Analysis of xx-top500-257-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: .95....4.....1.....2.......8.....1.6...4.2.........3..3...6....1..9........7...5. initial

Autosolve

position: 6953...41....1.....21....3.8..5..126916432...5721863943...6..1.1..9.3...2..741.53 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # G3: 5,7,9 => CTR => G3: 6,8
* DIS # F3: 5,9 => CTR => F3: 4
* DIS # G3: 5,9 => CTR => G3: 6,7,8
* DIS # G8: 2,8 => CTR => G8: 4,6,7
* PRF # G2: 6,7 => SOL
* DIS # H8: 8 => CTR => H8: 6,7
* DIS # H8: 7,8 => CTR => H8: 6
* DIS # B8: 6,8 => CTR => B8: 4,5
* DIS # B8: 6,8 => CTR => B8: 4,5
* DIS # G9: 6 => CTR => G9: 8,9
* CNT  10 HDP CHAINS /  29 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 # G3: 5,7,9 => CTR => G3: 6,8
* DIS G3: 6,8 # F3: 5,9 => CTR => F3: 4
* PRF G3: 6,8 + F3: 4 # G2: 6,7 => SOL
* STA G3: 6,8 + F3: 4 + G2: 6,7
* CNT   3 HDP CHAINS /   7 HYP OPENED

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

Details

Positions

.95....4.....1.....2.......8.....1.6...4.2.........3..3...6....1..9........7...5. initial
6953...41....1.....21....3.8..5..126916432...5721863943...6..1.1..9.3...2..741.53 autosolve
695378241483219675721654839834597126916432587572186394349865712157923468268741953 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (22)
A2: 4,7
B2: 3,8
C2: 3,8
A3: 4,7
E1: 2,7
F1: 7,8
D2: 2,6
D3: 6,8
E3: 5,9
G1: 2,8
H2: 6,7
B4: 3,4
C4: 3,4
E4: 7,9
F4: 7,9
H5: 7,8
B7: 4,5
B9: 6,8
C9: 8,9
D7: 2,8
F7: 5,8
E8: 2,5

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E1,D2: 2.. / E1 = 2  =>  0 pairs (X) / D2 = 2  =>  0 pairs (_)
D7,E8: 2.. / D7 = 2  =>  0 pairs (X) / E8 = 2  =>  0 pairs (_)
E1,G1: 2.. / E1 = 2  =>  0 pairs (X) / G1 = 2  =>  0 pairs (_)
D2,D7: 2.. / D2 = 2  =>  0 pairs (*) / D7 = 2  =>  0 pairs (X)
E1,E8: 2.. / E1 = 2  =>  0 pairs (X) / E8 = 2  =>  0 pairs (_)
B2,C2: 3.. / B2 = 3  =>  0 pairs (X) / C2 = 3  => 21 pairs (_)
B4,C4: 3.. / B4 = 3  => 21 pairs (_) / C4 = 3  =>  0 pairs (X)
B2,B4: 3.. / B2 = 3  =>  0 pairs (X) / B4 = 3  => 21 pairs (_)
C2,C4: 3.. / C2 = 3  => 21 pairs (_) / C4 = 3  =>  0 pairs (X)
A2,A3: 4.. / A2 = 4  => 21 pairs (_) / A3 = 4  =>  0 pairs (X)
F2,F3: 4.. / F2 = 4  =>  0 pairs (X) / F3 = 4  => 21 pairs (_)
B4,C4: 4.. / B4 = 4  =>  0 pairs (X) / C4 = 4  => 21 pairs (_)
G7,G8: 4.. / G7 = 4  =>  0 pairs (X) / G8 = 4  => 23 pairs (_)
A2,F2: 4.. / A2 = 4  => 21 pairs (_) / F2 = 4  =>  0 pairs (X)
A3,F3: 4.. / A3 = 4  =>  0 pairs (X) / F3 = 4  => 21 pairs (_)
G5,I5: 5.. / G5 = 5  => 23 pairs (_) / I5 = 5  => 23 pairs (_)
B7,B8: 5.. / B7 = 5  =>  0 pairs (X) / B8 = 5  =>  0 pairs (_)
F7,E8: 5.. / F7 = 5  =>  0 pairs (*) / E8 = 5  =>  0 pairs (X)
B7,F7: 5.. / B7 = 5  =>  0 pairs (X) / F7 = 5  =>  0 pairs (_)
B8,E8: 5.. / B8 = 5  =>  0 pairs (*) / E8 = 5  =>  0 pairs (X)
E3,E8: 5.. / E3 = 5  =>  0 pairs (*) / E8 = 5  =>  0 pairs (X)
D2,D3: 6.. / D2 = 6  =>  0 pairs (X) / D3 = 6  =>  0 pairs (_)
B8,B9: 6.. / B8 = 6  =>  0 pairs (X) / B9 = 6  => 22 pairs (_)
D3,G3: 6.. / D3 = 6  =>  0 pairs (*) / G3 = 6  =>  0 pairs (X)
B9,G9: 6.. / B9 = 6  => 22 pairs (_) / G9 = 6  =>  0 pairs (X)
H2,H8: 6.. / H2 = 6  =>  0 pairs (X) / H8 = 6  => 21 pairs (_)
A2,A3: 7.. / A2 = 7  =>  0 pairs (X) / A3 = 7  => 21 pairs (_)
E1,F1: 7.. / E1 = 7  =>  0 pairs (*) / F1 = 7  =>  0 pairs (X)
E4,F4: 7.. / E4 = 7  =>  0 pairs (X) / F4 = 7  =>  0 pairs (_)
C7,C8: 7.. / C7 = 7  => 24 pairs (_) / C8 = 7  => 25 pairs (_)
E1,E4: 7.. / E1 = 7  =>  0 pairs (*) / E4 = 7  =>  0 pairs (X)
F1,F4: 7.. / F1 = 7  =>  0 pairs (X) / F4 = 7  =>  0 pairs (_)
B2,C2: 8.. / B2 = 8  => 21 pairs (_) / C2 = 8  =>  0 pairs (X)
F1,D3: 8.. / F1 = 8  =>  0 pairs (*) / D3 = 8  =>  0 pairs (X)
D7,F7: 8.. / D7 = 8  =>  0 pairs (*) / F7 = 8  =>  0 pairs (X)
F1,G1: 8.. / F1 = 8  =>  0 pairs (*) / G1 = 8  =>  0 pairs (X)
D3,D7: 8.. / D3 = 8  =>  0 pairs (X) / D7 = 8  =>  0 pairs (_)
F1,F7: 8.. / F1 = 8  =>  0 pairs (*) / F7 = 8  =>  0 pairs (X)
H5,H8: 8.. / H5 = 8  => 24 pairs (_) / H8 = 8  =>  0 pairs (X)
E4,F4: 9.. / E4 = 9  =>  0 pairs (*) / F4 = 9  =>  0 pairs (X)
C7,C9: 9.. / C7 = 9  => 20 pairs (_) / C9 = 9  => 23 pairs (_)
C9,G9: 9.. / C9 = 9  => 23 pairs (_) / G9 = 9  => 20 pairs (_)
E3,E4: 9.. / E3 = 9  =>  0 pairs (X) / E4 = 9  =>  0 pairs (_)
* DURATION: 0:01:30.105284  START: 11:34:28.954043  END: 11:35:59.059327 2017-05-04
* CP COUNT: (43)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,B2,B4,B7,B9,C2,C4,C9,D2,D3,D7,E1,E3,E4,E8,F1,F4,F7,G1,H2,H5)
* 6953...41....1.....21....3.8..5..126916432...5721863943...6..1.1..9.3...2..741.53
* PAIR D2: 2,6 ROW 2
G2: 2,6,5,7,9                            # reduction candidate for 2,6
G2: 2,6                                  # 23 pairs
G2: 5,7,9                                # 22 pairs
* PAIR D3: 6,8 ROW 3
G3: 6,8,5,7,9                            # reduction candidate for 6,8
G3: 5,7,9 => CTR
* 695378241.8321.....2165..38834597126916432..5572186394347865912158923467269741853
G3: 6,8                                  # 26 pairs
* PAIR E3: 5,9 BLK 2
F2: 5,9,4                                # reduction candidate for 5,9
F2: 5,9                                  # 21 pairs
F3: 5,9,4                                # reduction candidate for 5,9
F3: 5,9 => CTR
* 695378241783214.6.421659.3.834597126916432...57218639434.865.1215.9236..26.741.53
F3: 4                                    # 21 pairs
* PAIR E3: 5,9 ROW 3
G3: 5,9,6,7,8                            # reduction candidate for 5,9
G3: 5,9 => CTR
* 695378241.8321....721654938834597126916432..55721863943..865.1.15.923..726.741.53
G3: 6,7,8                                # 22 pairs
I3: 5,9,7,8                              # reduction candidate for 5,9
I3: 5,9                                  # 26 pairs
* PAIR G1: 2,8 COL G
G8: 2,8,4,6,7                            # reduction candidate for 2,8
G8: 2,8 => CTR
* 695327841...61..7.7218946358..579126916432...57218639435..6841.1..953...2..741.53
G8: 4,6,7                                # 22 pairs
* PAIR H2: 6,7 BLK 3
G2: 6,7,2,5,9                            # reduction candidate for 6,7
G2: 6,7 => SOLVED
* 695378241483219675721654839834597126916432587572186394349865712157923468268741953
G2: 2,5,9                                # 22 pairs
G3: 6,7,5,8,9                            # reduction candidate for 6,7
G3: 6,7                                  # 23 pairs
* PAIR H2: 6,7 COL H
H8: 6,7,8                                # reduction candidate for 6,7
H8: 8 => CTR
* 6953...41....1..6..216...3.8..5..126916432.7.5721863943..865.1.15.923687268741953
H8: 6,7                                  # 24 pairs
* PAIR H5: 7,8 BLK 6
G5: 7,8,5                                # reduction candidate for 7,8
G5: 7,8                                  # 23 pairs
I5: 7,8,5                                # reduction candidate for 7,8
I5: 7,8                                  # 23 pairs
* PAIR H5: 7,8 COL H
H8: 7,8,6                                # reduction candidate for 7,8
H8: 7,8 => CTR
* 695378241.8321..6..2165..3.834597126916432...57218639434.865.1215.9236..26.741.53
H8: 6                                    # 21 pairs
* PAIR B7: 4,5 BLK 7
B8: 4,5,6,8                              # reduction candidate for 4,5
B8: 6,8 => CTR
* 695327841...61..7.72189463584357912691643258757218639435.268.191..953...2..741.53
B8: 4,5                                  # 21 pairs
* PAIR B9: 6,8 BLK 7
B8: 6,8,4,5                              # reduction candidate for 6,8
B8: 6,8 => CTR
* 695327841...61..7.72189463584357912691643258757218639435.268.191..953...2..741.53
B8: 4,5                                  # 21 pairs
* PAIR B9: 6,8 ROW 9
G9: 6,8,9                                # reduction candidate for 6,8
G9: 6,8                                  # 23 pairs
G9: 9                                    # 20 pairs
* PAIR C9: 8,9 ROW 9
G9: 8,9,6                                # reduction candidate for 8,9
G9: 6 => CTR
* 6953...41....1..6..216...3.8..5..126916432...5721863943..865.1.1..9.3...2.9741653
G9: 8,9                                  # 22 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-257-base-pr-000.dot
* REASONING
* DIS # G3: 5,7,9 => CTR => G3: 6,8
* DIS # F3: 5,9 => CTR => F3: 4
* DIS # G3: 5,9 => CTR => G3: 6,7,8
* DIS # G8: 2,8 => CTR => G8: 4,6,7
* PRF # G2: 6,7 => SOL
* DIS # H8: 8 => CTR => H8: 6,7
* DIS # H8: 7,8 => CTR => H8: 6
* DIS # B8: 6,8 => CTR => B8: 4,5
* DIS # B8: 6,8 => CTR => B8: 4,5
* DIS # G9: 6 => CTR => G9: 8,9
* CNT  10 HDP CHAINS /  29 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,B2,B4,B7,B9,C2,C4,C9,D2,D3,D7,E1,E3,E4,E8,F1,F4,F7,G1,H2,H5)
* 6953...41....1.....21....3.8..5..126916432...5721863943...6..1.1..9.3...2..741.53
* PAIR D2: 2,6 ROW 2
G2: 2,6,5,7,9                            # reduction candidate for 2,6
G2: 2,6                                  # 23 pairs
G2: 5,7,9                                # 22 pairs
* PAIR D3: 6,8 ROW 3
G3: 6,8,5,7,9                            # reduction candidate for 6,8
G3: 5,7,9 => CTR
* 695378241.8321.....2165..38834597126916432..5572186394347865912158923467269741853
* PAIR RESTART
* PAIR E3: 5,9 BLK 2
F2: 5,9,4                                # reduction candidate for 5,9
F2: 5,9                                  # 26 pairs
F3: 5,9,4                                # reduction candidate for 5,9
F3: 5,9 => CTR
* 69537824178321456942165983783459712691643278557218639434.865.1.15.9236.8268741953
* RESTART
* PAIR H2: 6,7 BLK 3
G2: 6,7,2,5,9                            # reduction candidate for 6,7
G2: 6,7 => SOLVED
* 695378241483219675721654839834597126916432587572186394349865712157923468268741953
* DURATION: 0:00:10.631508  START: 11:36:32.774582  END: 11:36:43.406090 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-257-base-pr-001.dot
* REASONING
* DIS # G3: 5,7,9 => CTR => G3: 6,8
* DIS G3: 6,8 # F3: 5,9 => CTR => F3: 4
* PRF G3: 6,8 + F3: 4 # G2: 6,7 => SOL
* STA G3: 6,8 + F3: 4 + G2: 6,7
* CNT   3 HDP CHAINS /   7 HYP OPENED

Header Info

Top 500 Minimum 17 257

solution: 695378241483219675721654839834597126916432587572186394349865712157923468268741953
info: 2080     FNBHWXY  S8.f     24718

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

Solution

position: 695378241483219675721654839834597126916432587572186394349865712157923468268741953 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 # G2: 2,6 => UNS
* INC # G2: 5,7,9 => UNS
* INC # G3: 6,8 => UNS
* DIS # G3: 5,7,9 => CTR => G3: 6,8
* INC # F2: 5,9 => UNS
* DIS # F3: 5,9 => CTR => F3: 4
* INC # F3: 4 => UNS
* DIS # G3: 5,9 => CTR => G3: 6,7,8
* INC # G3: 6,7,8 => UNS
* INC # I3: 5,9 => UNS
* DIS # G8: 2,8 => CTR => G8: 4,6,7
* INC # G8: 4,6,7 => UNS
* PRF # G2: 6,7 => SOL
* INC # G2: 2,5,9 => UNS
* INC # G3: 6,7 => UNS
* INC # H8: 6,7 => UNS
* DIS # H8: 8 => CTR => H8: 6,7
* INC # G5: 7,8 => UNS
* INC # I5: 7,8 => UNS
* DIS # H8: 7,8 => CTR => H8: 6
* INC # H8: 6 => UNS
* INC # B8: 4,5 => UNS
* DIS # B8: 6,8 => CTR => B8: 4,5
* DIS # B8: 6,8 => CTR => B8: 4,5
* INC # B8: 4,5 => UNS
* INC # G9: 6,8 => UNS
* INC # G9: 9 => UNS
* INC # G9: 8,9 => UNS
* DIS # G9: 6 => CTR => G9: 8,9
* CNT  29 HDP CHAINS /  29 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # G2: 2,6 => UNS
* INC # G2: 5,7,9 => UNS
* INC # G3: 6,8 => UNS
* DIS # G3: 5,7,9 => CTR => G3: 6,8
* INC G3: 6,8 # F2: 5,9 => UNS
* DIS G3: 6,8 # F3: 5,9 => CTR => F3: 4
* PRF G3: 6,8 + F3: 4 # G2: 6,7 => SOL
* STA G3: 6,8 + F3: 4 + G2: 6,7
* CNT   7 HDP CHAINS /   7 HYP OPENED