The New Sudoku Players' Forum

[Red Ed]

... The puzzle [dobrichev] posted has 16 solutions ...

Herb, no-one thought it was a proper (single solution) puzzle: note eleven's "uniqueness requirement is dropped".

[AR4793]

Geeze, must have had a senior moment. I forgot it was April fool's day.

Herb

[dobrichev]

Here are 7 more 40-clue minimal multi-solution puzzles

Code: Select all

...........1..2345.32145.6.....7...8.175.8436.834.157....8..7...28.17654.7..54.83
...........1..2345.321456......7...8.175.8436.834.175....8...7..28.17564.7..548.3
...........1..2345.321456......7..8..174.8563.835.17.4...8....7.28.17456.7..5483.
...........1..2345.32451..6....7.8...271.8654.8.5.4.37...8...7..18.47563.73.154.8
..........12.34.56.35.6214.....78.1..713.6.84.834.167...7..3.68.28.4.7..35..874..
........1..2.1345..415.23.6.....78...27.58.43.8423.7.5.183.....27..81.344...251.8
........1.12.34.5..3615.42.....7..8..285.3.74.7348.2.5.81..5...2..34..183.781.5.2


The last one is interesting in that it has no solvable cell; all 41 unknowns vary among its 21 solutions.

[eleven]

Nice.
So in this last puzzle not only the givens are minimal, but also the non-givens
(None can be derived from all the givens.)

[Added: btw. gsf's q2 rating of 475 is very moderate for a puzzle, where no eliminations at all are possible]

A lot more impressing than this one:

Code: Select all

 +-------+-------+-------+
 | 1 . . | 4 . . | 7 . . |
 | . 2 . | . 5 . | . 8 . |
 | . . 3 | . . 6 | . . 9 |
 +-------+-------+-------+
 | 4 . . | 7 . . | 1 . . |
 | . 5 . | . 8 . | . 2 . |
 | . . 6 | . . 9 | . . 3 |
 +-------+-------+-------+
 | 7 . . | 1 . . | 4 . . |
 | . 8 . | . 2 . | . 5 . |
 | . . 9 | . . 3 | . . 6 |
 +-------+-------+-------+

[gsf]

Nice.
So in this last puzzle not only the givens are minimal, but also the non-givens
(None can be derived from all the givens.)

[Added: btw. gsf's q2 rating of 475 is very moderate for a puzzle, where no eliminations at all are possible]
[/code]

these puzzles are neat

if you add the -v2 option it shows that there are 110 propositions on cells with degree 3 (3 pencilmark clues)

background: a proposition picks one of the pencilmark clues, sets that value, and applies the -q2 methods
-q2 looks at all propositions for each degree from 2..9, doing all of the same degree before proceeding to the next
nesting 1 means that propositions are done 1 cell at a time
nesting 2 means propositions are done 2 cells at a time
girth is the max number of iterations of the -q2 methods per proposition at the nesting level and pencilmark degree

this puzzle only requires one round of propositions with nesting 1 degree 3
5 of the propositions produced a contradiction (that erases bits in the pencilmark grid)
those are [15][49][57][66]^9 [36]^7
1 proposition lead to a solution
that move was [18]=6

the worst proposition round for the easter monster has
propositions 162706 solutions 0 contradictions 3 iterations 614253 girth 25 degree 5 nesting 2
and it has 9 proposition rounds

[eleven]

Thanks for the explanation.
So the q2 rating (different to SE's) includes (systematic) guessing. Maybe not bad to reflect manual solvers behaviour (when hopelessly stuck).

[gsf]

Thanks for the explanation.
So the q2 rating (different to SE's) includes (systematic) guessing. Maybe not bad to reflect manual solvers behaviour (when hopelessly stuck).

systematic guessing -- yes
it makes a proposition (guess) and instead of following chains it just iteratively applies the constraints (singles, box-line) in scope
this is a lot cheaper than following chains, allows all propositions to be checked, and provides a few deterministic measurements
it provides a measure of how lucky a guesser would have to be on hard puzzles
because at each proposition round only a certain percentage of propositions lead to placements/eliminations

[ttt]

So the q2 rating (different to SE's) includes (systematic) guessing. Maybe not bad to reflect manual solvers behaviour (when hopelessly stuck).

I’m not sure but gsf’s rating (q1&2) hardest puzzle (Plantium Blonde) almost solved here.

BTW, it seems that this furum or sudokuland is going to come to...die . Nothing new for long long... long time.
No, only Pattern games is still alive...

Wake up, please...! Allan Barker, SK, RW, MJ, DPB, DM... Where are you...?

ttt

[dobrichev]

After ~60 hours crunching hi-clue multi-solution puzzles the list consist of
- 2 new 39-clue puzzles.
- 148274 39-clue multi-solution minimal puzzles.
- 617 40-clue multi-solution minimal puzzles.

Cheers,
MD

[eleven]

Wow,

would you post the new unique 39's please?

[dobrichev]

Wow,

would you post the new unique 39's please?

Code: Select all

...........1.23.45.24.516.3....7...8.7258.36..863.2.57.47..58..2...475.66..23..74
........1.12.34.5..562.1.34..1..7.8..783.61.556.1.87.3.2..6...8.85...3..6.78.35.2


the puzzle count is:

Code: Select all

Clues   SS M    MS M
39      2       162295
40      0       637

[dobrichev]

Here is the first 41-clue multi-solution minimal puzzle

Code: Select all

........1.12.34.56.65.1243...7..81...8142...362..7158..582436.7.7.......2.6.873.5

All 43 solutions are essentially different.
Applying {-3/+1} resulted in 917 multi-solution minimal 39s and none unique.

Enjoy!

MD

[Pat]

---brought 14 more 39s [ making 138 ]

Now i have 82,456 38s
and 6.75 mio 37s

2 new 39-clue puzzles [ making 140 ]

Code: Select all

...........1.23.45.24.516.3....7...8.7258.36..863.2.57.47..58..2...475.66..23..74
........1.12.34.5..562.1.34..1..7.8..783.61.556.1.87.3.2..6...8.85...3..6.78.35.2

how many minimal-38s now?
( assuming you two are sharing amongst yourselves--- )

does this affect the estimate of 300 minimal-39s?

---my new guess of only 300 minimals with 39 givens

[dobrichev]

how many minimal-38s now?

85213, including eleven's 82456.

does this affect the estimate of 300 minimal-39s?

---my new guess of only 300 minimals with 39 givens

Have no idea

[eleven]

does this affect the estimate of 300 minimal-39s?

Not really. These 2 puzzles dont have a {-2+1} 38-clue, which i still think, is a rare property under 39's.
The estimate is very rough, not much more than an approximation, how much 39's i could find with my method (~150), multiplied by 2. I guess, i would have found a good part of the other puzzles by dobrichev (when running the program many years), but i cant know.

Some words to dobrichev's last findings, which contain 2 world records:

This 41 clue is the puzzle with the most known (independant/irreducible) minimal givens, i.e. you cannot derive one clue from the others or, (equivalently) dropping any one of the clues leads to more (than it's 43) solutions.

Code: Select all

 +-------+-------+-------+
 | . . . | . . . | . . 1 |
 | . 1 2 | . 3 4 | . 5 6 |
 | . 6 5 | . 1 2 | 4 3 . |
 +-------+-------+-------+
 | . . 7 | . . 8 | 1 . . |
 | . 8 1 | 4 2 . | . . 3 |
 | 6 2 . | . 7 1 | 5 8 . |
 +-------+-------+-------+
 | . 5 8 | 2 4 3 | 6 . 7 |
 | . 7 . | . . . | . . . |
 | 2 . 6 | . 8 7 | 3 . 5 |
 +-------+-------+-------+

(But you can place a 3 in r6c4)

This 40 clue is the puzzle with most known minimal givens, which dont allow to place a single number (all empty cells have at least 2 possible solution numbers / no new number can be derived from the givens).

Code: Select all

 +-------+-------+-------+
 | . . . | . . . | . . 1 |
 | . 1 2 | . 3 4 | . 5 . |
 | . 3 6 | 1 5 . | 4 2 . |
 +-------+-------+-------+
 | . . . | . 7 . | . 8 . |
 | . 2 8 | 5 . 3 | . 7 4 |
 | . 7 3 | 4 8 . | 2 . 5 |
 +-------+-------+-------+
 | . 8 1 | . . 5 | . . . |
 | 2 . . | 3 4 . | . 1 8 |
 | 3 . 7 | 8 1 . | 5 . 2 |
 +-------+-------+-------+

Its something like the opposite of a minimum clue puzzle, where the numbers of 64 cells can be derived from 17 givens.