Analysis of xx-top500-081-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: .......8473..........1.......8.5.......2..4...4......72......6......41......37... initial

Autosolve

position: .217.3.8473.845.2148.1.237.17845..3...327841..4231.8.72.4.817633.7.241.881..37.4. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # C3: 6,9 => CTR => C3: 5
* DIS # C9: 5 => CTR => C9: 6,9
* DIS # G1: 6,9 => CTR => G1: 5
* DIS # C3: 6,9 => CTR => C3: 5
* DIS # G1: 6,9 => CTR => G1: 5
* PRF # A6: 5 => SOL
* DIS # I5: 6 => CTR => I5: 5,9
* DIS # A6: 6 => CTR => A6: 5,9
* PRF # B8: 5,9 => SOL
* PRF # B5: 6 => SOL
* PRF # D9: 5,9 => SOL
* PRF # B8: 5,9 => SOL
* CNT  12 HDP CHAINS /  37 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 # C3: 6,9 => CTR => C3: 5
* PRF C3: 5 # G4: 2 => SOL
* STA C3: 5 + G4: 2
* CNT   2 HDP CHAINS /   4 HYP OPENED

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

Details

Positions

.......8473..........1.......8.5.......2..4...4......72......6......41......37... initial
.217.3.8473.845.2148.1.237.17845..3...327841..4231.8.72.4.817633.7.241.881..37.4. autosolve
621793584739845621485162379178459236963278415542316897254981763397624158816537942 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (10)
C2: 6,9
E1: 6,9
E3: 6,9
G2: 6,9
F4: 6,9
F6: 6,9
H6: 5,9
B7: 5,9
D7: 5,9
H8: 5,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G4,I4: 2.. / G4 = 2  => 13 pairs (_) / I4 = 2  => 16 pairs (_)
G9,I9: 2.. / G9 = 2  => 16 pairs (_) / I9 = 2  => 13 pairs (_)
G4,G9: 2.. / G4 = 2  => 13 pairs (_) / G9 = 2  => 16 pairs (_)
I4,I9: 2.. / I4 = 2  => 16 pairs (_) / I9 = 2  => 13 pairs (_)
A1,C3: 5.. / A1 = 5  =>  0 pairs (X) / C3 = 5  => 15 pairs (_)
G1,I3: 5.. / G1 = 5  => 15 pairs (_) / I3 = 5  =>  0 pairs (X)
I5,H6: 5.. / I5 = 5  =>  0 pairs (*) / H6 = 5  =>  0 pairs (X)
A1,G1: 5.. / A1 = 5  =>  0 pairs (X) / G1 = 5  => 15 pairs (_)
C3,I3: 5.. / C3 = 5  => 15 pairs (_) / I3 = 5  =>  0 pairs (X)
A6,H6: 5.. / A6 = 5  =>  0 pairs (*) / H6 = 5  =>  0 pairs (X)
B7,D7: 5.. / B7 = 5  => 16 pairs (_) / D7 = 5  => 14 pairs (_)
C3,C9: 5.. / C3 = 5  => 15 pairs (_) / C9 = 5  =>  0 pairs (X)
G1,G9: 5.. / G1 = 5  => 15 pairs (_) / G9 = 5  =>  0 pairs (X)
H6,H8: 5.. / H6 = 5  => 18 pairs (_) / H8 = 5  =>  0 pairs (*)
E1,E3: 6.. / E1 = 6  => 17 pairs (_) / E3 = 6  => 15 pairs (_)
F4,F6: 6.. / F4 = 6  =>  0 pairs (X) / F6 = 6  => 12 pairs (_)
B8,C9: 6.. / B8 = 6  => 14 pairs (_) / C9 = 6  =>  0 pairs (*)
D8,D9: 6.. / D8 = 6  =>  0 pairs (*) / D9 = 6  =>  0 pairs (X)
C2,G2: 6.. / C2 = 6  => 17 pairs (_) / G2 = 6  => 15 pairs (_)
A6,F6: 6.. / A6 = 6  =>  0 pairs (X) / F6 = 6  => 12 pairs (_)
B8,D8: 6.. / B8 = 6  => 14 pairs (_) / D8 = 6  =>  0 pairs (*)
C9,D9: 6.. / C9 = 6  =>  0 pairs (*) / D9 = 6  =>  0 pairs (X)
B5,B8: 6.. / B5 = 6  =>  0 pairs (*) / B8 = 6  =>  0 pairs (X)
E1,E3: 9.. / E1 = 9  => 15 pairs (_) / E3 = 9  => 17 pairs (_)
F4,F6: 9.. / F4 = 9  => 12 pairs (_) / F6 = 9  =>  0 pairs (X)
C2,G2: 9.. / C2 = 9  => 15 pairs (_) / G2 = 9  => 17 pairs (_)
B7,D7: 9.. / B7 = 9  => 14 pairs (_) / D7 = 9  => 16 pairs (_)
H6,H8: 9.. / H6 = 9  =>  0 pairs (*) / H8 = 9  =>  0 pairs (X)
* DURATION: 0:00:45.258512  START: 05:33:57.507176  END: 05:34:42.765688 2017-05-04
* CP COUNT: (28)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B7,C2,D7,E1,E3,F4,F6,G2,H6,H8)
* .217.3.8473.845.2148.1.237.17845..3...327841..4231.8.72.4.817633.7.241.881..37.4.
* PAIR C2: 6,9 BLK 1
A1: 6,9,5                                # reduction candidate for 6,9
A1: 6,9                                  # 15 pairs
C3: 6,9,5                                # reduction candidate for 6,9
C3: 6,9 => CTR
* 5217.3.8473.845.2148.1.237517845..3..5327841..4231.8572945817633679241.881..37.4.
C3: 5                                    # 15 pairs
* PAIR C2: 6,9 COL C
C9: 6,9,5                                # reduction candidate for 6,9
C9: 5 => CTR
* 5217.3.8473.845.2148.1.237517845..3..5327841..4231.857294581763367.241.8815637.4.
C9: 6,9                                  # 15 pairs
* PAIR E1: 6,9 ROW 1
A1: 6,9,5                                # reduction candidate for 6,9
A1: 6,9                                  # 15 pairs
G1: 6,9,5                                # reduction candidate for 6,9
G1: 6,9 => CTR
* 5217.3.8473.845.2148.1.237517845..3..5327841..4231.8572945817633679241.881..37.4.
G1: 5                                    # 15 pairs
* PAIR E3: 6,9 ROW 3
C3: 6,9,5                                # reduction candidate for 6,9
C3: 6,9 => CTR
* 5217.3.8473.845.2148.1.237517845..3..5327841..4231.8572945817633679241.881..37.4.
C3: 5                                    # 15 pairs
I3: 6,9,5                                # reduction candidate for 6,9
I3: 6,9                                  # 15 pairs
* PAIR G2: 6,9 BLK 3
G1: 6,9,5                                # reduction candidate for 6,9
G1: 6,9 => CTR
* 5217.3.8473.845.2148.1.237517845..3..5327841..4231.8572945817633679241.881..37.4.
G1: 5                                    # 15 pairs
I3: 6,9,5                                # reduction candidate for 6,9
I3: 6,9                                  # 15 pairs
* PAIR G2: 6,9 COL G
G4: 6,9,2                                # reduction candidate for 6,9
G4: 6,9                                  # 16 pairs
G4: 2                                    # 13 pairs
* PAIR F4: 6,9 ROW 4
G4: 6,9,2                                # reduction candidate for 6,9
G4: 6,9                                  # 16 pairs
I4: 6,9,2                                # reduction candidate for 6,9
I4: 6,9                                  # 13 pairs
* PAIR F6: 6,9 ROW 6
A6: 6,9,5                                # reduction candidate for 6,9
A6: 5 => SOLVED
* 621793584739845621485162379178459236963278415542316897254981763397624158816537942
A6: 6,9                                  # 18 pairs
* PAIR H6: 5,9 BLK 6
I5: 5,9,6                                # reduction candidate for 5,9
I5: 6 => CTR
* 92176358473.845.2148.1.237.178456.3...3278416642319857254981763367524198819637.4.
I5: 5,9                                  # 12 pairs
* PAIR H6: 5,9 ROW 6
A6: 5,9,6                                # reduction candidate for 5,9
A6: 6 => CTR
* 92176358473.845.2148.1.237.178456.3...3278416642319857254981763367524198819637.4.
A6: 5,9                                  # 12 pairs
* PAIR B7: 5,9 BLK 7
B8: 5,9,6                                # reduction candidate for 5,9
B8: 5,9 => SOLVED
* 621793584739845621485162379178459236963278415542316897254981763397624158816537942
B8: 6                                    # 14 pairs
C9: 5,9,6                                # reduction candidate for 5,9
C9: 5,9                                  # 14 pairs
* PAIR B7: 5,9 COL B
B5: 5,9,6                                # reduction candidate for 5,9
B5: 6 => SOLVED
* 621793584739845621485162379178459236963278415542316897254981763397624158816537942
B5: 5,9                                  # 14 pairs
* PAIR D7: 5,9 BLK 8
D8: 5,9,6                                # reduction candidate for 5,9
D8: 5,9                                  # 14 pairs
D9: 5,9,6                                # reduction candidate for 5,9
D9: 5,9 => SOLVED
* 621793584739845621485162379178459236963278415542316897254981763397624158816537942
D9: 6                                    # 14 pairs
* PAIR H8: 5,9 BLK 9
G9: 5,9,2                                # reduction candidate for 5,9
G9: 5,9                                  # 13 pairs
I9: 5,9,2                                # reduction candidate for 5,9
I9: 5,9                                  # 16 pairs
* PAIR H8: 5,9 ROW 8
B8: 5,9,6                                # reduction candidate for 5,9
B8: 5,9 => SOLVED
* 621793584739845621485162379178459236963278415542316897254981763397624158816537942
B8: 6                                    # 14 pairs
D8: 5,9,6                                # reduction candidate for 5,9
D8: 5,9                                  # 14 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-081-base-pr-000.dot
* REASONING
* DIS # C3: 6,9 => CTR => C3: 5
* DIS # C9: 5 => CTR => C9: 6,9
* DIS # G1: 6,9 => CTR => G1: 5
* DIS # C3: 6,9 => CTR => C3: 5
* DIS # G1: 6,9 => CTR => G1: 5
* PRF # A6: 5 => SOL
* DIS # I5: 6 => CTR => I5: 5,9
* DIS # A6: 6 => CTR => A6: 5,9
* PRF # B8: 5,9 => SOL
* PRF # B5: 6 => SOL
* PRF # D9: 5,9 => SOL
* PRF # B8: 5,9 => SOL
* CNT  12 HDP CHAINS /  37 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B7,C2,D7,E1,E3,F4,F6,G2,H6,H8)
* .217.3.8473.845.2148.1.237.17845..3...327841..4231.8.72.4.817633.7.241.881..37.4.
* PAIR C2: 6,9 BLK 1
A1: 6,9,5                                # reduction candidate for 6,9
A1: 6,9                                  # 15 pairs
C3: 6,9,5                                # reduction candidate for 6,9
C3: 6,9 => CTR
* 5217.3.8473.845.2148.1.237517845..3..5327841..4231.8572945817633679241.881..37.4.
* RESTART
* PAIR G2: 6,9 COL G
G4: 6,9,2                                # reduction candidate for 6,9
G4: 2 => SOLVED
* 621793584739845621485162379178459236963278415542316897254981763397624158816537942
* DURATION: 0:00:04.801220  START: 05:35:18.078699  END: 05:35:22.879919 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-081-base-pr-001.dot
* REASONING
* DIS # C3: 6,9 => CTR => C3: 5
* PRF C3: 5 # G4: 2 => SOL
* STA C3: 5 + G4: 2
* CNT   2 HDP CHAINS /   4 HYP OPENED

Header Info

Top 500 Minimum 17 081

solution: 621793584739845621485162379178459236963278415542316897254981763397624158816537942
info: 1550     FNWX     S8.f     46908

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

Solution

position: 621793584739845621485162379178459236963278415542316897254981763397624158816537942 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 # A1: 6,9 => UNS
* DIS # C3: 6,9 => CTR => C3: 5
* INC # C3: 5 => UNS
* INC # C9: 6,9 => UNS
* DIS # C9: 5 => CTR => C9: 6,9
* INC # A1: 6,9 => UNS
* DIS # G1: 6,9 => CTR => G1: 5
* INC # G1: 5 => UNS
* DIS # C3: 6,9 => CTR => C3: 5
* INC # C3: 5 => UNS
* INC # I3: 6,9 => UNS
* DIS # G1: 6,9 => CTR => G1: 5
* INC # G1: 5 => UNS
* INC # I3: 6,9 => UNS
* INC # G4: 6,9 => UNS
* INC # G4: 2 => UNS
* INC # G4: 6,9 => UNS
* INC # I4: 6,9 => UNS
* INC # A6: 6,9 => UNS
* PRF # A6: 5 => SOL
* INC # I5: 5,9 => UNS
* DIS # I5: 6 => CTR => I5: 5,9
* INC # A6: 5,9 => UNS
* DIS # A6: 6 => CTR => A6: 5,9
* PRF # B8: 5,9 => SOL
* INC # B8: 6 => UNS
* INC # C9: 5,9 => UNS
* INC # B5: 5,9 => UNS
* PRF # B5: 6 => SOL
* INC # D8: 5,9 => UNS
* PRF # D9: 5,9 => SOL
* INC # D9: 6 => UNS
* INC # G9: 5,9 => UNS
* INC # I9: 5,9 => UNS
* PRF # B8: 5,9 => SOL
* INC # B8: 6 => UNS
* INC # D8: 5,9 => UNS
* CNT  37 HDP CHAINS /  37 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A1: 6,9 => UNS
* DIS # C3: 6,9 => CTR => C3: 5
* INC C3: 5 # G4: 6,9 => UNS
* PRF C3: 5 # G4: 2 => SOL
* STA C3: 5 + G4: 2
* CNT   4 HDP CHAINS /   4 HYP OPENED