The New Sudoku Players' Forum

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Hi champagne

Do you have high ratings with a "45 + 3 clues" puzzle with other 4 digits?

No. There were only 66 of them, and the best ones were:

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1.34.678.4.7.8..3668.73...4.6.347..83..6.8427748...36..3486.97.8...7364..76..48.3 1259 8.4/8.4/2.6
.234.678.4.7.8..3668.73...4.6.347..83.56.84.7748...36..3486..7.8...7364..76..4813 1259 8.4/8.4/2.6
1...567.9.571.9..66.97..15.261..759..9561...77...95.615.4.6197..1.97.6.59765...13 2348 8.4/8.4/2.8

With my constraint to have all pairs of digits with only one UA, I have only 2 of the seven (1567 1579) and my estimate was about 70% of the grids with such a pattern.

note : my estimate for a 5 digits with the same constraint is that it can be seen in about 8% of the solution grids.

Yeah, I got 74% and 8%.

For the 5 digits case, about 98.5% of them have a digit set {a,b1,b2,b3,b4} where for the {a,bi} pairs there's one size 18 UA, and for the {bi,bj} pairs there are 1 or 2 UA's (with sizes adding to 18). Almost none of them have 36+4 puzzle though -- too many 3+ digit UA's in the 5-templates, I guess.
From ~500000 random grids, I only got three 36+4 puzzles:

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..43256..589.6.3.4.36..4.5..4.6.31.53..5..4.66.5.4..3..5.4.6..34...3.56..63.5..4. 1.7/1.2/1.2
4..5.8..98.5.9.2.4.9.4..85..58..49...4.95..8.9...8..45....49518684.35.9.5.98..4.. 6.6/1.2/1.2
.1...23.43.2.461..4..31...22951...431.3..42...4.823.1..312..4....4.3..21.2.4.1.3. 6.6/1.2/1.2

Update: I was stopping after the first puzzle for each grid. It should have been "3 puzzles each, on 3 grids":

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..43256..589.6.3.4.36..4.5..4.6.31.53..5..4.66.5.4..3..5.4.6..34...3.56..63.5..4. 1.7/1.2/1.2
..43.56..5...6.324.36984.5..4.6.31.53..5..4.66.5.4..3..5.4.6..34...3.56..63.5..4. 1.5/1.2/1.2
..43.56985...6.3.4236..4.5..4.6.31.53..5..4.66.5.4..3..5.4.6..34...3.56..63.5..4. 1.5/1.2/1.2

4..5.8..98.5.9.2.4.9.4..85..58..49...4.95..8.9...8..45....49518684.35.9.5.98..4.. 6.6/1.2/1.2
4..5.8..98.5.9.2.4.9.4..85..58..49...4.95..8.9...8..45....495.8.841.5.9.5.98..463 6.6/1.2/1.2
4..5.8..98.5.9.2.4.9.4..85..58..49...4.95..8.9...8..45...6495.8.84.35.9.5198..4.. 6.6/1.2/1.2

.1...23.43.2.461..4..31...22951...431.3..42...4.823.1..312..4....4.3..21.2.4.1.3. 6.6/1.2/1.2
.1...23.43.2.461..4..31...22..1..8431.39542...4..23.1..312..4....4.3..21.2.4.1.3. 6.6/1.2/1.2
.1...23.43.2.461..4..31...22..1...43183..42...4..23519.312..4....4.3..21.2.4.1.3. 6.6/1.2/1.2

[champagne]

All this fits with what I got from the solution grid with a 5 digits pattern.
I have the 2 next days off and I am not yet ready to report on it, so I'll open the thread next week.

[coloin]

[There are only 759 of them -- 4-rookeries with 24 "1234" solutions, differing by relabelling only.

And for each 4-template I got 1202 [ x 120 ] different 5 templates ...
The way that the clues get removed from the 5 template determines the complexity of the puzzle.
Thats a lot of probably "fruitless" puzzles [ as usual]

[champagne]

My code still misses some puzzles having the required level for the potential hardest database, but is now good enough to scan the solution grid.

I have more than 2000 starts (3 digits out of 1567) to test. I tried about 50 of them, including the known start having skfr 11.1 in the database, and many starts with a high skfr ED (as diamonds 9.1 9.1 9.1)
Only 2 of them have ratings >= 10.5, but I got 51.5K such puzzles

Rating 10.5 and 11.1 for the known start,
Rating 10.5 and 10.9 for the second start

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.2.45..894...892...........2..3..........842...8.9.3.....86..7.8....3.4.9...2...3;105
...45....4....92...8.......2..3....8.9...842.....9.3...3..6.97.8....3.4.9...2.8.3;109
    x                                                     x  x


I’ll have more results in the next days, but I don’t expect to have many ‘active’ starts.

Clearly something to find explaining when and why a good start can end with very high ratings

[champagne]

I ahve covered more than half of the starts;
High skfr ED were very disappointing. The rest to test is mainly ER 9.1 9.0 and 8.9 with an ED 2.6

I got 2 more starts rating >=10.5, the cutoff for the potential hardest database. More starts are in the area 10.0 to 10.4.

I now have 12715 more puzzles rating mainly 10.5, but also some 10.6 with these 2 starts

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.........4....923..8..3...42..3....8.9....42..48.....1.3.86.9.....9...4.9..52.8.3;105
                                                     x    x                x

.........4....923..8..3...42..34...8.9.....2...8.....1.3.8..9....29...4.97.5..8.3;105
.........4....923..8..3...42..34...8.9.....2...8.....1.3.8..9.....9...4.97.52.8.3;106
                                                     x                   x x