Analysis of xx-top500-238-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: ...8..3..4..7............2..21....5....4.........3.....6....2.7....2.4..5....1... initial

Autosolve

position: 21785.34.43.7.25.1...14372.321..7.54...41..32..423.17..635.42.7...32.4.5542.71..3 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # F5: 6,9 => SOL
* DIS # F6: 6,9 => CTR => F6: 5,8
* DIS # F8: 6,9 => CTR => F8: 8
* PRF # F8: 8 => SOL
* DIS # C2: 6,9 => CTR => C2: 8
* DIS # E4: 6,9 => CTR => E4: 8
* PRF # E4: 8 => SOL
* DIS # I3: 6,9 => CTR => I3: 8
* DIS # I6: 8 => CTR => I6: 6,9
* DIS # E4: 6,9 => CTR => E4: 8
* PRF # E4: 8 => SOL
* PRF # F5: 6,9 => SOL
* DIS # F6: 6,9 => CTR => F6: 5,8
* PRF # G4: 6,9 => SOL
* DIS # G4: 8 => CTR => G4: 6,9
* DIS # A8: 8,9 => CTR => A8: 1,7
* DIS # B8: 8,9 => CTR => B8: 7
* DIS # F8: 6 => CTR => F8: 8,9
* DIS # C3: 8,9 => CTR => C3: 5,6
* DIS # C5: 8,9 => CTR => C5: 5,6
* DIS # F8: 6 => CTR => F8: 8,9
* DIS # A7: 1 => CTR => A7: 8,9
* DIS # E4: 6 => CTR => E4: 8,9
* DIS # F8: 6,9 => CTR => F8: 8
* PRF # F8: 8 => SOL
* DIS # H9: 6,9 => CTR => H9: 8
* DIS # H8: 1,9 => CTR => H8: 6
* DIS # A7: 1,9 => CTR => A7: 8
* PRF # A7: 8 => SOL
* CNT  29 HDP CHAINS /  51 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 # F5: 6,9 => SOL
* STA F5: 6,9
* CNT   1 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

...8..3..4..7............2..21....5....4.........3.....6....2.7....2.4..5....1... initial
21785.34.43.7.25.1...14372.321..7.54...41..32..423.17..635.42.7...32.4.5542.71..3 autosolve
217859346438762591956143728321987654795416832684235179863594217179328465542671983 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (8)
F1: 6,9
E2: 6,9
I1: 6,9
D4: 6,9
C8: 8,9
E7: 8,9
D9: 6,9
H7: 1,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A7,A8: 1.. / A7 = 1  =>  0 pairs (X) / A8 = 1  =>  9 pairs (_)
H7,H8: 1.. / H7 = 1  =>  9 pairs (_) / H8 = 1  =>  0 pairs (X)
A7,H7: 1.. / A7 = 1  =>  0 pairs (X) / H7 = 1  =>  9 pairs (_)
A8,H8: 1.. / A8 = 1  =>  9 pairs (_) / H8 = 1  =>  0 pairs (X)
B3,C3: 5.. / B3 = 5  => 10 pairs (_) / C3 = 5  =>  9 pairs (_)
F5,F6: 5.. / F5 = 5  =>  9 pairs (_) / F6 = 5  =>  9 pairs (_)
B6,F6: 5.. / B6 = 5  =>  9 pairs (_) / F6 = 5  =>  9 pairs (_)
C3,C5: 5.. / C3 = 5  =>  9 pairs (_) / C5 = 5  => 10 pairs (_)
F1,E2: 6.. / F1 = 6  =>  0 pairs (X) / E2 = 6  => 15 pairs (_)
F8,D9: 6.. / F8 = 6  =>  0 pairs (X) / D9 = 6  => 13 pairs (_)
F1,I1: 6.. / F1 = 6  =>  0 pairs (X) / I1 = 6  => 15 pairs (_)
F8,H8: 6.. / F8 = 6  =>  0 pairs (X) / H8 = 6  => 13 pairs (_)
D4,D9: 6.. / D4 = 6  =>  0 pairs (X) / D9 = 6  => 13 pairs (_)
E2,E4: 6.. / E2 = 6  => 15 pairs (_) / E4 = 6  =>  0 pairs (X)
A5,B5: 7.. / A5 = 7  =>  8 pairs (_) / B5 = 7  =>  0 pairs (X)
A8,B8: 7.. / A8 = 7  =>  0 pairs (X) / B8 = 7  =>  8 pairs (_)
A5,A8: 7.. / A5 = 7  =>  8 pairs (_) / A8 = 7  =>  0 pairs (X)
B5,B8: 7.. / B5 = 7  =>  0 pairs (X) / B8 = 7  =>  8 pairs (_)
H2,I3: 8.. / H2 = 8  =>  0 pairs (X) / I3 = 8  => 18 pairs (_)
E7,F8: 8.. / E7 = 8  =>  0 pairs (X) / F8 = 8  =>  0 pairs (_)
G9,H9: 8.. / G9 = 8  =>  0 pairs (X) / H9 = 8  => 18 pairs (_)
C2,H2: 8.. / C2 = 8  => 18 pairs (_) / H2 = 8  =>  0 pairs (X)
E4,G4: 8.. / E4 = 8  =>  0 pairs (*) / G4 = 8  =>  0 pairs (X)
A7,E7: 8.. / A7 = 8  =>  0 pairs (*) / E7 = 8  =>  0 pairs (X)
E4,E7: 8.. / E4 = 8  =>  0 pairs (*) / E7 = 8  =>  0 pairs (X)
H2,H9: 8.. / H2 = 8  =>  0 pairs (X) / H9 = 8  => 18 pairs (_)
I3,I6: 8.. / I3 = 8  => 18 pairs (_) / I6 = 8  =>  0 pairs (X)
F1,E2: 9.. / F1 = 9  => 15 pairs (_) / E2 = 9  =>  0 pairs (X)
F1,I1: 9.. / F1 = 9  => 15 pairs (_) / I1 = 9  =>  0 pairs (X)
D4,D9: 9.. / D4 = 9  => 13 pairs (_) / D9 = 9  =>  0 pairs (X)
* DURATION: 0:00:47.051517  START: 10:57:14.391890  END: 10:58:01.443407 2017-05-04
* CP COUNT: (30)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C8,D4,D9,E2,E7,F1,H7,I1)
* 21785.34.43.7.25.1...14372.321..7.54...41..32..423.17..635.42.7...32.4.5542.71..3
* PAIR F1: 6,9 COL F
F5: 6,9,5,8                              # reduction candidate for 6,9
F5: 6,9 => SOLVED
* 217859346438762591956143728321987654795416832684235179863594217179328465542671983
F5: 5,8                                  #  9 pairs
F6: 6,9,5,8                              # reduction candidate for 6,9
F6: 6,9 => CTR
* 21785934643.762591695143728321987654...415.32.5423617.863594217179328465542671..3
F6: 5,8                                  #  9 pairs
F8: 6,9,8                                # reduction candidate for 6,9
F8: 6,9 => CTR
* 2178593464387.25.1...143728321..7854...41..32..423.17..635842.7..9326415542971683
F8: 8 => SOLVED
* 217859346438762591956143728321987654795416832684235179863594217179328465542671983
* PAIR E2: 6,9 ROW 2
C2: 6,9,8                                # reduction candidate for 6,9
C2: 6,9 => CTR
* 21785.34.43.7.2581...14372.321.87.54...41..32..423.178863594217179328465542671893
C2: 8                                    # 18 pairs
H2: 6,9,8                                # reduction candidate for 6,9
H2: 6,9                                  # 18 pairs
* PAIR E2: 6,9 COL E
E4: 6,9,8                                # reduction candidate for 6,9
E4: 6,9 => CTR
* 2178593464387.25.1...143728321..7854...41..32..423.17..635842.7..9326415542971683
E4: 8 => SOLVED
* 217859346438762591956143728321987654795416832684235179863594217179328465542671983
* PAIR I1: 6,9 BLK 3
H2: 6,9,8                                # reduction candidate for 6,9
H2: 6,9                                  # 18 pairs
I3: 6,9,8                                # reduction candidate for 6,9
I3: 6,9 => CTR
* 21785.34.43.7.2581...14372.321.87.54...41..32..423.178863594217179328465542671893
I3: 8                                    # 18 pairs
* PAIR I1: 6,9 COL I
I6: 6,9,8                                # reduction candidate for 6,9
I6: 8 => CTR
* 21785.34.43.7.2581...14372.321.87.54...41..32..423.178863594217179328465542671893
I6: 6,9                                  # 18 pairs
* PAIR D4: 6,9 BLK 5
E4: 6,9,8                                # reduction candidate for 6,9
E4: 6,9 => CTR
* 2178593464387.25.1...143728321..7854...41..32..423.17..635842.7..9326415542971683
E4: 8 => SOLVED
* 217859346438762591956143728321987654795416832684235179863594217179328465542671983
F5: 6,9,5,8                              # reduction candidate for 6,9
F5: 6,9 => SOLVED
* 217859346438762591956143728321987654795416832684235179863594217179328465542671983
F5: 5,8                                  #  9 pairs
F6: 6,9,5,8                              # reduction candidate for 6,9
F6: 6,9 => CTR
* 21785934643.762591695143728321987654...415.32.5423617.863594217179328465542671..3
F6: 5,8                                  #  9 pairs
* PAIR D4: 6,9 ROW 4
G4: 6,9,8                                # reduction candidate for 6,9
G4: 6,9 => SOLVED
* 217859346438762591956143728321987654795416832684235179863594217179328465542671983
G4: 8 => CTR
* 2178593464387.25.1...143728321..7854...41..32..423.17..635842.7..9326415542971683
* PAIR C8: 8,9 BLK 7
A7: 8,9,1                                # reduction candidate for 8,9
A7: 8,9                                  #  9 pairs
A8: 8,9,1,7                              # reduction candidate for 8,9
A8: 8,9 => CTR
* 21785.34.43.7.25.1...14372.3216978547..41.932..423.176163584297.7.326415542971..3
A8: 1,7                                  #  9 pairs
B8: 8,9,7                                # reduction candidate for 8,9
B8: 8,9 => CTR
* 217859346439762581...143729321697854.7.41..32..423.17.1635842977..326415542971..3
B8: 7                                    #  8 pairs
* PAIR C8: 8,9 ROW 8
F8: 8,9,6                                # reduction candidate for 8,9
F8: 6 => CTR
* 21785934643.7625.1...14372.321697854...41..32..423.17..635842.7...3264.5542971..3
F8: 8,9                                  # 13 pairs
* PAIR C8: 8,9 COL C
C2: 8,9,6                                # reduction candidate for 8,9
C2: 8,9                                  # 12 pairs
C3: 8,9,5,6                              # reduction candidate for 8,9
C3: 8,9 => CTR
* 21785.34.436792581.5.143726321.67854..5418632684235179.635.42.7...32.4.5542.71..3
C3: 5,6                                  #  9 pairs
C5: 8,9,5,6                              # reduction candidate for 8,9
C5: 8,9 => CTR
* 21785.34.436792581..5143726321.67854...41.6326.423.179.635.42.7...32.4.5542.71..3
C5: 5,6                                  #  9 pairs
* PAIR E7: 8,9 BLK 8
F8: 8,9,6                                # reduction candidate for 8,9
F8: 6 => CTR
* 21785934643.7625.1...14372.321697854...41..32..423.17..635842.7...3264.5542971..3
F8: 8,9                                  # 13 pairs
* PAIR E7: 8,9 ROW 7
A7: 8,9,1                                # reduction candidate for 8,9
A7: 1 => CTR
* 21785.34.43.7.25.1...14372.321697854...41.932..423.176163584297...326415542971..3
A7: 8,9                                  #  9 pairs
* PAIR E7: 8,9 COL E
E4: 8,9,6                                # reduction candidate for 8,9
E4: 6 => CTR
* 217856349438792561...143728321967854...41.632..423.17..635842.7...32.4.5542671983
E4: 8,9                                  # 15 pairs
* PAIR D9: 6,9 BLK 8
F8: 6,9,8                                # reduction candidate for 6,9
F8: 6,9 => CTR
* 2178593464387.25.1...143728321..7854...41..32..423.17..635842.7..9326415542971683
F8: 8 => SOLVED
* 217859346438762591956143728321987654795416832684235179863594217179328465542671983
* PAIR D9: 6,9 ROW 9
G9: 6,9,8                                # reduction candidate for 6,9
G9: 6,9                                  # 18 pairs
H9: 6,9,8                                # reduction candidate for 6,9
H9: 6,9 => CTR
* 21785.34.43.7.2581...14372.321.87.54...41..32..423.178863594217179328465542671893
H9: 8                                    # 18 pairs
* PAIR H7: 1,9 BLK 9
H8: 1,9,6                                # reduction candidate for 1,9
H8: 1,9 => CTR
* 21785934643.7625.1...14372.321697854...41..32..423.17..635.42.7...3264.5542971..3
H8: 6                                    # 13 pairs
* PAIR H7: 1,9 ROW 7
A7: 1,9,8                                # reduction candidate for 1,9
A7: 1,9 => CTR
* 2178593464387.25.1...143728321..7854...41..32..423.17..635842.7..9326415542971683
A7: 8 => SOLVED
* 217859346438762591956143728321987654795416832684235179863594217179328465542671983
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-238-base-pr-000.dot
* REASONING
* PRF # F5: 6,9 => SOL
* DIS # F6: 6,9 => CTR => F6: 5,8
* DIS # F8: 6,9 => CTR => F8: 8
* PRF # F8: 8 => SOL
* DIS # C2: 6,9 => CTR => C2: 8
* DIS # E4: 6,9 => CTR => E4: 8
* PRF # E4: 8 => SOL
* DIS # I3: 6,9 => CTR => I3: 8
* DIS # I6: 8 => CTR => I6: 6,9
* DIS # E4: 6,9 => CTR => E4: 8
* PRF # E4: 8 => SOL
* PRF # F5: 6,9 => SOL
* DIS # F6: 6,9 => CTR => F6: 5,8
* PRF # G4: 6,9 => SOL
* DIS # G4: 8 => CTR => G4: 6,9
* DIS # A8: 8,9 => CTR => A8: 1,7
* DIS # B8: 8,9 => CTR => B8: 7
* DIS # F8: 6 => CTR => F8: 8,9
* DIS # C3: 8,9 => CTR => C3: 5,6
* DIS # C5: 8,9 => CTR => C5: 5,6
* DIS # F8: 6 => CTR => F8: 8,9
* DIS # A7: 1 => CTR => A7: 8,9
* DIS # E4: 6 => CTR => E4: 8,9
* DIS # F8: 6,9 => CTR => F8: 8
* PRF # F8: 8 => SOL
* DIS # H9: 6,9 => CTR => H9: 8
* DIS # H8: 1,9 => CTR => H8: 6
* DIS # A7: 1,9 => CTR => A7: 8
* PRF # A7: 8 => SOL
* CNT  29 HDP CHAINS /  51 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C8,D4,D9,E2,E7,F1,H7,I1)
* 21785.34.43.7.25.1...14372.321..7.54...41..32..423.17..635.42.7...32.4.5542.71..3
* PAIR F1: 6,9 COL F
F5: 6,9,5,8                              # reduction candidate for 6,9
F5: 6,9 => SOLVED
* 217859346438762591956143728321987654795416832684235179863594217179328465542671983
* DURATION: 0:00:02.131210  START: 10:58:48.961396  END: 10:58:51.092606 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-238-base-pr-001.dot
* REASONING
* PRF # F5: 6,9 => SOL
* STA F5: 6,9
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

Top 500 Minimum 17 238

solution: 217859346438762591956143728321987654795416832684235179863594217179328465542671983
info: 2069     FNBWXY   S8.f     12156

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

Solution

position: 217859346438762591956143728321987654795416832684235179863594217179328465542671983 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:

* PRF # F5: 6,9 => SOL
* INC # F5: 5,8 => UNS
* DIS # F6: 6,9 => CTR => F6: 5,8
* INC # F6: 5,8 => UNS
* DIS # F8: 6,9 => CTR => F8: 8
* PRF # F8: 8 => SOL
* DIS # C2: 6,9 => CTR => C2: 8
* INC # C2: 8 => UNS
* INC # H2: 6,9 => UNS
* DIS # E4: 6,9 => CTR => E4: 8
* PRF # E4: 8 => SOL
* INC # H2: 6,9 => UNS
* DIS # I3: 6,9 => CTR => I3: 8
* INC # I3: 8 => UNS
* INC # I6: 6,9 => UNS
* DIS # I6: 8 => CTR => I6: 6,9
* DIS # E4: 6,9 => CTR => E4: 8
* PRF # E4: 8 => SOL
* PRF # F5: 6,9 => SOL
* INC # F5: 5,8 => UNS
* DIS # F6: 6,9 => CTR => F6: 5,8
* INC # F6: 5,8 => UNS
* PRF # G4: 6,9 => SOL
* DIS # G4: 8 => CTR => G4: 6,9
* INC # A7: 8,9 => UNS
* DIS # A8: 8,9 => CTR => A8: 1,7
* INC # A8: 1,7 => UNS
* DIS # B8: 8,9 => CTR => B8: 7
* INC # B8: 7 => UNS
* INC # F8: 8,9 => UNS
* DIS # F8: 6 => CTR => F8: 8,9
* INC # C2: 8,9 => UNS
* DIS # C3: 8,9 => CTR => C3: 5,6
* INC # C3: 5,6 => UNS
* DIS # C5: 8,9 => CTR => C5: 5,6
* INC # C5: 5,6 => UNS
* INC # F8: 8,9 => UNS
* DIS # F8: 6 => CTR => F8: 8,9
* INC # A7: 8,9 => UNS
* DIS # A7: 1 => CTR => A7: 8,9
* INC # E4: 8,9 => UNS
* DIS # E4: 6 => CTR => E4: 8,9
* DIS # F8: 6,9 => CTR => F8: 8
* PRF # F8: 8 => SOL
* INC # G9: 6,9 => UNS
* DIS # H9: 6,9 => CTR => H9: 8
* INC # H9: 8 => UNS
* DIS # H8: 1,9 => CTR => H8: 6
* INC # H8: 6 => UNS
* DIS # A7: 1,9 => CTR => A7: 8
* PRF # A7: 8 => SOL
* CNT  51 HDP CHAINS /  51 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # F5: 6,9 => SOL
* STA F5: 6,9
* CNT   1 HDP CHAINS /   1 HYP OPENED