Analysis of xx-top95-046-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: .834.........7..5...........4.1.8..........27...3.....2.6.5....5.....8........1.. initial

Autosolve

position: .834.52......7..58....8.....4.1.8......5...27...3.7.812.685....5.....8.2......1.5 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # G2: 6,9 => SOL
* DIS # G2: 3 => CTR => G2: 6,9
* DIS # G3: 6,9 => CTR => G3: 3,7
* DIS # I3: 6,9 => CTR => I3: 3,4
* DIS # A1: 6,9 => CTR => A1: 1,7
* PRF # E1: 6,9 => SOL
* DIS # E1: 1 => CTR => E1: 6,9
* DIS # I4: 3 => CTR => I4: 6,9
* DIS # A4: 6,9 => CTR => A4: 3,7
* DIS # A5: 6,9 => CTR => A5: 1,3,8
* PRF # B5: 6,9 => SOL
* DIS # B6: 6,9 => CTR => B6: 2,5
* DIS # G6: 6,9 => CTR => G6: 4,5
* DIS # A1: 6,9 => CTR => A1: 1,7
* DIS # A2: 6,9 => CTR => A2: 1,4
* DIS # G4: 3,9 => CTR => G4: 5,6
* DIS # I4: 3,9 => CTR => I4: 6
* DIS # A4: 6,7 => CTR => A4: 3,9
* PRF # H3: 3,9 => SOL
* CNT  19 HDP CHAINS /  40 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 # G2: 6,9 => SOL
* STA G2: 6,9
* CNT   1 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

.834.........7..5...........4.1.8..........27...3.....2.6.5....5.....8........1.. initial
.834.52......7..58....8.....4.1.8......5...27...3.7.812.685....5.....8.2......1.5 autosolve
783465219421973658965281734347128596198546327652397481216854973534719862879632145 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (3)
I1: 6,9
A6: 6,9
H4: 3,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H1,H3: 1.. / H1 = 1  =>  0 pairs (*) / H3 = 1  =>  0 pairs (X)
B7,F7: 1.. / B7 = 1  =>  6 pairs (_) / F7 = 1  =>  0 pairs (X)
E1,E8: 1.. / E1 = 1  =>  0 pairs (X) / E8 = 1  =>  0 pairs (_)
E4,E6: 2.. / E4 = 2  =>  3 pairs (_) / E6 = 2  =>  0 pairs (X)
D9,F9: 2.. / D9 = 2  =>  0 pairs (X) / F9 = 2  =>  3 pairs (_)
C4,E4: 2.. / C4 = 2  =>  0 pairs (X) / E4 = 2  =>  3 pairs (_)
F2,F3: 3.. / F2 = 3  =>  0 pairs (*) / F3 = 3  =>  0 pairs (X)
E8,E9: 3.. / E8 = 3  =>  0 pairs (X) / E9 = 3  =>  4 pairs (_)
F2,G2: 3.. / F2 = 3  =>  0 pairs (*) / G2 = 3  =>  0 pairs (X)
A2,C2: 4.. / A2 = 4  =>  3 pairs (_) / C2 = 4  =>  0 pairs (X)
H3,I3: 4.. / H3 = 4  =>  0 pairs (X) / I3 = 4  =>  4 pairs (_)
G5,G6: 4.. / G5 = 4  =>  0 pairs (X) / G6 = 4  =>  3 pairs (_)
E6,G6: 4.. / E6 = 4  =>  0 pairs (X) / G6 = 4  =>  3 pairs (_)
A2,A9: 4.. / A2 = 4  =>  3 pairs (_) / A9 = 4  =>  0 pairs (X)
I3,I7: 4.. / I3 = 4  =>  4 pairs (_) / I7 = 4  =>  0 pairs (X)
B3,C3: 5.. / B3 = 5  =>  3 pairs (_) / C3 = 5  =>  4 pairs (_)
G4,G6: 5.. / G4 = 5  =>  3 pairs (_) / G6 = 5  =>  0 pairs (X)
C4,G4: 5.. / C4 = 5  =>  0 pairs (X) / G4 = 5  =>  3 pairs (_)
B3,B6: 5.. / B3 = 5  =>  3 pairs (_) / B6 = 5  =>  4 pairs (_)
H8,H9: 6.. / H8 = 6  =>  4 pairs (_) / H9 = 6  =>  3 pairs (_)
A4,C4: 7.. / A4 = 7  =>  0 pairs (X) / C4 = 7  =>  5 pairs (_)
D8,D9: 7.. / D8 = 7  =>  3 pairs (_) / D9 = 7  =>  5 pairs (_)
A1,H1: 7.. / A1 = 7  =>  6 pairs (_) / H1 = 7  =>  0 pairs (X)
G3,G7: 7.. / G3 = 7  =>  7 pairs (_) / G7 = 7  =>  0 pairs (X)
A5,C5: 8.. / A5 = 8  =>  4 pairs (_) / C5 = 8  =>  3 pairs (_)
A9,C9: 8.. / A9 = 8  =>  3 pairs (_) / C9 = 8  =>  4 pairs (_)
A5,A9: 8.. / A5 = 8  =>  4 pairs (_) / A9 = 8  =>  3 pairs (_)
C5,C9: 8.. / C5 = 8  =>  3 pairs (_) / C9 = 8  =>  4 pairs (_)
* DURATION: 0:00:39.007772  START: 23:45:56.467478  END: 23:46:35.475250 2017-05-03
* CP COUNT: (28)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,H4,I1)
* .834.52......7..58....8.....4.1.8......5...27...3.7.812.685....5.....8.2......1.5
* PAIR I1: 6,9 BLK 3
G2: 6,9,3                                # reduction candidate for 6,9
G2: 6,9 => SOLVED
* 783465219421973658965281734347128596198546327652397481216854973534719862879632145
G2: 3 => CTR
* .834.52..4...71358....83....4.1.8......5...27...3.7.8121685....5.4.1.8.2..8.3.1.5
G3: 6,9,3,7                              # reduction candidate for 6,9
G3: 6,9 => CTR
* .834.52..4...71358....83..4.4.1.8......5...27...3.7.8121685.7..5.4.1.8.2..8.3.1.5
G3: 3,7                                  #  4 pairs
I3: 6,9,3,4                              # reduction candidate for 6,9
I3: 6,9 => CTR
* 7834.521.....7.358....8374..471285933.85...27...3.7.81216859..45...1.8.2....3.1.5
I3: 3,4                                  #  4 pairs
* PAIR I1: 6,9 ROW 1
A1: 6,9,1,7                              # reduction candidate for 6,9
A1: 6,9 => CTR
* .8341527.....7..58....8..14.4.1.8......5...27...3.7.812.685.7..5.....8.2......1.5
A1: 1,7                                  #  4 pairs
E1: 6,9,1                                # reduction candidate for 6,9
E1: 6,9 => SOLVED
* 783465219421973658965281734347128596198546327652397481216854973534719862879632145
E1: 1 => CTR
* .834152......7..58....8..14.4.1.8......5...27...3.7.812.685....5.....8.2......1.5
* PAIR I1: 6,9 COL I
I4: 6,9,3                                # reduction candidate for 6,9
I4: 3 => CTR
* .834.52..4...71358....83....4.1.8.93...5...27...3.7.81216854.395.4.1.8.2..8.3.1.5
I4: 6,9                                  #  6 pairs
* PAIR A6: 6,9 BLK 4
A4: 6,9,3,7                              # reduction candidate for 6,9
A4: 6,9 => CTR
* .834.52..4...71358....83....471285.....5...27...3.7.8121685....5.4.1.8.2..8.3.1.5
A4: 3,7                                  #  4 pairs
A5: 6,9,1,3,8                            # reduction candidate for 6,9
A5: 6,9 => CTR
* .834.52..4...7..58....8....347128596.185..327...3.74812.6851...5.1...8.28.4...1.5
A5: 1,3,8                                #  3 pairs
B5: 6,9,1,3                              # reduction candidate for 6,9
B5: 6,9 => SOLVED
* 783465219421973658965281734347128596198546327652397481216854973534719862879632145
B5: 1,3                                  #  7 pairs
B6: 6,9,2,5                              # reduction candidate for 6,9
B6: 6,9 => CTR
* .834.527.42967135865728391474.1.8......5...2796.3.7.8121685.7..5.4.1.8.2..8.321.5
B6: 2,5                                  #  4 pairs
* PAIR A6: 6,9 ROW 6
E6: 6,9,2,4                              # reduction candidate for 6,9
E6: 6,9                                  #  7 pairs
G6: 6,9,4,5                              # reduction candidate for 6,9
G6: 6,9 => CTR
* .834.52..4...71358....83....4.1285.....5..427...347.8121685....5.4.1.8.2..8.3.1.5
G6: 4,5                                  #  4 pairs
* PAIR A6: 6,9 COL A
A1: 6,9,1,7                              # reduction candidate for 6,9
A1: 6,9 => CTR
* .8341527.....7..58....8..14.4.1.8......5...27...3.7.812.685.7..5.....8.2......1.5
A1: 1,7                                  #  4 pairs
A2: 6,9,1,4                              # reduction candidate for 6,9
A2: 6,9 => CTR
* 7834652199142736586...8.7..3471285968..5..327...3.74812.685.9..5.....8.24.8...1.5
A2: 1,4                                  #  4 pairs
A3: 6,9,1,7                              # reduction candidate for 6,9
A3: 6,9                                  #  7 pairs
* PAIR H4: 3,9 BLK 6
G4: 3,9,5,6                              # reduction candidate for 3,9
G4: 3,9 => CTR
* 1834652794..971358957283614745128936...59642762934758121685.7.35.4.19862.98...1.5
G4: 5,6                                  #  4 pairs
I4: 3,9,6                                # reduction candidate for 3,9
I4: 3,9 => CTR
* .834.52..4...71358....83....4.1.8......5...27...3.7.8121685....5.4.1.8.2..8.3.1.5
I4: 6                                    #  8 pairs
G5: 3,9,4,6                              # reduction candidate for 3,9
G5: 3,9                                  #  9 pairs
* PAIR H4: 3,9 ROW 4
A4: 3,9,6,7                              # reduction candidate for 3,9
A4: 6,7 => CTR
* .834.52..4...71358....83....4.1.8......5...27...3.7.8121685....5.4.1.8.2..8.3.1.5
A4: 3,9                                  # 11 pairs
* PAIR H4: 3,9 COL H
H3: 3,9,1,4,7                            # reduction candidate for 3,9
H3: 3,9 => SOLVED
* 783465219421973658965281734347128596198546327652397481216854973534719862879632145
H3: 1,4,7                                #  3 pairs
H7: 3,9,4,7                              # reduction candidate for 3,9
H7: 3,9                                  #  7 pairs
H8: 3,9,4,6,7                            # reduction candidate for 3,9
H8: 3,9                                  #  7 pairs
H9: 3,9,4,6,7                            # reduction candidate for 3,9
H9: 3,9                                  #  8 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top95-046-base-pr-000.dot
* REASONING
* PRF # G2: 6,9 => SOL
* DIS # G2: 3 => CTR => G2: 6,9
* DIS # G3: 6,9 => CTR => G3: 3,7
* DIS # I3: 6,9 => CTR => I3: 3,4
* DIS # A1: 6,9 => CTR => A1: 1,7
* PRF # E1: 6,9 => SOL
* DIS # E1: 1 => CTR => E1: 6,9
* DIS # I4: 3 => CTR => I4: 6,9
* DIS # A4: 6,9 => CTR => A4: 3,7
* DIS # A5: 6,9 => CTR => A5: 1,3,8
* PRF # B5: 6,9 => SOL
* DIS # B6: 6,9 => CTR => B6: 2,5
* DIS # G6: 6,9 => CTR => G6: 4,5
* DIS # A1: 6,9 => CTR => A1: 1,7
* DIS # A2: 6,9 => CTR => A2: 1,4
* DIS # G4: 3,9 => CTR => G4: 5,6
* DIS # I4: 3,9 => CTR => I4: 6
* DIS # A4: 6,7 => CTR => A4: 3,9
* PRF # H3: 3,9 => SOL
* CNT  19 HDP CHAINS /  40 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,H4,I1)
* .834.52......7..58....8.....4.1.8......5...27...3.7.812.685....5.....8.2......1.5
* PAIR I1: 6,9 BLK 3
G2: 6,9,3                                # reduction candidate for 6,9
G2: 6,9 => SOLVED
* 783465219421973658965281734347128596198546327652397481216854973534719862879632145
* DURATION: 0:00:02.664323  START: 23:47:07.667030  END: 23:47:10.331353 2017-05-03
* SOLUTION FOUND
* SAVE PR GRAPH xx-top95-046-base-pr-001.dot
* REASONING
* PRF # G2: 6,9 => SOL
* STA G2: 6,9
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

Top 95 Sudokus 046
[sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt

Solution

position: 783465219421973658965281734347128596198546327652397481216854973534719862879632145 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 # G2: 6,9 => SOL
* DIS # G2: 3 => CTR => G2: 6,9
* DIS # G3: 6,9 => CTR => G3: 3,7
* INC # G3: 3,7 => UNS
* DIS # I3: 6,9 => CTR => I3: 3,4
* INC # I3: 3,4 => UNS
* DIS # A1: 6,9 => CTR => A1: 1,7
* INC # A1: 1,7 => UNS
* PRF # E1: 6,9 => SOL
* DIS # E1: 1 => CTR => E1: 6,9
* INC # I4: 6,9 => UNS
* DIS # I4: 3 => CTR => I4: 6,9
* DIS # A4: 6,9 => CTR => A4: 3,7
* INC # A4: 3,7 => UNS
* DIS # A5: 6,9 => CTR => A5: 1,3,8
* INC # A5: 1,3,8 => UNS
* PRF # B5: 6,9 => SOL
* INC # B5: 1,3 => UNS
* DIS # B6: 6,9 => CTR => B6: 2,5
* INC # B6: 2,5 => UNS
* INC # E6: 6,9 => UNS
* DIS # G6: 6,9 => CTR => G6: 4,5
* INC # G6: 4,5 => UNS
* DIS # A1: 6,9 => CTR => A1: 1,7
* INC # A1: 1,7 => UNS
* DIS # A2: 6,9 => CTR => A2: 1,4
* INC # A2: 1,4 => UNS
* INC # A3: 6,9 => UNS
* DIS # G4: 3,9 => CTR => G4: 5,6
* INC # G4: 5,6 => UNS
* DIS # I4: 3,9 => CTR => I4: 6
* INC # I4: 6 => UNS
* INC # G5: 3,9 => UNS
* INC # A4: 3,9 => UNS
* DIS # A4: 6,7 => CTR => A4: 3,9
* PRF # H3: 3,9 => SOL
* INC # H3: 1,4,7 => UNS
* INC # H7: 3,9 => UNS
* INC # H8: 3,9 => UNS
* INC # H9: 3,9 => UNS
* CNT  40 HDP CHAINS /  40 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # G2: 6,9 => SOL
* STA G2: 6,9
* CNT   1 HDP CHAINS /   1 HYP OPENED