Analysis of xx-top500-279-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: ....2..4.1.....5.......6....6..4..2.5..3..1..............1.8....2.....7....5..3.. initial

Autosolve

position: ....2.64.1764835922.4..6....6.84..2.54236.18....2..4.6...1.82...2.6.4.7....5.23.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # A8: 8 => SOL
* PRF # I9: 8 => SOL
* DIS # I9: 4 => CTR => I9: 8,9
* CNT   3 HDP CHAINS /  26 HYP OPENED

See Appendix: Full HDP Chains for full list of HDP chains.

Pair Reduction

Pair Reduction

The following important HDP chains were detected:

* PRF # A8: 8 => SOL
* STA A8: 8
* CNT   1 HDP CHAINS /  16 HYP OPENED

See Appendix: Full HDP Chains for full list of HDP chains.

Details

Positions

....2..4.1.....5.......6....6..4..2.5..3..1..............1.8....2.....7....5..3.. initial
....2.64.1764835922.4..6....6.84..2.54236.18....2..4.6...1.82...2.6.4.7....5.23.. autosolve
958721643176483592234956817361849725542367189789215436693178254825634971417592368 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (22)
D1: 7,9
F1: 1,5
D3: 7,9
E3: 1,5
G3: 7,8
H3: 1,3
F5: 7,9
E6: 1,5
G4: 7,9
I4: 3,5
I5: 7,9
H6: 3,5
A7: 4,6
C8: 1,5
A9: 4,6
E8: 3,9
E9: 7,9
H7: 5,6
I7: 4,9
G8: 8,9
I8: 1,5
H9: 1,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
F1,E3: 1.. / F1 = 1  => 16 pairs (_) / E3 = 1  =>  0 pairs (X)
I8,H9: 1.. / I8 = 1  => 16 pairs (_) / H9 = 1  =>  0 pairs (X)
F1,I1: 1.. / F1 = 1  => 16 pairs (_) / I1 = 1  =>  0 pairs (X)
C4,F4: 1.. / C4 = 1  => 16 pairs (_) / F4 = 1  =>  0 pairs (X)
C8,I8: 1.. / C8 = 1  =>  0 pairs (X) / I8 = 1  => 16 pairs (_)
B6,B9: 1.. / B6 = 1  =>  0 pairs (X) / B9 = 1  => 16 pairs (_)
E3,E6: 1.. / E3 = 1  =>  0 pairs (X) / E6 = 1  => 16 pairs (_)
H3,H9: 1.. / H3 = 1  => 16 pairs (_) / H9 = 1  =>  0 pairs (X)
I4,H6: 3.. / I4 = 3  =>  0 pairs (X) / H6 = 3  => 16 pairs (_)
E7,E8: 3.. / E7 = 3  => 19 pairs (_) / E8 = 3  => 23 pairs (_)
A8,E8: 3.. / A8 = 3  => 19 pairs (_) / E8 = 3  => 23 pairs (_)
H3,H6: 3.. / H3 = 3  =>  0 pairs (X) / H6 = 3  => 16 pairs (_)
A7,A9: 4.. / A7 = 4  =>  0 pairs (X) / A9 = 4  => 16 pairs (_)
I7,I9: 4.. / I7 = 4  => 16 pairs (_) / I9 = 4  =>  0 pairs (X)
A7,I7: 4.. / A7 = 4  =>  0 pairs (X) / I7 = 4  => 16 pairs (_)
A9,I9: 4.. / A9 = 4  => 16 pairs (_) / I9 = 4  =>  0 pairs (X)
F1,E3: 5.. / F1 = 5  =>  0 pairs (X) / E3 = 5  => 16 pairs (_)
I4,H6: 5.. / I4 = 5  => 16 pairs (_) / H6 = 5  =>  0 pairs (X)
H7,I8: 5.. / H7 = 5  => 16 pairs (_) / I8 = 5  =>  0 pairs (X)
B3,E3: 5.. / B3 = 5  =>  0 pairs (X) / E3 = 5  => 16 pairs (_)
F4,I4: 5.. / F4 = 5  =>  0 pairs (X) / I4 = 5  => 16 pairs (_)
C8,I8: 5.. / C8 = 5  => 16 pairs (_) / I8 = 5  =>  0 pairs (X)
E3,E6: 5.. / E3 = 5  => 16 pairs (_) / E6 = 5  =>  0 pairs (X)
H6,H7: 5.. / H6 = 5  =>  0 pairs (X) / H7 = 5  => 16 pairs (_)
I4,I8: 5.. / I4 = 5  => 16 pairs (_) / I8 = 5  =>  0 pairs (X)
A7,A9: 6.. / A7 = 6  => 16 pairs (_) / A9 = 6  =>  0 pairs (X)
H7,H9: 6.. / H7 = 6  =>  0 pairs (X) / H9 = 6  => 16 pairs (_)
A7,H7: 6.. / A7 = 6  => 16 pairs (_) / H7 = 6  =>  0 pairs (X)
A9,H9: 6.. / A9 = 6  =>  0 pairs (X) / H9 = 6  => 16 pairs (_)
D1,D3: 7.. / D1 = 7  => 20 pairs (_) / D3 = 7  =>  0 pairs (X)
A4,A6: 7.. / A4 = 7  => 19 pairs (_) / A6 = 7  => 23 pairs (_)
G4,I5: 7.. / G4 = 7  =>  0 pairs (*) / I5 = 7  =>  0 pairs (X)
C7,C9: 7.. / C7 = 7  => 22 pairs (_) / C9 = 7  => 23 pairs (_)
E7,E9: 7.. / E7 = 7  => 23 pairs (_) / E9 = 7  => 22 pairs (_)
D1,I1: 7.. / D1 = 7  => 20 pairs (_) / I1 = 7  =>  0 pairs (X)
F5,I5: 7.. / F5 = 7  =>  0 pairs (*) / I5 = 7  =>  0 pairs (X)
A6,F6: 7.. / A6 = 7  => 23 pairs (_) / F6 = 7  => 19 pairs (_)
C7,E7: 7.. / C7 = 7  => 22 pairs (_) / E7 = 7  => 23 pairs (_)
C9,E9: 7.. / C9 = 7  => 23 pairs (_) / E9 = 7  => 22 pairs (_)
G3,G4: 7.. / G3 = 7  => 19 pairs (_) / G4 = 7  =>  0 pairs (*)
G8,I9: 8.. / G8 = 8  => 19 pairs (_) / I9 = 8  =>  0 pairs (*)
A8,G8: 8.. / A8 = 8  =>  0 pairs (*) / G8 = 8  =>  0 pairs (X)
G3,G8: 8.. / G3 = 8  =>  0 pairs (*) / G8 = 8  =>  0 pairs (X)
D1,D3: 9.. / D1 = 9  =>  0 pairs (X) / D3 = 9  => 20 pairs (_)
G4,I5: 9.. / G4 = 9  => 19 pairs (_) / I5 = 9  =>  0 pairs (*)
B3,D3: 9.. / B3 = 9  =>  0 pairs (X) / D3 = 9  => 20 pairs (_)
F5,I5: 9.. / F5 = 9  => 19 pairs (_) / I5 = 9  =>  0 pairs (*)
G4,G8: 9.. / G4 = 9  => 19 pairs (_) / G8 = 9  =>  0 pairs (*)
* DURATION: 0:01:49.350304  START: 12:28:10.988344  END: 12:30:00.338648 2017-05-04
* CP COUNT: (48)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,A9,C8,D1,D3,E3,E6,E8,E9,F1,F5,G3,G4,G8,H3,H6,H7,H9,I4,I5,I7,I8)
* ....2.64.1764835922.4..6....6.84..2.54236.18....2..4.6...1.82...2.6.4.7....5.23..
* PAIR F1: 1,5 COL F
F4: 1,5,7,9                              # reduction candidate for 1,5
F4: 1,5                                  # 24 pairs
F6: 1,5,7,9                              # reduction candidate for 1,5
F6: 1,5                                  # 16 pairs
* PAIR G3: 7,8 BLK 3
I1: 7,8,1,3                              # reduction candidate for 7,8
I1: 7,8                                  # 18 pairs
I3: 7,8,1,3                              # reduction candidate for 7,8
I3: 7,8                                  # 23 pairs
* PAIR H3: 1,3 BLK 3
I1: 1,3,7,8                              # reduction candidate for 1,3
I1: 1,3                                  # 23 pairs
I3: 1,3,7,8                              # reduction candidate for 1,3
I3: 1,3                                  # 18 pairs
* PAIR F5: 7,9 BLK 5
F4: 7,9,1,5                              # reduction candidate for 7,9
F4: 7,9                                  # 16 pairs
F6: 7,9,1,5                              # reduction candidate for 7,9
F6: 7,9                                  # 24 pairs
* PAIR E6: 1,5 BLK 5
F4: 1,5,7,9                              # reduction candidate for 1,5
F4: 1,5                                  # 24 pairs
F6: 1,5,7,9                              # reduction candidate for 1,5
F6: 1,5                                  # 16 pairs
* PAIR G4: 7,9 ROW 4
A4: 7,9,3                                # reduction candidate for 7,9
A4: 7,9                                  # 26 pairs
F4: 7,9,1,5                              # reduction candidate for 7,9
F4: 7,9                                  # 16 pairs
* PAIR E8: 3,9 BLK 8
E7: 3,9,7                                # reduction candidate for 3,9
E7: 7                                    # 23 pairs
E7: 3,9                                  # 22 pairs
* PAIR E8: 3,9 ROW 8
A8: 3,9,8                                # reduction candidate for 3,9
A8: 8 => SOLVED
* 958721643176483592234956817361849725542367189789215436693178254825634971417592368
A8: 3,9                                  # 19 pairs
* PAIR E9: 7,9 BLK 8
E7: 7,9,3                                # reduction candidate for 7,9
E7: 7,9                                  # 23 pairs
E7: 3                                    # 19 pairs
* PAIR E9: 7,9 ROW 9
C9: 7,9,1,8                              # reduction candidate for 7,9
C9: 7,9                                  # 25 pairs
C9: 1,8                                  # 23 pairs
* PAIR I7: 4,9 BLK 9
I9: 4,9,8                                # reduction candidate for 4,9
I9: 8 => SOLVED
* 958721643176483592234956817361849725542367189789215436693178254825634971417592368
I9: 4,9                                  # 19 pairs
* PAIR G8: 8,9 BLK 9
I9: 8,9,4                                # reduction candidate for 8,9
I9: 4 => CTR
* ...72.64.1764835922.49.673..6.845923542369187.1.2..4.64..1.8269.2.6.48756..5.2314
I9: 8,9                                  # 16 pairs
* PAIR G8: 8,9 ROW 8
A8: 8,9,3                                # reduction candidate for 8,9
A8: 8,9                                  # 23 pairs
A8: 3                                    # 19 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-279-base-pr-000.dot
* REASONING
* PRF # A8: 8 => SOL
* PRF # I9: 8 => SOL
* DIS # I9: 4 => CTR => I9: 8,9
* CNT   3 HDP CHAINS /  26 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,A9,C8,D1,D3,E3,E6,E8,E9,F1,F5,G3,G4,G8,H3,H6,H7,H9,I4,I5,I7,I8)
* ....2.64.1764835922.4..6....6.84..2.54236.18....2..4.6...1.82...2.6.4.7....5.23..
* PAIR F1: 1,5 COL F
F4: 1,5,7,9                              # reduction candidate for 1,5
F4: 1,5                                  # 24 pairs
F6: 1,5,7,9                              # reduction candidate for 1,5
F6: 1,5                                  # 16 pairs
* PAIR G3: 7,8 BLK 3
I1: 7,8,1,3                              # reduction candidate for 7,8
I1: 7,8                                  # 18 pairs
I3: 7,8,1,3                              # reduction candidate for 7,8
I3: 7,8                                  # 23 pairs
* PAIR H3: 1,3 BLK 3
I1: 1,3,7,8                              # reduction candidate for 1,3
I1: 1,3                                  # 23 pairs
I3: 1,3,7,8                              # reduction candidate for 1,3
I3: 1,3                                  # 18 pairs
* PAIR F5: 7,9 BLK 5
F4: 7,9,1,5                              # reduction candidate for 7,9
F4: 7,9                                  # 16 pairs
F6: 7,9,1,5                              # reduction candidate for 7,9
F6: 7,9                                  # 24 pairs
* PAIR E6: 1,5 BLK 5
F4: 1,5,7,9                              # reduction candidate for 1,5
F4: 1,5                                  # 24 pairs
F6: 1,5,7,9                              # reduction candidate for 1,5
F6: 1,5                                  # 16 pairs
* PAIR G4: 7,9 ROW 4
A4: 7,9,3                                # reduction candidate for 7,9
A4: 7,9                                  # 26 pairs
F4: 7,9,1,5                              # reduction candidate for 7,9
F4: 7,9                                  # 16 pairs
* PAIR E8: 3,9 BLK 8
E7: 3,9,7                                # reduction candidate for 3,9
E7: 7                                    # 23 pairs
E7: 3,9                                  # 22 pairs
* PAIR E8: 3,9 ROW 8
A8: 3,9,8                                # reduction candidate for 3,9
A8: 8 => SOLVED
* 958721643176483592234956817361849725542367189789215436693178254825634971417592368
* DURATION: 0:00:20.946129  START: 12:30:33.487170  END: 12:30:54.433299 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-279-base-pr-001.dot
* REASONING
* PRF # A8: 8 => SOL
* STA A8: 8
* CNT   1 HDP CHAINS /  16 HYP OPENED

Header Info

Top 500 Minimum 17 279

solution: 958721643176483592234956817361849725542367189789215436693178254825634971417592368
info: 2253     FNBTHWXY S8.f     3212

http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/

Solution

position: 958721643176483592234956817361849725542367189789215436693178254825634971417592368 solved
Solution

See section Pair Reduction for the HDP chains leading to this result.

Appendix: Full HDP Chains

A1. Pair Reduction Analysis

Full list of HDP chains traversed:

* INC # F4: 1,5 => UNS
* INC # F6: 1,5 => UNS
* INC # I1: 7,8 => UNS
* INC # I3: 7,8 => UNS
* INC # I1: 1,3 => UNS
* INC # I3: 1,3 => UNS
* INC # F4: 7,9 => UNS
* INC # F6: 7,9 => UNS
* INC # F4: 1,5 => UNS
* INC # F6: 1,5 => UNS
* INC # A4: 7,9 => UNS
* INC # F4: 7,9 => UNS
* INC # E7: 3,9 => UNS
* INC # E7: 7 => UNS
* INC # A8: 3,9 => UNS
* PRF # A8: 8 => SOL
* INC # E7: 7,9 => UNS
* INC # E7: 3 => UNS
* INC # C9: 7,9 => UNS
* INC # C9: 1,8 => UNS
* INC # I9: 4,9 => UNS
* PRF # I9: 8 => SOL
* INC # I9: 8,9 => UNS
* DIS # I9: 4 => CTR => I9: 8,9
* INC # A8: 8,9 => UNS
* INC # A8: 3 => UNS
* CNT  26 HDP CHAINS /  26 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # F4: 1,5 => UNS
* INC # F6: 1,5 => UNS
* INC # I1: 7,8 => UNS
* INC # I3: 7,8 => UNS
* INC # I1: 1,3 => UNS
* INC # I3: 1,3 => UNS
* INC # F4: 7,9 => UNS
* INC # F6: 7,9 => UNS
* INC # F4: 1,5 => UNS
* INC # F6: 1,5 => UNS
* INC # A4: 7,9 => UNS
* INC # F4: 7,9 => UNS
* INC # E7: 3,9 => UNS
* INC # E7: 7 => UNS
* INC # A8: 3,9 => UNS
* PRF # A8: 8 => SOL
* STA A8: 8
* CNT  16 HDP CHAINS /  16 HYP OPENED