Analysis of xx-top500-360-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: 52.....8....6.1............1.64..5......9..3.2.........3.78..........1..........2 initial

Autosolve

position: 52.93.6813.8651.296192.835.1.642359....19.23.2938.5.1.431782965..25..1.3...31.8.2 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # I6: 4,7 => SOL
* DIS # I6: 6 => CTR => I6: 4,7
* PRF # B8: 7,8 => SOL
* DIS # B8: 6 => CTR => B8: 7,8
* DIS # I5: 7,8 => CTR => I5: 6
* PRF # I5: 6 => SOL
* PRF # A8: 9 => SOL
* PRF # I5: 6,7 => SOL
* DIS # I5: 8 => CTR => I5: 6,7
* PRF # I6: 6,7 => SOL
* DIS # I6: 4 => CTR => I6: 6,7
* DIS # I5: 7,8 => CTR => I5: 6
* PRF # I5: 6 => SOL
* PRF # I6: 4,7 => SOL
* DIS # I6: 6 => CTR => I6: 4,7
* PRF # A8: 7,9 => SOL
* DIS # A8: 8 => CTR => A8: 7,9
* DIS # B9: 5,7 => CTR => B9: 6
* PRF # B9: 6 => SOL
* PRF # F8: 4,6 => SOL
* CNT  20 HDP CHAINS /  23 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 # I6: 4,7 => SOL
* STA I6: 4,7
* CNT   1 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

52.....8....6.1............1.64..5......9..3.2.........3.78..........1..........2 initial
52.93.6813.8651.296192.835.1.642359....19.23.2938.5.1.431782965..25..1.3...31.8.2 autosolve
527934681348651729619278354176423598854197236293865417431782965982546173765319842 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (19)
C1: 4,7
B2: 4,7
F1: 4,7
E3: 4,7
G2: 4,7
I3: 4,7
B4: 7,8
A5: 7,8
B5: 4,5
C5: 4,5
F5: 6,7
E6: 6,7
I4: 7,8
G6: 4,7
A9: 7,9
C9: 5,7
E8: 4,6
H8: 4,7
H9: 4,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
C1,B2: 4.. / C1 = 4  =>  0 pairs (X) / B2 = 4  =>  0 pairs (_)
F1,E3: 4.. / F1 = 4  =>  0 pairs (*) / E3 = 4  =>  0 pairs (X)
G2,I3: 4.. / G2 = 4  =>  0 pairs (X) / I3 = 4  =>  0 pairs (_)
B5,C5: 4.. / B5 = 4  =>  0 pairs (X) / C5 = 4  =>  0 pairs (_)
G6,I6: 4.. / G6 = 4  =>  0 pairs (*) / I6 = 4  =>  0 pairs (X)
H8,H9: 4.. / H8 = 4  =>  0 pairs (X) / H9 = 4  => 20 pairs (_)
C1,F1: 4.. / C1 = 4  =>  0 pairs (X) / F1 = 4  =>  0 pairs (_)
B2,G2: 4.. / B2 = 4  =>  0 pairs (*) / G2 = 4  =>  0 pairs (X)
E3,I3: 4.. / E3 = 4  =>  0 pairs (X) / I3 = 4  =>  0 pairs (_)
F9,H9: 4.. / F9 = 4  =>  0 pairs (X) / H9 = 4  => 20 pairs (_)
B2,B5: 4.. / B2 = 4  =>  0 pairs (*) / B5 = 4  =>  0 pairs (X)
C1,C5: 4.. / C1 = 4  =>  0 pairs (X) / C5 = 4  =>  0 pairs (_)
E3,E8: 4.. / E3 = 4  =>  0 pairs (X) / E8 = 4  =>  0 pairs (_)
G2,G6: 4.. / G2 = 4  =>  0 pairs (X) / G6 = 4  =>  0 pairs (_)
I3,I6: 4.. / I3 = 4  =>  0 pairs (*) / I6 = 4  =>  0 pairs (X)
B5,C5: 5.. / B5 = 5  =>  0 pairs (*) / C5 = 5  =>  0 pairs (X)
B9,C9: 5.. / B9 = 5  =>  0 pairs (X) / C9 = 5  =>  0 pairs (_)
B5,B9: 5.. / B5 = 5  =>  0 pairs (*) / B9 = 5  =>  0 pairs (X)
C5,C9: 5.. / C5 = 5  =>  0 pairs (X) / C9 = 5  =>  0 pairs (_)
F5,E6: 6.. / F5 = 6  =>  0 pairs (X) / E6 = 6  =>  0 pairs (_)
I5,I6: 6.. / I5 = 6  =>  0 pairs (*) / I6 = 6  =>  0 pairs (X)
B8,B9: 6.. / B8 = 6  =>  0 pairs (X) / B9 = 6  =>  0 pairs (_)
F5,I5: 6.. / F5 = 6  =>  0 pairs (X) / I5 = 6  =>  0 pairs (_)
E6,I6: 6.. / E6 = 6  =>  0 pairs (*) / I6 = 6  =>  0 pairs (X)
B9,F9: 6.. / B9 = 6  =>  0 pairs (*) / F9 = 6  =>  0 pairs (X)
E6,E8: 6.. / E6 = 6  =>  0 pairs (*) / E8 = 6  =>  0 pairs (X)
C1,B2: 7.. / C1 = 7  =>  0 pairs (*) / B2 = 7  =>  0 pairs (X)
F1,E3: 7.. / F1 = 7  =>  0 pairs (X) / E3 = 7  =>  0 pairs (_)
G2,I3: 7.. / G2 = 7  =>  0 pairs (*) / I3 = 7  =>  0 pairs (X)
B4,A5: 7.. / B4 = 7  =>  0 pairs (*) / A5 = 7  =>  0 pairs (X)
F5,E6: 7.. / F5 = 7  =>  0 pairs (*) / E6 = 7  =>  0 pairs (X)
H8,H9: 7.. / H8 = 7  => 20 pairs (_) / H9 = 7  =>  0 pairs (X)
C1,F1: 7.. / C1 = 7  =>  0 pairs (*) / F1 = 7  =>  0 pairs (X)
B2,G2: 7.. / B2 = 7  =>  0 pairs (X) / G2 = 7  =>  0 pairs (_)
E3,I3: 7.. / E3 = 7  =>  0 pairs (*) / I3 = 7  =>  0 pairs (X)
B4,I4: 7.. / B4 = 7  =>  0 pairs (*) / I4 = 7  =>  0 pairs (X)
C1,C9: 7.. / C1 = 7  =>  0 pairs (*) / C9 = 7  =>  0 pairs (X)
E3,E6: 7.. / E3 = 7  =>  0 pairs (*) / E6 = 7  =>  0 pairs (X)
F1,F5: 7.. / F1 = 7  =>  0 pairs (X) / F5 = 7  =>  0 pairs (_)
G2,G6: 7.. / G2 = 7  =>  0 pairs (*) / G6 = 7  =>  0 pairs (X)
B4,A5: 8.. / B4 = 8  =>  0 pairs (X) / A5 = 8  =>  0 pairs (_)
I4,I5: 8.. / I4 = 8  =>  0 pairs (*) / I5 = 8  =>  0 pairs (X)
A8,B8: 8.. / A8 = 8  =>  0 pairs (X) / B8 = 8  =>  0 pairs (_)
B4,I4: 8.. / B4 = 8  =>  0 pairs (X) / I4 = 8  =>  0 pairs (_)
A5,I5: 8.. / A5 = 8  =>  0 pairs (*) / I5 = 8  =>  0 pairs (X)
A5,A8: 8.. / A5 = 8  =>  0 pairs (*) / A8 = 8  =>  0 pairs (X)
B4,B8: 8.. / B4 = 8  =>  0 pairs (X) / B8 = 8  =>  0 pairs (_)
A8,A9: 9.. / A8 = 9  =>  0 pairs (*) / A9 = 9  =>  0 pairs (X)
F8,F9: 9.. / F8 = 9  => 20 pairs (_) / F9 = 9  =>  0 pairs (*)
A8,F8: 9.. / A8 = 9  =>  0 pairs (*) / F8 = 9  =>  0 pairs (X)
A9,F9: 9.. / A9 = 9  => 20 pairs (_) / F9 = 9  =>  0 pairs (*)
* DURATION: 0:01:35.592790  START: 15:04:36.862139  END: 15:06:12.454929 2017-05-04
* CP COUNT: (51)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A9,B2,B4,B5,C1,C5,C9,E3,E6,E8,F1,F5,G2,G6,H8,H9,I3,I4)
* 52.93.6813.8651.296192.835.1.642359....19.23.2938.5.1.431782965..25..1.3...31.8.2
* PAIR I3: 4,7 COL I
I6: 4,7,6                                # reduction candidate for 4,7
I6: 4,7 => SOLVED
* 527934681348651729619278354176423598854197236293865417431782965982546173765319842
I6: 6 => CTR
* 52.93.6813.8651.296192.83541.642359....19.23.2938.5416431782965..25..1.3...31.8.2
* PAIR B4: 7,8 COL B
B8: 7,8,6                                # reduction candidate for 7,8
B8: 7,8 => SOLVED
* 527934681348651729619278354176423598854197236293865417431782965982546173765319842
B8: 6 => CTR
* 52.93.6813.8651.296192.835.1864235977..19623829387541643178296586254.1.3...31.8.2
* PAIR A5: 7,8 ROW 5
I5: 7,8,6                                # reduction candidate for 7,8
I5: 7,8 => CTR
* 52.93.6813.8651.296192.835.1.642359....19623.293875416431782965..25..1.3...31.8.2
I5: 6 => SOLVED
* 527934681348651729619278354176423598854197236293865417431782965982546173765319842
* PAIR A5: 7,8 COL A
A8: 7,8,9                                # reduction candidate for 7,8
A8: 9 => SOLVED
* 527934681348651729619278354176423598854197236293865417431782965982546173765319842
A8: 7,8                                  # 20 pairs
* PAIR F5: 6,7 ROW 5
I5: 6,7,8                                # reduction candidate for 6,7
I5: 6,7 => SOLVED
* 527934681348651729619278354176423598854197236293865417431782965982546173765319842
I5: 8 => CTR
* 52.93.6813.8651.296192.835.1.642359....196238293875416431782965..25..1.3...31.8.2
* PAIR E6: 6,7 ROW 6
I6: 6,7,4                                # reduction candidate for 6,7
I6: 6,7 => SOLVED
* 527934681348651729619278354176423598854197236293865417431782965982546173765319842
I6: 4 => CTR
* 52.93.6813.8651.296192.835.1.642359....19.236293865714431782965..254.1.3...31.8.2
* PAIR I4: 7,8 BLK 6
I5: 7,8,6                                # reduction candidate for 7,8
I5: 7,8 => CTR
* 52.93.6813.8651.296192.835.1.642359....19623.293875416431782965..25..1.3...31.8.2
I5: 6 => SOLVED
* 527934681348651729619278354176423598854197236293865417431782965982546173765319842
* PAIR G6: 4,7 BLK 6
I6: 4,7,6                                # reduction candidate for 4,7
I6: 4,7 => SOLVED
* 527934681348651729619278354176423598854197236293865417431782965982546173765319842
I6: 6 => CTR
* 52.93.6813.8651.296192.83541.642359....19.23.2938.5416431782965..25..1.3...31.8.2
* PAIR A9: 7,9 BLK 7
A8: 7,9,8                                # reduction candidate for 7,9
A8: 7,9 => SOLVED
* 527934681348651729619278354176423598854197236293865417431782965982546173765319842
A8: 8 => CTR
* 52.93.6813.8651.296192.835.1864235977..1962382938754164317829658.2569143965314872
* PAIR C9: 5,7 BLK 7
B9: 5,7,6                                # reduction candidate for 5,7
B9: 5,7 => CTR
* 52.934681348651729619278354186423597...19.23.2938.5.1.431782965.625491739..316842
B9: 6 => SOLVED
* 527934681348651729619278354176423598854197236293865417431782965982546173765319842
* PAIR E8: 4,6 BLK 8
F8: 4,6,9                                # reduction candidate for 4,6
F8: 4,6 => SOLVED
* 527934681348651729619278354176423598854197236293865417431782965982546173765319842
F8: 9                                    # 20 pairs
F9: 4,6,9                                # reduction candidate for 4,6
F9: 4,6                                  # 20 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-360-base-pr-000.dot
* REASONING
* PRF # I6: 4,7 => SOL
* DIS # I6: 6 => CTR => I6: 4,7
* PRF # B8: 7,8 => SOL
* DIS # B8: 6 => CTR => B8: 7,8
* DIS # I5: 7,8 => CTR => I5: 6
* PRF # I5: 6 => SOL
* PRF # A8: 9 => SOL
* PRF # I5: 6,7 => SOL
* DIS # I5: 8 => CTR => I5: 6,7
* PRF # I6: 6,7 => SOL
* DIS # I6: 4 => CTR => I6: 6,7
* DIS # I5: 7,8 => CTR => I5: 6
* PRF # I5: 6 => SOL
* PRF # I6: 4,7 => SOL
* DIS # I6: 6 => CTR => I6: 4,7
* PRF # A8: 7,9 => SOL
* DIS # A8: 8 => CTR => A8: 7,9
* DIS # B9: 5,7 => CTR => B9: 6
* PRF # B9: 6 => SOL
* PRF # F8: 4,6 => SOL
* CNT  20 HDP CHAINS /  23 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A9,B2,B4,B5,C1,C5,C9,E3,E6,E8,F1,F5,G2,G6,H8,H9,I3,I4)
* 52.93.6813.8651.296192.835.1.642359....19.23.2938.5.1.431782965..25..1.3...31.8.2
* PAIR I3: 4,7 COL I
I6: 4,7,6                                # reduction candidate for 4,7
I6: 4,7 => SOLVED
* 527934681348651729619278354176423598854197236293865417431782965982546173765319842
* DURATION: 0:00:02.344611  START: 15:06:42.462830  END: 15:06:44.807441 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-360-base-pr-001.dot
* REASONING
* PRF # I6: 4,7 => SOL
* STA I6: 4,7
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

Top 500 Minimum 17 360

solution: 527934681348651729619278354176423598854197236293865417431782965982546173765319842
info: 4899     FNBTWX   S8.f     33586

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

Solution

position: 527934681348651729619278354176423598854197236293865417431782965982546173765319842 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 # I6: 4,7 => SOL
* DIS # I6: 6 => CTR => I6: 4,7
* PRF # B8: 7,8 => SOL
* DIS # B8: 6 => CTR => B8: 7,8
* DIS # I5: 7,8 => CTR => I5: 6
* PRF # I5: 6 => SOL
* INC # A8: 7,8 => UNS
* PRF # A8: 9 => SOL
* PRF # I5: 6,7 => SOL
* DIS # I5: 8 => CTR => I5: 6,7
* PRF # I6: 6,7 => SOL
* DIS # I6: 4 => CTR => I6: 6,7
* DIS # I5: 7,8 => CTR => I5: 6
* PRF # I5: 6 => SOL
* PRF # I6: 4,7 => SOL
* DIS # I6: 6 => CTR => I6: 4,7
* PRF # A8: 7,9 => SOL
* DIS # A8: 8 => CTR => A8: 7,9
* DIS # B9: 5,7 => CTR => B9: 6
* PRF # B9: 6 => SOL
* PRF # F8: 4,6 => SOL
* INC # F8: 9 => UNS
* INC # F9: 4,6 => UNS
* CNT  23 HDP CHAINS /  23 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # I6: 4,7 => SOL
* STA I6: 4,7
* CNT   1 HDP CHAINS /   1 HYP OPENED