..  6 ED=3.6/3.6/2.9
.12...3...............4......5....6.  6 ED=3.6/3.6/2.9
12.3.4......5.................6.....  6 ED=3.4/3.4/2.9
12......3......4.........5........6.  6 ED=3.4/3.4/2.9
1..2........3.........4.5..6........  6 ED=3.2/3.2/2.9
.1.2.............3.4.....5.6........  6 ED=3.2/3.2/2.9
12.3..4........5......6.............  6 ED=3.0/3.0/2.9
12.3............4..........5..6.....  6 ED=3.0/3.0/2.9
12.34.......5....................6..  6 ED=2.9/2.9/2.9
12.34.............5..............6..  6 ED=2.9/2.9/2.9
12.....34................5........6.  6 ED=2.8/2.8/2.8
12......3......4.....5........6.....  6 ED=2.8/2.8/2.8
123..........4................5.6...  6 ED=2.6/2.6/2.6
12.3...........4......5...6.........  6 ED=2.6/2.6/2.6
1..2.....3............4.5.....6.....  6 ED=2.5/2.0/2.0
1...2.....3.......4......5.....6....  6 ED=2.5/2.0/2.0
12.3...4..........5...6.............  6 ED=2.3/2.3/2.3
12..........3..4....5............6..  6 ED=2.3/2.3/2.3
123.........45..............6.......  6 ED=2.0/2.0/2.0
123.........4....5............6.....  6 ED=2.0/2.0/2.0
1..2......3..............4...5....6.  6 ED=1.7/1.7/1.7
1...2......3.............4.5.......6  6 ED=1.7/1.7/1.7
123.4..............5.6..............  6 ED=1.5/1.5/1.5
123............4.5...6..............  6 ED=1.5/1.5/1.5
123..........4.5...6................  6 ED=1.2/1.2/1.2
12.3..........4.5...6...............  6 ED=1.2/1.2/1.2


For 6-clues 6x6 sudoku-x puzzles allowing repeated digit - the highest rated found is ED=9.0

Code: Select all

.1.2...............3......4....5.4..  6 ED=9.0/9.0/2.8
.1.2....2....3.................4.5..  6 ED=9.0/9.0/2.8


[1to9only]

6x6 sudoku-x, 2Rx3C, 5-clues [61864 puzzles].zip
6x6 sudoku-x, 2Rx3C, 6-clues [1-6] [190344 puzzles].zip

There are no 5-clues in this collection, and some 6-clues [1-6] from previous collection will be duplicated here.
6x6 sudoku-x, 2Rx3C, 6,7,8-clues [278503 puzzles].zip

[philvo]

Interesting puzzles.
After normalization, the 2 puzzles rated 9.0 are identical and equivalent to: ..1.2.................3....4....4.5.
phil