Analysis of xx-top500-093-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: 5..2...3.6.1..5............1....64...3..7..8...........7.83..........6.1......... initial

Autosolve

position: 5..26713.6213.58.77.3.18.6.1.7.86423.3.17..8686...371..76831.5.3..7..6.1.1.6..378 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B1: 4,9 => CTR => B1: 8
* DIS # B8: 4,9 => CTR => B8: 5,8
* DIS # E9: 4,9 => CTR => E9: 2,5
* PRF # D6: 4,9 => SOL
* DIS # D6: 5 => CTR => D6: 4,9
* DIS # B1: 4,9 => CTR => B1: 8
* DIS # I7: 4,9 => CTR => I7: 2
* PRF # I7: 2 => SOL
* PRF # C6: 5,9 => SOL
* PRF # B8: 5,9 => SOL
* DIS # B8: 4,8 => CTR => B8: 5,9
* DIS # D6: 5,9 => CTR => D6: 4
* PRF # D6: 4 => SOL
* PRF # C5: 2,4 => SOL
* PRF # C6: 5,9 => SOL
* DIS # D6: 5,9 => CTR => D6: 4
* PRF # D6: 4 => SOL
* DIS # B8: 4,9 => CTR => B8: 5,8
* DIS # C8: 4,9 => CTR => C8: 2,5,8
* DIS # I7: 4,9 => CTR => I7: 2
* PRF # I7: 2 => SOL
* PRF # I7: 2,9 => SOL
* DIS # I7: 4 => CTR => I7: 2,9
* DIS # I7: 4,9 => CTR => I7: 2
* PRF # I7: 2 => SOL
* DIS # B8: 4,9 => CTR => B8: 5,8
* DIS # C8: 4,9 => CTR => C8: 2,5,8
* CNT  27 HDP CHAINS /  49 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 # B1: 4,9 => CTR => B1: 8
* DIS B1: 8 # B8: 4,9 => CTR => B8: 5
* PRF B1: 8 + B8: 5 => SOL
* STA B1: 8 + B8: 5
* CNT   3 HDP CHAINS /   2 HYP OPENED

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

Details

Positions

5..2...3.6.1..5............1....64...3..7..8...........7.83..........6.1......... initial
5..26713.6213.58.77.3.18.6.1.7.86423.3.17..8686...371..76831.5.3..7..6.1.1.6..378 autosolve
589267134621345897743918265197586423234179586865423719476831952358792641912654378 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (14)
B3: 4,9
E2: 4,9
D3: 4,9
I1: 4,9
H2: 4,9
G3: 2,5
I3: 2,5
B4: 5,9
D4: 5,9
G5: 5,9
I6: 5,9
A7: 4,9
G7: 2,9
H8: 4,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G3,I3: 2.. / G3 = 2  =>  0 pairs (*) / I3 = 2  =>  0 pairs (X)
F5,E6: 2.. / F5 = 2  => 22 pairs (_) / E6 = 2  => 15 pairs (_)
G7,I7: 2.. / G7 = 2  =>  0 pairs (X) / I7 = 2  =>  0 pairs (_)
C6,E6: 2.. / C6 = 2  => 22 pairs (_) / E6 = 2  => 15 pairs (_)
A5,A9: 2.. / A5 = 2  => 19 pairs (_) / A9 = 2  => 16 pairs (_)
G3,G7: 2.. / G3 = 2  =>  0 pairs (*) / G7 = 2  =>  0 pairs (X)
I3,I7: 2.. / I3 = 2  =>  0 pairs (X) / I7 = 2  =>  0 pairs (_)
E2,D3: 4.. / E2 = 4  =>  0 pairs (*) / D3 = 4  =>  0 pairs (X)
I1,H2: 4.. / I1 = 4  =>  0 pairs (*) / H2 = 4  =>  0 pairs (X)
I7,H8: 4.. / I7 = 4  =>  0 pairs (X) / H8 = 4  =>  0 pairs (_)
E2,H2: 4.. / E2 = 4  =>  0 pairs (*) / H2 = 4  =>  0 pairs (X)
B3,D3: 4.. / B3 = 4  =>  0 pairs (*) / D3 = 4  =>  0 pairs (X)
A7,I7: 4.. / A7 = 4  =>  0 pairs (*) / I7 = 4  =>  0 pairs (X)
D3,D6: 4.. / D3 = 4  =>  0 pairs (X) / D6 = 4  =>  0 pairs (_)
H2,H8: 4.. / H2 = 4  =>  0 pairs (X) / H8 = 4  =>  0 pairs (_)
I1,I7: 4.. / I1 = 4  =>  0 pairs (*) / I7 = 4  =>  0 pairs (X)
G3,I3: 5.. / G3 = 5  =>  0 pairs (X) / I3 = 5  =>  0 pairs (_)
D4,D6: 5.. / D4 = 5  =>  0 pairs (*) / D6 = 5  =>  0 pairs (X)
G5,I6: 5.. / G5 = 5  =>  0 pairs (*) / I6 = 5  =>  0 pairs (X)
E8,E9: 5.. / E8 = 5  =>  0 pairs (X) / E9 = 5  => 18 pairs (_)
B4,D4: 5.. / B4 = 5  =>  0 pairs (X) / D4 = 5  =>  0 pairs (_)
C5,G5: 5.. / C5 = 5  =>  0 pairs (X) / G5 = 5  =>  0 pairs (_)
C9,E9: 5.. / C9 = 5  =>  0 pairs (X) / E9 = 5  => 18 pairs (_)
B4,B8: 5.. / B4 = 5  =>  0 pairs (X) / B8 = 5  =>  0 pairs (_)
G3,G5: 5.. / G3 = 5  =>  0 pairs (X) / G5 = 5  =>  0 pairs (_)
I3,I6: 5.. / I3 = 5  =>  0 pairs (*) / I6 = 5  =>  0 pairs (X)
B1,C1: 8.. / B1 = 8  => 16 pairs (_) / C1 = 8  =>  0 pairs (X)
B8,C8: 8.. / B8 = 8  =>  0 pairs (X) / C8 = 8  => 16 pairs (_)
B1,B8: 8.. / B1 = 8  => 16 pairs (_) / B8 = 8  =>  0 pairs (X)
C1,C8: 8.. / C1 = 8  =>  0 pairs (X) / C8 = 8  => 16 pairs (_)
E2,D3: 9.. / E2 = 9  =>  0 pairs (X) / D3 = 9  =>  0 pairs (_)
I1,H2: 9.. / I1 = 9  =>  0 pairs (X) / H2 = 9  =>  0 pairs (_)
G5,I6: 9.. / G5 = 9  =>  0 pairs (X) / I6 = 9  =>  0 pairs (_)
E2,H2: 9.. / E2 = 9  =>  0 pairs (X) / H2 = 9  =>  0 pairs (_)
B3,D3: 9.. / B3 = 9  =>  0 pairs (X) / D3 = 9  =>  0 pairs (_)
B4,D4: 9.. / B4 = 9  =>  0 pairs (*) / D4 = 9  =>  0 pairs (X)
G5,G7: 9.. / G5 = 9  =>  0 pairs (X) / G7 = 9  =>  0 pairs (_)
H2,H8: 9.. / H2 = 9  =>  0 pairs (*) / H8 = 9  =>  0 pairs (X)
* DURATION: 0:01:12.310903  START: 05:57:23.249301  END: 05:58:35.560204 2017-05-04
* CP COUNT: (38)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B3,B4,D3,D4,E2,G3,G5,G7,H2,H8,I1,I3,I6)
* 5..26713.6213.58.77.3.18.6.1.7.86423.3.17..8686...371..76831.5.3..7..6.1.1.6..378
* PAIR B3: 4,9 BLK 1
B1: 4,9,8                                # reduction candidate for 4,9
B1: 4,9 => CTR
* 5.826713.6213.58.77.3.18.6.157986423.3.17.58686.5.3719.7683195238.7..641.1.6..378
B1: 8                                    # 16 pairs
C1: 4,9,8                                # reduction candidate for 4,9
C1: 4,9                                  # 16 pairs
* PAIR B3: 4,9 COL B
B8: 4,9,5,8                              # reduction candidate for 4,9
B8: 4,9 => CTR
* 58.26713.6213.58.77.3.18.6.157986423.3.17.58686.5.3719.768319523.8752641.156.9378
B8: 5,8                                  # 16 pairs
* PAIR E2: 4,9 COL E
E6: 4,9,2                                # reduction candidate for 4,9
E6: 4,9                                  # 22 pairs
E8: 4,9,2,5                              # reduction candidate for 4,9
E8: 4,9                                  # 20 pairs
E9: 4,9,2,5                              # reduction candidate for 4,9
E9: 4,9 => CTR
* 5..26713.6213.58.77.3.18.6.157986423.3.17.58686.523719.768319523..75.641.156..378
E9: 2,5                                  # 15 pairs
* PAIR D3: 4,9 COL D
D6: 4,9,5                                # reduction candidate for 4,9
D6: 4,9 => SOLVED
* 589267134621345897743918265197586423234179586865423719476831952358792641912654378
D6: 5 => CTR
* 5..26713.6213.58.77.3418.6.1.7986423.3.17..8686.5.3719.768319523..7..641.1.6..378
* PAIR I1: 4,9 ROW 1
B1: 4,9,8                                # reduction candidate for 4,9
B1: 4,9 => CTR
* 5.826713.6213.58.77.3.18.6.157986423.3.17.58686.5.3719.7683195238.7..641.1.6..378
B1: 8                                    # 16 pairs
C1: 4,9,8                                # reduction candidate for 4,9
C1: 4,9                                  # 16 pairs
* PAIR I1: 4,9 COL I
I7: 4,9,2                                # reduction candidate for 4,9
I7: 4,9 => CTR
* 5892671346213.58.7743918562197586423.3517.98686.493715.7683125.35872.6.1.14659378
I7: 2 => SOLVED
* 589267134621345897743918265197586423234179586865423719476831952358792641912654378
* PAIR B4: 5,9 BLK 4
C5: 5,9,2,4                              # reduction candidate for 5,9
C5: 5,9                                  # 18 pairs
C6: 5,9,2,4                              # reduction candidate for 5,9
C6: 5,9 => SOLVED
* 589267134621345897743918265197586423234179586865423719476831952358792641912654378
C6: 2,4                                  # 15 pairs
* PAIR B4: 5,9 COL B
B8: 5,9,4,8                              # reduction candidate for 5,9
B8: 5,9 => SOLVED
* 589267134621345897743918265197586423234179586865423719476831952358792641912654378
B8: 4,8 => CTR
* 5..26713.6213.58.77.3.18.6.157986423.3.17.58686.5.3719.768319523..7..641.1.6..378
* PAIR D4: 5,9 BLK 5
D6: 5,9,4                                # reduction candidate for 5,9
D6: 5,9 => CTR
* 5..26713.621395847793418.6.157986423.3.17.58686.5.3719.76831.5.3..7..6.1.1.6..378
D6: 4 => SOLVED
* 589267134621345897743918265197586423234179586865423719476831952358792641912654378
* PAIR G5: 5,9 ROW 5
C5: 5,9,2,4                              # reduction candidate for 5,9
C5: 2,4 => SOLVED
* 589267134621345897743918265197586423234179586865423719476831952358792641912654378
C5: 5,9                                  # 18 pairs
* PAIR I6: 5,9 ROW 6
C6: 5,9,2,4                              # reduction candidate for 5,9
C6: 5,9 => SOLVED
* 589267134621345897743918265197586423234179586865423719476831952358792641912654378
C6: 2,4                                  # 15 pairs
D6: 5,9,4                                # reduction candidate for 5,9
D6: 5,9 => CTR
* 5..26713.621395847793418.6.157986423.3.17.58686.5.3719.76831.5.3..7..6.1.1.6..378
D6: 4 => SOLVED
* 589267134621345897743918265197586423234179586865423719476831952358792641912654378
* PAIR A7: 4,9 BLK 7
B8: 4,9,5,8                              # reduction candidate for 4,9
B8: 4,9 => CTR
* 58.26713.6213.58.77.3.18.6.157986423.3.17.58686.5.3719.768319523.8752641.156.9378
B8: 5,8                                  # 16 pairs
C8: 4,9,2,5,8                            # reduction candidate for 4,9
C8: 4,9 => CTR
* 5.826713.6213.58.77.3.18.6.157986423.3.174586864523719.7683195238975264121564.378
C8: 2,5,8                                # 14 pairs
A9: 4,9,2                                # reduction candidate for 4,9
A9: 4,9                                  # 19 pairs
C9: 4,9,2,5                              # reduction candidate for 4,9
C9: 4,9                                  # 20 pairs
* PAIR A7: 4,9 ROW 7
I7: 4,9,2                                # reduction candidate for 4,9
I7: 4,9 => CTR
* 5892671346213.58.7743918562197586423.3517.98686.493715.7683125.35872.6.1.14659378
I7: 2 => SOLVED
* 589267134621345897743918265197586423234179586865423719476831952358792641912654378
* PAIR A7: 4,9 COL A
A5: 4,9,2                                # reduction candidate for 4,9
A5: 2                                    # 19 pairs
A5: 4,9                                  # 16 pairs
* PAIR G7: 2,9 BLK 9
I7: 2,9,4                                # reduction candidate for 2,9
I7: 2,9 => SOLVED
* 589267134621345897743918265197586423234179586865423719476831952358792641912654378
I7: 4 => CTR
* 5..267139621395847793418.621.7.86423.3.17..8686...3715.768312543..7..691.1.6..378
* PAIR H8: 4,9 BLK 9
I7: 4,9,2                                # reduction candidate for 4,9
I7: 4,9 => CTR
* 5892671346213.58.7743918562197586423.3517.98686.493715.7683125.35872.6.1.14659378
I7: 2 => SOLVED
* 589267134621345897743918265197586423234179586865423719476831952358792641912654378
* PAIR H8: 4,9 ROW 8
B8: 4,9,5,8                              # reduction candidate for 4,9
B8: 4,9 => CTR
* 58.26713.6213.58.77.3.18.6.157986423.3.17.58686.5.3719.768319523.8752641.156.9378
B8: 5,8                                  # 16 pairs
C8: 4,9,2,5,8                            # reduction candidate for 4,9
C8: 4,9 => CTR
* 5.826713.6213.58.77.3.18.6.157986423.3.174586864523719.7683195238975264121564.378
C8: 2,5,8                                # 14 pairs
E8: 4,9,2,5                              # reduction candidate for 4,9
E8: 4,9                                  # 20 pairs
F8: 4,9,2                                # reduction candidate for 4,9
F8: 4,9                                  # 18 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-093-base-pr-000.dot
* REASONING
* DIS # B1: 4,9 => CTR => B1: 8
* DIS # B8: 4,9 => CTR => B8: 5,8
* DIS # E9: 4,9 => CTR => E9: 2,5
* PRF # D6: 4,9 => SOL
* DIS # D6: 5 => CTR => D6: 4,9
* DIS # B1: 4,9 => CTR => B1: 8
* DIS # I7: 4,9 => CTR => I7: 2
* PRF # I7: 2 => SOL
* PRF # C6: 5,9 => SOL
* PRF # B8: 5,9 => SOL
* DIS # B8: 4,8 => CTR => B8: 5,9
* DIS # D6: 5,9 => CTR => D6: 4
* PRF # D6: 4 => SOL
* PRF # C5: 2,4 => SOL
* PRF # C6: 5,9 => SOL
* DIS # D6: 5,9 => CTR => D6: 4
* PRF # D6: 4 => SOL
* DIS # B8: 4,9 => CTR => B8: 5,8
* DIS # C8: 4,9 => CTR => C8: 2,5,8
* DIS # I7: 4,9 => CTR => I7: 2
* PRF # I7: 2 => SOL
* PRF # I7: 2,9 => SOL
* DIS # I7: 4 => CTR => I7: 2,9
* DIS # I7: 4,9 => CTR => I7: 2
* PRF # I7: 2 => SOL
* DIS # B8: 4,9 => CTR => B8: 5,8
* DIS # C8: 4,9 => CTR => C8: 2,5,8
* CNT  27 HDP CHAINS /  49 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B3,B4,D3,D4,E2,G3,G5,G7,H2,H8,I1,I3,I6)
* 5..26713.6213.58.77.3.18.6.1.7.86423.3.17..8686...371..76831.5.3..7..6.1.1.6..378
* PAIR B3: 4,9 BLK 1
B1: 4,9,8                                # reduction candidate for 4,9
B1: 4,9 => CTR
* 5.826713.6213.58.77.3.18.6.157986423.3.17.58686.5.3719.7683195238.7..641.1.6..378
* RESTART
* PAIR B3: 4,9 COL B
B8: 4,9,5                                # reduction candidate for 4,9
B8: 4,9 => CTR
* 58.26713.6213.58.77.3.18.6.157986423.3.17.58686.5.3719.768319523.8752641.156.9378
B8: 5 => SOLVED
* 589267134621345897743918265197586423234179586865423719476831952358792641912654378
* DURATION: 0:00:04.476814  START: 05:59:29.834850  END: 05:59:34.311664 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-093-base-pr-001.dot
* REASONING
* DIS # B1: 4,9 => CTR => B1: 8
* DIS B1: 8 # B8: 4,9 => CTR => B8: 5
* PRF B1: 8 + B8: 5 => SOL
* STA B1: 8 + B8: 5
* CNT   3 HDP CHAINS /   2 HYP OPENED

Header Info

Top 500 Minimum 17 093

solution: 589267134621345897743918265197586423234179586865423719476831952358792641912654378
info: 1570     FNBTWXY  S8.f     32754

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

Solution

position: 589267134621345897743918265197586423234179586865423719476831952358792641912654378 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 # B1: 4,9 => CTR => B1: 8
* INC # B1: 8 => UNS
* INC # C1: 4,9 => UNS
* DIS # B8: 4,9 => CTR => B8: 5,8
* INC # B8: 5,8 => UNS
* INC # E6: 4,9 => UNS
* INC # E8: 4,9 => UNS
* DIS # E9: 4,9 => CTR => E9: 2,5
* INC # E9: 2,5 => UNS
* PRF # D6: 4,9 => SOL
* DIS # D6: 5 => CTR => D6: 4,9
* DIS # B1: 4,9 => CTR => B1: 8
* INC # B1: 8 => UNS
* INC # C1: 4,9 => UNS
* DIS # I7: 4,9 => CTR => I7: 2
* PRF # I7: 2 => SOL
* INC # C5: 5,9 => UNS
* PRF # C6: 5,9 => SOL
* INC # C6: 2,4 => UNS
* PRF # B8: 5,9 => SOL
* DIS # B8: 4,8 => CTR => B8: 5,9
* DIS # D6: 5,9 => CTR => D6: 4
* PRF # D6: 4 => SOL
* INC # C5: 5,9 => UNS
* PRF # C5: 2,4 => SOL
* PRF # C6: 5,9 => SOL
* INC # C6: 2,4 => UNS
* DIS # D6: 5,9 => CTR => D6: 4
* PRF # D6: 4 => SOL
* DIS # B8: 4,9 => CTR => B8: 5,8
* INC # B8: 5,8 => UNS
* DIS # C8: 4,9 => CTR => C8: 2,5,8
* INC # C8: 2,5,8 => UNS
* INC # A9: 4,9 => UNS
* INC # C9: 4,9 => UNS
* DIS # I7: 4,9 => CTR => I7: 2
* PRF # I7: 2 => SOL
* INC # A5: 4,9 => UNS
* INC # A5: 2 => UNS
* PRF # I7: 2,9 => SOL
* DIS # I7: 4 => CTR => I7: 2,9
* DIS # I7: 4,9 => CTR => I7: 2
* PRF # I7: 2 => SOL
* DIS # B8: 4,9 => CTR => B8: 5,8
* INC # B8: 5,8 => UNS
* DIS # C8: 4,9 => CTR => C8: 2,5,8
* INC # C8: 2,5,8 => UNS
* INC # E8: 4,9 => UNS
* INC # F8: 4,9 => UNS
* CNT  49 HDP CHAINS /  49 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # B1: 4,9 => CTR => B1: 8
* DIS B1: 8 # B8: 4,9 => CTR => B8: 5
* PRF B1: 8 + B8: 5 => SOL
* STA B1: 8 + B8: 5
* CNT   3 HDP CHAINS /   2 HYP OPENED