Analysis of xx-top500-321-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: .5.....614...3..............67....8.2.1..........4.3.....7.6...5.....2.....1..... initial

Autosolve

position: .53....614...3.............367....8.241........5.4.3.....7.6...5.....2.....1..... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A1: 8,9 => CTR => A1: 7
* PRF # A1: 7 => SOL
* DIS # A3: 8,9 => CTR => A3: 1,6,7
* PRF # A7: 8,9 => SOL
* DIS # A7: 1 => CTR => A7: 8,9
* DIS # A9: 8,9 => CTR => A9: 6,7
* PRF # B2: 8,9 => SOL
* DIS # B8: 8,9 => CTR => B8: 1,3,7
* PRF # I6: 7 => SOL
* DIS # B8: 8,9 => CTR => B8: 1,3,7
* PRF # C8: 8,9 => SOL
* DIS # I8: 8,9 => CTR => I8: 3,4,6,7
* PRF # E1: 8,9 => SOL
* DIS # E3: 8,9 => CTR => E3: 1,5,6,7
* DIS # E5: 8,9 => CTR => E5: 5,6,7
* CNT  15 HDP CHAINS /  34 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 # A1: 8,9 => CTR => A1: 7
* PRF A1: 7 => SOL
* STA A1: 7
* CNT   2 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

.5.....614...3..............67....8.2.1..........4.3.....7.6...5.....2.....1..... initial
.53....614...3.............367....8.241........5.4.3.....7.6...5.....2.....1..... autosolve
753294861496831725128567943367915482241378659985642317832756194519483276674129538 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (4)
A6: 8,9
B6: 8,9
D6: 2,6
E8: 8,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G4,H6: 1.. / G4 = 1  =>  0 pairs (X) / H6 = 1  =>  0 pairs (_)
B2,F2: 1.. / B2 = 1  =>  0 pairs (X) / F2 = 1  =>  0 pairs (_)
F6,H6: 1.. / F6 = 1  =>  0 pairs (X) / H6 = 1  =>  0 pairs (_)
B8,H8: 1.. / B8 = 1  =>  0 pairs (*) / H8 = 1  =>  0 pairs (X)
A3,A7: 1.. / A3 = 1  =>  0 pairs (*) / A7 = 1  =>  0 pairs (X)
E3,E4: 1.. / E3 = 1  =>  0 pairs (X) / E4 = 1  =>  0 pairs (_)
G4,G7: 1.. / G4 = 1  =>  0 pairs (X) / G7 = 1  =>  0 pairs (_)
H3,I3: 3.. / H3 = 3  =>  4 pairs (_) / I3 = 3  =>  4 pairs (_)
D5,F5: 3.. / D5 = 3  =>  4 pairs (_) / F5 = 3  =>  4 pairs (_)
D5,D8: 3.. / D5 = 3  =>  4 pairs (_) / D8 = 3  =>  4 pairs (_)
G4,I4: 4.. / G4 = 4  =>  0 pairs (*) / I4 = 4  =>  0 pairs (X)
C2,D2: 6.. / C2 = 6  =>  0 pairs (*) / D2 = 6  =>  0 pairs (X)
D6,I6: 6.. / D6 = 6  =>  0 pairs (*) / I6 = 6  =>  0 pairs (X)
C8,I8: 6.. / C8 = 6  =>  0 pairs (X) / I8 = 6  =>  0 pairs (_)
A3,A9: 6.. / A3 = 6  =>  0 pairs (X) / A9 = 6  =>  0 pairs (_)
E3,E5: 6.. / E3 = 6  =>  0 pairs (*) / E5 = 6  =>  0 pairs (X)
G5,G9: 6.. / G5 = 6  =>  0 pairs (*) / G9 = 6  =>  0 pairs (X)
A6,B6: 8.. / A6 = 8  =>  4 pairs (_) / B6 = 8  =>  4 pairs (_)
A6,B6: 9.. / A6 = 9  =>  4 pairs (_) / B6 = 9  =>  4 pairs (_)
* DURATION: 0:00:28.668495  START: 13:54:16.051675  END: 13:54:44.720170 2017-05-04
* CP COUNT: (19)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B6,D6,E8)
* .53....614...3.............367....8.241........5.4.3.....7.6...5.....2.....1.....
* PAIR A6: 8,9 COL A
A1: 8,9,7                                # reduction candidate for 8,9
A1: 8,9 => CTR
* .53....6141..3........1....367...184241.67.....52413..1..7.6...5.....21....1.....
A1: 7 => SOLVED
* 753294861496831725128567943367915482241378659985642317832756194519483276674129538
A3: 8,9,1,6,7                            # reduction candidate for 8,9
A3: 8,9 => CTR
* 753....614...3.............367...184241...6....56413..1..7.6...5.....2166..1.....
A3: 1,6,7                                #  4 pairs
A7: 8,9,1                                # reduction candidate for 8,9
A7: 8,9 => SOLVED
* 753294861496831725128567943367915482241378659985642317832756194519483276674129538
A7: 1 => CTR
* .53....6141..3........1....367...184241.67.....52413..1..7.6...5.....21....1.....
A9: 8,9,6,7                              # reduction candidate for 8,9
A9: 8,9 => CTR
* 753....614..63....6...7....367.1..82241.6......52473.61..7.6...5.6...21....1..6..
A9: 6,7                                  #  5 pairs
* PAIR B6: 8,9 COL B
B2: 8,9,1,2,7                            # reduction candidate for 8,9
B2: 8,9 => SOLVED
* 753294861496831725128567943367915482241378659985642317832756194519483276674129538
B2: 1,2,7                                #  4 pairs
B3: 8,9,1,2,7                            # reduction candidate for 8,9
B3: 8,9                                  #  5 pairs
B7: 8,9,1,2,3                            # reduction candidate for 8,9
B7: 8,9                                  #  5 pairs
B8: 8,9,1,3,7                            # reduction candidate for 8,9
B8: 8,9 => CTR
* .53....6141.63.............367...184241........5.41372...7.6...5.6...217...1.....
B8: 1,3,7                                #  4 pairs
B9: 8,9,2,3,7                            # reduction candidate for 8,9
B9: 8,9                                  #  5 pairs
* PAIR D6: 2,6 ROW 6
I6: 2,6,7                                # reduction candidate for 2,6
I6: 7 => SOLVED
* 753294861496831725128567943367915482241378659985642317832756194519483276674129538
I6: 2,6                                  #  7 pairs
* PAIR E8: 8,9 BLK 8
E7: 8,9,2,5                              # reduction candidate for 8,9
E7: 8,9                                  # 12 pairs
D8: 8,9,3,4                              # reduction candidate for 8,9
D8: 8,9                                  # 11 pairs
F8: 8,9,3,4                              # reduction candidate for 8,9
F8: 8,9                                  # 11 pairs
E9: 8,9,2,5                              # reduction candidate for 8,9
E9: 8,9                                  # 12 pairs
F9: 8,9,2,3,4,5                          # reduction candidate for 8,9
F9: 8,9                                  # 10 pairs
* PAIR E8: 8,9 ROW 8
B8: 8,9,1,3,7                            # reduction candidate for 8,9
B8: 8,9 => CTR
* .53....6141.63.............367...184241........5.41372...7.6...5.6...217...1.....
B8: 1,3,7                                #  4 pairs
C8: 8,9,4,6                              # reduction candidate for 8,9
C8: 8,9 => SOLVED
* 753294861496831725128567943367915482241378659985642317832756194519483276674129538
C8: 4,6                                  #  5 pairs
I8: 8,9,3,4,6,7                          # reduction candidate for 8,9
I8: 8,9 => CTR
* .53....614..63....6........367...18.241.6......524.3.61..7.6...5.6...21....1..6..
I8: 3,4,6,7                              #  4 pairs
* PAIR E8: 8,9 COL E
E1: 8,9,2,7                              # reduction candidate for 8,9
E1: 8,9 => SOLVED
* 753294861496831725128567943367915482241378659985642317832756194519483276674129538
E1: 2,7                                  #  5 pairs
E3: 8,9,1,5,6,7                          # reduction candidate for 8,9
E3: 8,9 => CTR
* .53....614...3.............367.1..8.241.6......5247316...7.61..516...2.....1..6..
E3: 1,5,6,7                              #  4 pairs
E5: 8,9,5,6,7                            # reduction candidate for 8,9
E5: 8,9 => CTR
* .53.7..614.6.3........6....367.1..8.241........5.4.31....7.61..51....2..67.1.....
E5: 5,6,7                                #  6 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-321-base-pr-000.dot
* REASONING
* DIS # A1: 8,9 => CTR => A1: 7
* PRF # A1: 7 => SOL
* DIS # A3: 8,9 => CTR => A3: 1,6,7
* PRF # A7: 8,9 => SOL
* DIS # A7: 1 => CTR => A7: 8,9
* DIS # A9: 8,9 => CTR => A9: 6,7
* PRF # B2: 8,9 => SOL
* DIS # B8: 8,9 => CTR => B8: 1,3,7
* PRF # I6: 7 => SOL
* DIS # B8: 8,9 => CTR => B8: 1,3,7
* PRF # C8: 8,9 => SOL
* DIS # I8: 8,9 => CTR => I8: 3,4,6,7
* PRF # E1: 8,9 => SOL
* DIS # E3: 8,9 => CTR => E3: 1,5,6,7
* DIS # E5: 8,9 => CTR => E5: 5,6,7
* CNT  15 HDP CHAINS /  34 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B6,D6,E8)
* .53....614...3.............367....8.241........5.4.3.....7.6...5.....2.....1.....
* PAIR A6: 8,9 COL A
A1: 8,9,7                                # reduction candidate for 8,9
A1: 8,9 => CTR
* .53....6141..3........1....367...184241.67.....52413..1..7.6...5.....21....1.....
A1: 7 => SOLVED
* 753294861496831725128567943367915482241378659985642317832756194519483276674129538
* DURATION: 0:00:01.891457  START: 13:55:09.467909  END: 13:55:11.359366 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-321-base-pr-001.dot
* REASONING
* DIS # A1: 8,9 => CTR => A1: 7
* PRF A1: 7 => SOL
* STA A1: 7
* CNT   2 HDP CHAINS /   1 HYP OPENED

Header Info

Top 500 Minimum 17 321

solution: 753294861496831725128567943367915482241378659985642317832756194519483276674129538
info: 2931     FNBTHWY  S8.f     19683

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

Solution

position: 753294861496831725128567943367915482241378659985642317832756194519483276674129538 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:

* DIS # A1: 8,9 => CTR => A1: 7
* PRF # A1: 7 => SOL
* DIS # A3: 8,9 => CTR => A3: 1,6,7
* INC # A3: 1,6,7 => UNS
* PRF # A7: 8,9 => SOL
* DIS # A7: 1 => CTR => A7: 8,9
* DIS # A9: 8,9 => CTR => A9: 6,7
* INC # A9: 6,7 => UNS
* PRF # B2: 8,9 => SOL
* INC # B2: 1,2,7 => UNS
* INC # B3: 8,9 => UNS
* INC # B7: 8,9 => UNS
* DIS # B8: 8,9 => CTR => B8: 1,3,7
* INC # B8: 1,3,7 => UNS
* INC # B9: 8,9 => UNS
* INC # I6: 2,6 => UNS
* PRF # I6: 7 => SOL
* INC # E7: 8,9 => UNS
* INC # D8: 8,9 => UNS
* INC # F8: 8,9 => UNS
* INC # E9: 8,9 => UNS
* INC # F9: 8,9 => UNS
* DIS # B8: 8,9 => CTR => B8: 1,3,7
* INC # B8: 1,3,7 => UNS
* PRF # C8: 8,9 => SOL
* INC # C8: 4,6 => UNS
* DIS # I8: 8,9 => CTR => I8: 3,4,6,7
* INC # I8: 3,4,6,7 => UNS
* PRF # E1: 8,9 => SOL
* INC # E1: 2,7 => UNS
* DIS # E3: 8,9 => CTR => E3: 1,5,6,7
* INC # E3: 1,5,6,7 => UNS
* DIS # E5: 8,9 => CTR => E5: 5,6,7
* INC # E5: 5,6,7 => UNS
* CNT  34 HDP CHAINS /  34 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # A1: 8,9 => CTR => A1: 7
* PRF A1: 7 => SOL
* STA A1: 7
* CNT   2 HDP CHAINS /   1 HYP OPENED