The New Sudoku Players' Forum

[daj95376]

My puzzle generator is in its infancy where the embedded logic solver currently only supports: Naked/Hidden Singles/Pairs/Triples/Quads, Locked Candidates (1&2), X-Wing, Swordfish, Jellyfish, and XY-Wing. Still, it produced a few puzzles that made me curious about their difficulty level. Besides (Multi-)Colors and Remote Pairs, are there any solver techniques that I'm missing but are needed to solve these puzzles? TIA!!!

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.....7..21...8...76.82.5.....7.....4.6..1..9.8.....3.....8.64.97...9...62..5.....
....3.7...6......15..1.643.7....2.5...6.7.9...8.4....7.719.8..44......8...8.4....
...3..21.61.8........7...5..6..7.19.8.......2.93.2..7..2...7........3.29.84..6...
...45.6....62.9..3.3.....9.4..5...26....2....78...1..5.6.....7.9..1.53....5.37...
...8.....28..31..6..6..4..1..3918.6..4.6.7.5..7.4531..4..1..6..1..34..98.....5...
..1.7.....395.8..65.8.2......69...3....2.7....8...34......9.3.49..8.127.....3.8..
..2.7.8.6.8.94........8...18.923..1...4...2...2..149.86...2........93.8.4.5.6.3..
..8..7....7.5...2..593..4.77....8..9..3.2.7..8..7....65.4..367..3...4.9....1..3..
..84..23.19...5...2.48......1....3.65.......73.6....4......96.3...1...58.75..41..
.3.......46...8.3.2.531...6....23...37..5..61...97....5...368.9.1.7...23.......4.
.4.7.9.32.7.6......36...9....8.6.....5.....4.....5.8....1...35......4.2.76.5.2.9.
.9...32..6.325...8..2.....9...86....2.......7....41...4.....1..5...378.4..69...5.
.9..8..74..6..92....1.4...63..2......8..9..2......8..72...1.5....98..7..63..2..8.
1.......7.....62...9.5..14..3.64..7...2.3.4...6..57.9..87..4.3...67.....5.......4
1..5..4......1.6...9.6...7....8.154.....5.....794.3....2...4.6...7.3......8..5..3
2....1.6....4.3..54.5...3....3.49..112.....597..61.2....2...8.78..1.6....9.7....6
2..3.61.4.6.....93.1.4..2...7.9.5.....8.6.3.....7.8.4...1..3.2.32.....8.7.68.2..1
2.5..74.8..8.......6.4.....9....57...2..3..1...31....6.....4.2.......3..1.49..5.7
2.9..6..3.....154...53.....196....5..7.....1..5....697.....32...246.....3..2..9.4
28.7....3.6......4...3.5..8.27.9.....4.....3.....7.65.6..8.7...1......8.4....2.97
3.....4......4.73..4.61...9.....58...9.864.7...37.....8...56.2..61.2......5.....4
3...9...2.5...74.....5...79......79..4.6.8.1..62......89...5.....38...6.4...1...5
35....9...2..1.6.37.1.....297.12.......9.3.......76.986.....8.42.3.6..7...7....36
4.....9...19....5.7.592..14..42...7...73.42...2...54..27..895.3.4....82...3.....7
4..63.2.8.1..7..49............7..5.1.8.....9.5.7..3............75..1..2.1.9.82..4
6....3...78..6..9...594....5.2....8..1..8..3..7....2.1....957...6..7..53...4....9
6.43.5....5....69.....1...2.....2..1.23...76.7..5.....9...3.....16....4....1.89.6
6.8..7.1.4..3....8.2....3....6.7...3...6.8...7...9.8....7....4.2....4..1.8.7..5.6
7.........2...94...614.82...3.2.......89.65.......5.3...38.467...73...4.........1
9...7......2..64....5..3.7635..19.8...7...3...2.73..5454.8..7....63..8......6...1
9..6.48.3.76........859......43.....13.4.5.68.....93......437........98.7.19.6..2
9..73....74......8..5...97..9.31.6..1.......9..6.92.5..24...7..6......25....27..3
9.2.7654...194..8......2.....74..83...5.8.6...68..71.....7......1..987...7923.4.8
9.87....2.5.3...8.......7....26.743.8.......1.461.29....5.......8...1.4.6....48.9
95.7...3.81..249..........5...4.5..8.........1..6.8...6..........195..72.2...3.46


[Mike Barker]

There are typically many ways to solve a puzzle. Depending on the order of the techniques used a technique may appear critical or not useful at all. For example, running only grouped nice loops and singles, will solve just about as many puzzles as running a full spectrum of fish, X-cycles, XY-cycles, UR and bugs. Here are the techniques my solver used for your puzzles given the following technique order: 1) locked sets, 2) N*N fish, 3) X-cycles/strong loops (I prefer the stong link implementation, but Turbot Fish, etc seem more common so they come first - both are equivalent), 4) XY-cycles - my name (XY wings, chains, rings, mYZ-wings (eg WXYZ)) with SueDeCoq and ALS xz-rule with 1 bivalue cell, 5) unique rectangles, 6) BUG-lite with 2 lines (bigger BUGs take to long with my solver), 7) Nice loops, 8) ALS xz-rule and xy-rule with multiple exclusion rules, and 9) grouped nice loops (with ALS sizes limited to speed things up). As you can see most are used in solving your puzzles, but again I could eliminate anything but grouped nice loops and singles (though I guess technically you could consider a single as a very short loop) and still solve the puzzles. Not all of the eliminations performed are useful or necessarily desirable (its possible for one elimination to prevent another which could crack the puzzle). Even with all of these techniques not all of the puzzles are solved (4, 8, 18, 21, 26, 29, 30, 31 were not solved). This could be because of a coding error, the fact that for speed I limit the size of ALS, BUGs, and the number of nodes for nice loops, or because even more advanced techniques (Forcing Chains, Tabling, etc) are required. The techniques are ordered by the number of times they are used in successfully solved puzzles which is the number in parenthesis.

1) Naked Single (765)
2) Hidden Single (303)
3) Locked Candidate (116)
4) Naked Pair (60)
5) Finned X-wing (53)
6) Nice Loops with 4 Strong Links/Bivalue Cells (53)
7) Nice Loops with 3 Strong Links/Bivalue Cells (49)
8) ALS-xz rule with A=1 cell (25)
9) Nice Loops with 5 Strong Links/Bivalue Cells (18)
10) Naked Triple (14)
11) Generalized WXYZ-wing (14)
12) Generalized XYZ-wing (11)
13) UR+3(X,C,N,U,E)/2SL (11)
14) FrankenFish (10)
15) XY-wing (10)
16) Hidden Pair (9)
17) Grouped Nice Loops with 3 GSL/ALS (9)
18) Generalized VWXYZ-wing (8)
19) UR+2K(X,D),UR+3K(X,D) (8)
20) X-wing (7)
21) Big Finned Fish (7)
22) Grouped 7-node Turbot Chain (7)
23) UR+2(X,D,B)/1SL (7)
24) Nice Loops with 6 Strong Links/Bivalue Cells (7)
25) Nice Loops with 7 Strong Links/Bivalue Cells (7)
26) UR+4(X,C)/3SL,UR+4(x,X)/2SL (6)
27) ALS-xy rule with B=3 cells (6)
28) 4-node XY-chain (5)
29) Generalized UVWXYZ-wing (5)
30) UR+2d,UR+3x,UR+2r(x,d) (5)
31) ALS-xy rule with B=2 cells (5)
32) ALS-xy rule with B=1 cell (4)
33) Hidden Triple (3)
34) Swordfish (3)
35) Finned Swordfish (3)
36) Finned Jellyfish (3)
37) UR+2k(x,d) (3)
38) Naked Quadruple (2)
39) UR+2x (2)
40) Bug-Lite with 2 buglets (2)
41) ALS-xz rule with A=2 cells (2)
42) ALS-xz rule with A=3 cells (2)
43) Grouped Nice Loops with 4 GSL/ALS (2)
44) Turbot Fish (1)
45) 7-node Turbot Chain (1)
46) Grouped Turbot Fish (1)
47) 5-node XY-chain (1)
48) UR+2X (1)
49) ALS-xz rule with A=5 cells (1)
50) ALS-xy rule with B=4 cells (1)
51) Grouped Nice Loops with 6 GSL/ALS (1)

[daj95376]

Thanks Havard (pm) and Mike Barker (thread) for your very informative replies!!! Your information lets me know that I have a long way to go if I want to solve these puzzles using recognized techniques.