Analysis of xx-top500-040-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: 64...23.....5........1.....1.57.........3.2..8...............17.3..4...........5. initial

Autosolve

position: 641.723.5...5..1...5.1..7..1.572..34....352.182341.57....35..17537.41....1.2.7.53 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # D8: 8,9 => CTR => D8: 6
* DIS # H2: 8,9 => CTR => H2: 2,4,6
* PRF # H3: 8,9 => SOL
* DIS # H8: 8,9 => CTR => H8: 2,6
* PRF # F4: 6,9 => SOL
* PRF # F4: 6,9 => SOL
* PRF # F7: 8 => SOL
* PRF # H5: 6,9 => SOL
* DIS # C9: 4,9 => CTR => C9: 6,8
* DIS # D8: 8,9 => CTR => D8: 6
* DIS # G9: 8,9 => CTR => G9: 4,6
* CNT  11 HDP CHAINS /  48 HYP OPENED

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

Pair Reduction

Pair Reduction

The following important HDP chains were detected:

* DIS # D8: 8,9 => CTR => D8: 6
* DIS D8: 6 # H2: 8,9 => CTR => H2: 2,4,6
* PRF D8: 6 + H2: 2,4,6 # H3: 8,9 => SOL
* STA D8: 6 + H2: 2,4,6 + H3: 8,9
* CNT   3 HDP CHAINS /   9 HYP OPENED

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

Details

Positions

64...23.....5........1.....1.57.........3.2..8...............17.3..4...........5. initial
641.723.5...5..1...5.1..7..1.572..34....352.182341.57....35..17537.41....1.2.7.53 autosolve
641972385789563142352184796165729834974835261823416579296358417537641928418297653 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (9)
D1: 8,9
F2: 3,4
F3: 3,4
H1: 8,9
B4: 6,9
F6: 6,9
I6: 6,9
A9: 4,9
E9: 8,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A7,C7: 2.. / A7 = 2  => 10 pairs (_) / C7 = 2  => 20 pairs (_)
H8,I8: 2.. / H8 = 2  =>  9 pairs (_) / I8 = 2  =>  0 pairs (X)
A2,A3: 3.. / A2 = 3  => 15 pairs (_) / A3 = 3  =>  7 pairs (_)
F2,F3: 3.. / F2 = 3  =>  7 pairs (_) / F3 = 3  => 15 pairs (_)
A2,F2: 3.. / A2 = 3  => 15 pairs (_) / F2 = 3  =>  7 pairs (_)
A3,F3: 3.. / A3 = 3  =>  7 pairs (_) / F3 = 3  => 15 pairs (_)
F2,F3: 4.. / F2 = 4  => 15 pairs (_) / F3 = 4  =>  7 pairs (_)
H2,H3: 4.. / H2 = 4  =>  7 pairs (_) / H3 = 4  => 15 pairs (_)
A5,C5: 4.. / A5 = 4  => 16 pairs (_) / C5 = 4  => 11 pairs (_)
G7,G9: 4.. / G7 = 4  => 10 pairs (_) / G9 = 4  => 19 pairs (_)
F2,H2: 4.. / F2 = 4  => 15 pairs (_) / H2 = 4  =>  7 pairs (_)
F3,H3: 4.. / F3 = 4  =>  7 pairs (_) / H3 = 4  => 15 pairs (_)
E2,E3: 6.. / E2 = 6  => 10 pairs (_) / E3 = 6  => 10 pairs (_)
F7,D8: 6.. / F7 = 6  =>  0 pairs (X) / D8 = 6  => 15 pairs (_)
F6,I6: 6.. / F6 = 6  =>  0 pairs (*) / I6 = 6  =>  0 pairs (X)
C9,G9: 6.. / C9 = 6  => 16 pairs (_) / G9 = 6  => 14 pairs (_)
D5,D8: 6.. / D5 = 6  =>  0 pairs (X) / D8 = 6  => 15 pairs (_)
A2,B2: 7.. / A2 = 7  =>  9 pairs (_) / B2 = 7  => 15 pairs (_)
A5,B5: 7.. / A5 = 7  => 15 pairs (_) / B5 = 7  =>  9 pairs (_)
A2,A5: 7.. / A2 = 7  =>  9 pairs (_) / A5 = 7  => 15 pairs (_)
B2,B5: 7.. / B2 = 7  => 15 pairs (_) / B5 = 7  =>  9 pairs (_)
F4,D5: 8.. / F4 = 8  => 13 pairs (_) / D5 = 8  =>  0 pairs (*)
G4,H5: 8.. / G4 = 8  =>  0 pairs (*) / H5 = 8  =>  0 pairs (X)
D1,H1: 8.. / D1 = 8  => 13 pairs (_) / H1 = 8  =>  0 pairs (*)
F4,G4: 8.. / F4 = 8  => 13 pairs (_) / G4 = 8  =>  0 pairs (*)
D5,H5: 8.. / D5 = 8  =>  0 pairs (*) / H5 = 8  =>  0 pairs (X)
B2,B7: 8.. / B2 = 8  => 13 pairs (_) / B7 = 8  => 15 pairs (_)
F4,F7: 8.. / F4 = 8  => 13 pairs (_) / F7 = 8  =>  0 pairs (*)
D1,H1: 9.. / D1 = 9  =>  0 pairs (*) / H1 = 9  =>  0 pairs (X)
F6,I6: 9.. / F6 = 9  => 15 pairs (_) / I6 = 9  =>  0 pairs (*)
* DURATION: 0:00:54.520662  START: 04:02:05.217925  END: 04:02:59.738587 2017-05-04
* CP COUNT: (30)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B4,D1,E9,F2,F3,F6,H1,I6)
* 641.723.5...5..1...5.1..7..1.572..34....352.182341.57....35..17537.41....1.2.7.53
* PAIR D1: 8,9 BLK 2
E2: 8,9,6                                # reduction candidate for 8,9
E2: 8,9                                  # 10 pairs
E3: 8,9,6                                # reduction candidate for 8,9
E3: 8,9                                  # 10 pairs
* PAIR D1: 8,9 COL D
D5: 8,9,6                                # reduction candidate for 8,9
D5: 8,9                                  # 15 pairs
D8: 8,9,6                                # reduction candidate for 8,9
D8: 8,9 => CTR
* 641872395...5..1...5.1..7..165728934...635281823419576...356.17537941628916287453
D8: 6                                    # 15 pairs
* PAIR H1: 8,9 BLK 3
H2: 8,9,2,4,6                            # reduction candidate for 8,9
H2: 8,9 => CTR
* 641.723.537.5.41...5.1.374.1.572..347.4.35261823416579.8.359.17537641.2..1.2.7.53
H2: 2,4,6                                #  9 pairs
I2: 8,9,2,6                              # reduction candidate for 8,9
I2: 8,9                                  # 11 pairs
H3: 8,9,2,4,6                            # reduction candidate for 8,9
H3: 8,9 => SOLVED
* 641972385789563142352184796165729834974835261823416579296358417537641928418297653
H3: 2,4,6                                #  9 pairs
I3: 8,9,2,6                              # reduction candidate for 8,9
I3: 8,9                                  # 11 pairs
* PAIR H1: 8,9 COL H
H5: 8,9,6                                # reduction candidate for 8,9
H5: 8,9                                  # 11 pairs
H8: 8,9,2,6                              # reduction candidate for 8,9
H8: 8,9 => CTR
* 641872395...5..1...5.1..7..1.5728934....3528182341.57....35..17537.41..2.1.2.7.53
H8: 2,6                                  # 10 pairs
* PAIR B4: 6,9 BLK 4
B5: 6,9,7                                # reduction candidate for 6,9
B5: 6,9                                  # 15 pairs
C5: 6,9,4                                # reduction candidate for 6,9
C5: 6,9                                  # 16 pairs
* PAIR B4: 6,9 ROW 4
F4: 6,9,8                                # reduction candidate for 6,9
F4: 6,9 => SOLVED
* 641972385789563142352184796165729834974835261823416579296358417537641928418297653
F4: 8                                    # 13 pairs
G4: 6,9,8                                # reduction candidate for 6,9
G4: 6,9                                  # 13 pairs
* PAIR B4: 6,9 COL B
B7: 6,9,8                                # reduction candidate for 6,9
B7: 8                                    # 15 pairs
B7: 6,9                                  # 13 pairs
* PAIR F6: 6,9 BLK 5
F4: 6,9,8                                # reduction candidate for 6,9
F4: 6,9 => SOLVED
* 641972385789563142352184796165729834974835261823416579296358417537641928418297653
F4: 8                                    # 13 pairs
D5: 6,9,8                                # reduction candidate for 6,9
D5: 6,9                                  # 13 pairs
* PAIR F6: 6,9 COL F
F7: 6,9,8                                # reduction candidate for 6,9
F7: 8 => SOLVED
* 641972385789563142352184796165729834974835261823416579296358417537641928418297653
F7: 6,9                                  # 13 pairs
* PAIR I6: 6,9 BLK 6
G4: 6,9,8                                # reduction candidate for 6,9
G4: 6,9                                  # 13 pairs
H5: 6,9,8                                # reduction candidate for 6,9
H5: 6,9 => SOLVED
* 641972385789563142352184796165729834974835261823416579296358417537641928418297653
H5: 8                                    # 13 pairs
* PAIR I6: 6,9 COL I
I2: 6,9,2,8                              # reduction candidate for 6,9
I2: 6,9                                  # 12 pairs
I3: 6,9,2,8                              # reduction candidate for 6,9
I3: 6,9                                  # 12 pairs
I8: 6,9,2,8                              # reduction candidate for 6,9
I8: 6,9                                  # 17 pairs
* PAIR A9: 4,9 BLK 7
A7: 4,9,2                                # reduction candidate for 4,9
A7: 4,9                                  # 20 pairs
C7: 4,9,2,6,8                            # reduction candidate for 4,9
C7: 4,9                                  # 13 pairs
C9: 4,9,6,8                              # reduction candidate for 4,9
C9: 4,9 => CTR
* 641872395...5..1...5.1..7..1.5728934...9352.182341.57....35.417537641....1.287653
C9: 6,8                                  # 10 pairs
* PAIR A9: 4,9 ROW 9
G9: 4,9,6,8                              # reduction candidate for 4,9
G9: 4,9                                  # 16 pairs
G9: 6,8                                  # 12 pairs
* PAIR A9: 4,9 COL A
A5: 4,9,7                                # reduction candidate for 4,9
A5: 7                                    # 15 pairs
A5: 4,9                                  #  9 pairs
* PAIR E9: 8,9 BLK 8
F7: 8,9,6                                # reduction candidate for 8,9
F7: 8,9                                  # 15 pairs
D8: 8,9,6                                # reduction candidate for 8,9
D8: 8,9 => CTR
* 641872395...5..1...5.1..7..165728934...635281823419576...356.17537941628916287453
D8: 6                                    # 15 pairs
* PAIR E9: 8,9 ROW 9
C9: 8,9,4,6                              # reduction candidate for 8,9
C9: 8,9                                  # 16 pairs
G9: 8,9,4,6                              # reduction candidate for 8,9
G9: 8,9 => CTR
* 641872395...5..1...5.1..7..165728934..4635281823419576...3564175379416..4162.7853
G9: 4,6                                  # 10 pairs
* PAIR E9: 8,9 COL E
E2: 8,9,6                                # reduction candidate for 8,9
E2: 8,9                                  # 10 pairs
E3: 8,9,6                                # reduction candidate for 8,9
E3: 8,9                                  # 10 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-040-base-pr-000.dot
* REASONING
* DIS # D8: 8,9 => CTR => D8: 6
* DIS # H2: 8,9 => CTR => H2: 2,4,6
* PRF # H3: 8,9 => SOL
* DIS # H8: 8,9 => CTR => H8: 2,6
* PRF # F4: 6,9 => SOL
* PRF # F4: 6,9 => SOL
* PRF # F7: 8 => SOL
* PRF # H5: 6,9 => SOL
* DIS # C9: 4,9 => CTR => C9: 6,8
* DIS # D8: 8,9 => CTR => D8: 6
* DIS # G9: 8,9 => CTR => G9: 4,6
* CNT  11 HDP CHAINS /  48 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B4,D1,E9,F2,F3,F6,H1,I6)
* 641.723.5...5..1...5.1..7..1.572..34....352.182341.57....35..17537.41....1.2.7.53
* PAIR D1: 8,9 BLK 2
E2: 8,9,6                                # reduction candidate for 8,9
E2: 8,9                                  # 10 pairs
E3: 8,9,6                                # reduction candidate for 8,9
E3: 8,9                                  # 10 pairs
* PAIR D1: 8,9 COL D
D5: 8,9,6                                # reduction candidate for 8,9
D5: 8,9                                  # 15 pairs
D8: 8,9,6                                # reduction candidate for 8,9
D8: 8,9 => CTR
* 641872395...5..1...5.1..7..165728934...635281823419576...356.17537941628916287453
* RESTART
* PAIR RESTART
* PAIR D1: 8,9 BLK 2
E2: 8,9,6                                # reduction candidate for 8,9
E2: 8,9                                  # 16 pairs
E3: 8,9,6                                # reduction candidate for 8,9
E3: 8,9                                  # 16 pairs
* PAIR H1: 8,9 BLK 3
H2: 8,9,2,4,6                            # reduction candidate for 8,9
H2: 8,9 => CTR
* 641.723.537.5.41...5.1.374.165729834794835261823416579.8.35..17537641928.1.2.7.53
I2: 8,9,2,6                              # reduction candidate for 8,9
I2: 8,9                                  # 17 pairs
H3: 8,9,2,4,6                            # reduction candidate for 8,9
H3: 8,9 => SOLVED
* 641972385789563142352184796165729834974835261823416579296358417537641928418297653
* DURATION: 0:00:10.216353  START: 04:03:47.132033  END: 04:03:57.348386 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-040-base-pr-001.dot
* REASONING
* DIS # D8: 8,9 => CTR => D8: 6
* DIS D8: 6 # H2: 8,9 => CTR => H2: 2,4,6
* PRF D8: 6 + H2: 2,4,6 # H3: 8,9 => SOL
* STA D8: 6 + H2: 2,4,6 + H3: 8,9
* CNT   3 HDP CHAINS /   9 HYP OPENED

Header Info

Top 500 Minimum 17 040

solution: 641972385789563142352184796165729834974835261823416579296358417537641928418297653
info: 1370     FNBHWXY  S8.f     35909

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

Solution

position: 641972385789563142352184796165729834974835261823416579296358417537641928418297653 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 # E2: 8,9 => UNS
* INC # E3: 8,9 => UNS
* INC # D5: 8,9 => UNS
* DIS # D8: 8,9 => CTR => D8: 6
* INC # D8: 6 => UNS
* DIS # H2: 8,9 => CTR => H2: 2,4,6
* INC # H2: 2,4,6 => UNS
* INC # I2: 8,9 => UNS
* PRF # H3: 8,9 => SOL
* INC # H3: 2,4,6 => UNS
* INC # I3: 8,9 => UNS
* INC # H5: 8,9 => UNS
* DIS # H8: 8,9 => CTR => H8: 2,6
* INC # H8: 2,6 => UNS
* INC # B5: 6,9 => UNS
* INC # C5: 6,9 => UNS
* PRF # F4: 6,9 => SOL
* INC # F4: 8 => UNS
* INC # G4: 6,9 => UNS
* INC # B7: 6,9 => UNS
* INC # B7: 8 => UNS
* PRF # F4: 6,9 => SOL
* INC # F4: 8 => UNS
* INC # D5: 6,9 => UNS
* INC # F7: 6,9 => UNS
* PRF # F7: 8 => SOL
* INC # G4: 6,9 => UNS
* PRF # H5: 6,9 => SOL
* INC # H5: 8 => UNS
* INC # I2: 6,9 => UNS
* INC # I3: 6,9 => UNS
* INC # I8: 6,9 => UNS
* INC # A7: 4,9 => UNS
* INC # C7: 4,9 => UNS
* DIS # C9: 4,9 => CTR => C9: 6,8
* INC # C9: 6,8 => UNS
* INC # G9: 4,9 => UNS
* INC # G9: 6,8 => UNS
* INC # A5: 4,9 => UNS
* INC # A5: 7 => UNS
* INC # F7: 8,9 => UNS
* DIS # D8: 8,9 => CTR => D8: 6
* INC # D8: 6 => UNS
* INC # C9: 8,9 => UNS
* DIS # G9: 8,9 => CTR => G9: 4,6
* INC # G9: 4,6 => UNS
* INC # E2: 8,9 => UNS
* INC # E3: 8,9 => UNS
* CNT  48 HDP CHAINS /  48 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # E2: 8,9 => UNS
* INC # E3: 8,9 => UNS
* INC # D5: 8,9 => UNS
* DIS # D8: 8,9 => CTR => D8: 6
* INC D8: 6 # E2: 8,9 => UNS
* INC D8: 6 # E3: 8,9 => UNS
* DIS D8: 6 # H2: 8,9 => CTR => H2: 2,4,6
* INC D8: 6 + H2: 2,4,6 # I2: 8,9 => UNS
* PRF D8: 6 + H2: 2,4,6 # H3: 8,9 => SOL
* STA D8: 6 + H2: 2,4,6 + H3: 8,9
* CNT   9 HDP CHAINS /   9 HYP OPENED