Analysis of xx-top95-035-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: ..8.9.1...6.5...2......6....3.1.7.5.........9..4...3...5....2...7...3.8.2..7....4 initial

Autosolve

position: ..839.1...6.5...2......6....3.1.7.5.....3...9..4...3...5....2...7...3.8.2..7....4 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A3: 5,7 => CTR => A3: 1,3,9
* DIS # A5: 5,7 => CTR => A5: 1,6,8
* DIS # E3: 2,4 => CTR => E3: 1,7,8
* PRF # I1: 5 => SOL
* DIS # H5: 6,7 => CTR => H5: 1,4
* CNT   5 HDP CHAINS /  21 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 # A3: 5,7 => CTR => A3: 1,3,9
* DIS A3: 1,3,9 # A5: 5,7 => CTR => A5: 1,6,8
* DIS A3: 1,3,9 + A5: 1,6,8 # E3: 2,4 => CTR => E3: 1,7,8
* PRF A3: 1,3,9 + A5: 1,6,8 + E3: 1,7,8 # I1: 5 => SOL
* STA A3: 1,3,9 + A5: 1,6,8 + E3: 1,7,8 + I1: 5
* CNT   4 HDP CHAINS /  21 HYP OPENED

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

Details

Positions

..8.9.1...6.5...2......6....3.1.7.5.........9..4...3...5....2...7...3.8.2..7....4 initial
..839.1...6.5...2......6....3.1.7.5.....3...9..4...3...5....2...7...3.8.2..7....4 autosolve
748392165369514728125876943932147856687235419514689372853461297476923581291758634 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (4)
A1: 5,7
B1: 2,4
F1: 2,4
H1: 6,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
I4,I6: 2.. / I4 = 2  => 10 pairs (_) / I6 = 2  =>  6 pairs (_)
D8,E8: 2.. / D8 = 2  =>  5 pairs (_) / E8 = 2  =>  5 pairs (_)
B1,F1: 2.. / B1 = 2  =>  0 pairs (X) / F1 = 2  =>  3 pairs (_)
C9,H9: 3.. / C9 = 3  =>  6 pairs (_) / H9 = 3  =>  4 pairs (_)
B1,B3: 4.. / B1 = 4  =>  3 pairs (_) / B3 = 4  =>  0 pairs (X)
A7,A8: 4.. / A7 = 4  =>  0 pairs (X) / A8 = 4  =>  4 pairs (_)
B1,F1: 4.. / B1 = 4  =>  3 pairs (_) / F1 = 4  =>  0 pairs (X)
E4,G4: 4.. / E4 = 4  =>  5 pairs (_) / G4 = 4  => 14 pairs (_)
H3,H5: 4.. / H3 = 4  => 14 pairs (_) / H5 = 4  =>  6 pairs (_)
A1,I1: 5.. / A1 = 5  =>  6 pairs (_) / I1 = 5  =>  0 pairs (*)
C3,C5: 5.. / C3 = 5  =>  0 pairs (*) / C5 = 5  =>  0 pairs (X)
H1,I1: 6.. / H1 = 6  =>  5 pairs (_) / I1 = 6  =>  7 pairs (_)
E2,E3: 7.. / E2 = 7  => 17 pairs (_) / E3 = 7  =>  4 pairs (_)
H7,I7: 7.. / H7 = 7  =>  8 pairs (_) / I7 = 7  =>  6 pairs (_)
A7,B9: 8.. / A7 = 8  =>  7 pairs (_) / B9 = 8  =>  0 pairs (X)
A4,C4: 9.. / A4 = 9  =>  5 pairs (_) / C4 = 9  => 12 pairs (_)
D6,F6: 9.. / D6 = 9  =>  4 pairs (_) / F6 = 9  =>  4 pairs (_)
B3,B9: 9.. / B3 = 9  =>  0 pairs (X) / B9 = 9  =>  9 pairs (_)
* DURATION: 0:00:23.559405  START: 23:30:58.286088  END: 23:31:21.845493 2017-05-03
* CP COUNT: (18)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B1,F1,H1)
* ..839.1...6.5...2......6....3.1.7.5.....3...9..4...3...5....2...7...3.8.2..7....4
* PAIR A1: 5,7 BLK 1
A3: 5,7,1,3,9                            # reduction candidate for 5,7
A3: 5,7 => CTR
* ..839.1...6.5...2......6....3.1.7.5.....3...9..4...3...5....2...7...3.8.2..7....4
A3: 1,3,9                                #  4 pairs
C3: 5,7,1,2,3,9                          # reduction candidate for 5,7
C3: 5,7                                  # 15 pairs
* PAIR A1: 5,7 ROW 1
I1: 5,7,6                                # reduction candidate for 5,7
I1: 6                                    #  7 pairs
I1: 5,7                                  #  5 pairs
* PAIR A1: 5,7 COL A
A5: 5,7,1,6,8                            # reduction candidate for 5,7
A5: 5,7 => CTR
* 728394165.6.5..42..45..679.9321.7.565.7632..96.4...37285....2.747...3.812..7....4
A5: 1,6,8                                #  6 pairs
A6: 5,7,1,6,8                            # reduction candidate for 5,7
A6: 5,7                                  #  6 pairs
* PAIR B1: 2,4 BLK 1
B3: 2,4,1,9                              # reduction candidate for 2,4
B3: 2,4                                  # 15 pairs
B3: 1,9                                  # 10 pairs
* PAIR F1: 2,4 BLK 2
D3: 2,4,8                                # reduction candidate for 2,4
D3: 2,4                                  # 16 pairs
E3: 2,4,1,7,8                            # reduction candidate for 2,4
E3: 2,4 => CTR
* 5283941..36957142814.826.93.3.14785....63.7497.49..3..85.4.92..47.2.398.29.7..6.4
E3: 1,7,8                                #  4 pairs
* PAIR F1: 2,4 COL F
F5: 2,4,5,8                              # reduction candidate for 2,4
F5: 2,4                                  #  6 pairs
F5: 5,8                                  #  5 pairs
* PAIR H1: 6,7 BLK 3
I1: 6,7,5                                # reduction candidate for 6,7
I1: 5 => SOLVED
* 748392165369514728125876943932147856687235419514689372853461297476923581291758634
I1: 6,7                                  #  6 pairs
* PAIR H1: 6,7 COL H
H5: 6,7,1,4                              # reduction candidate for 6,7
H5: 6,7 => CTR
* 548392176.6.5..8233..8.694563918745218523476972465.31.853...2974769235812917..634
H5: 1,4                                  #  5 pairs
H6: 6,7,1                                # reduction candidate for 6,7
H6: 6,7                                  #  9 pairs
H7: 6,7,1,3,9                            # reduction candidate for 6,7
H7: 6,7                                  #  9 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top95-035-base-pr-000.dot
* REASONING
* DIS # A3: 5,7 => CTR => A3: 1,3,9
* DIS # A5: 5,7 => CTR => A5: 1,6,8
* DIS # E3: 2,4 => CTR => E3: 1,7,8
* PRF # I1: 5 => SOL
* DIS # H5: 6,7 => CTR => H5: 1,4
* CNT   5 HDP CHAINS /  21 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B1,F1,H1)
* ..839.1...6.5...2......6....3.1.7.5.....3...9..4...3...5....2...7...3.8.2..7....4
* PAIR A1: 5,7 BLK 1
A3: 5,7,1,3,9                            # reduction candidate for 5,7
A3: 5,7 => CTR
* ..839.1...6.5...2......6....3.1.7.5.....3...9..4...3...5....2...7...3.8.2..7....4
C3: 5,7,1,2,3,9                          # reduction candidate for 5,7
C3: 5,7                                  # 15 pairs
* RESTART
* PAIR A1: 5,7 BLK 1
C3: 5,7,1,2,3,9                          # reduction candidate for 5,7
C3: 5,7                                  # 15 pairs
C3: 1,2,3,9                              #  7 pairs
* PAIR A1: 5,7 ROW 1
I1: 5,7,6                                # reduction candidate for 5,7
I1: 6                                    #  7 pairs
I1: 5,7                                  #  5 pairs
* PAIR A1: 5,7 COL A
A5: 5,7,1,6,8                            # reduction candidate for 5,7
A5: 5,7 => CTR
* 728394165.6.5..42..45..679.9321.7.565.7632..96.4...37285....2.747...3.812..7....4
* RESTART
* PAIR RESTART
* PAIR A1: 5,7 BLK 1
C3: 5,7,1,2,3,9                          # reduction candidate for 5,7
C3: 5,7                                  # 16 pairs
C3: 1,2,3,9                              #  7 pairs
* PAIR A1: 5,7 ROW 1
I1: 5,7,6                                # reduction candidate for 5,7
I1: 6                                    #  7 pairs
I1: 5,7                                  #  7 pairs
* PAIR B1: 2,4 BLK 1
B3: 2,4,1,9                              # reduction candidate for 2,4
B3: 2,4                                  # 16 pairs
B3: 1,9                                  # 10 pairs
* PAIR F1: 2,4 BLK 2
D3: 2,4,8                                # reduction candidate for 2,4
D3: 2,4                                  # 20 pairs
E3: 2,4,1,7,8                            # reduction candidate for 2,4
E3: 2,4 => CTR
* ..83941...6.571428.4.826....32147.5661.23..49.84...3.285.4.92..47.6.3.8.29.785..4
* RESTART
* PAIR F1: 2,4 BLK 2
D3: 2,4,8                                # reduction candidate for 2,4
D3: 2,4                                  # 20 pairs
D3: 8                                    #  6 pairs
* PAIR F1: 2,4 COL F
F5: 2,4,5,8                              # reduction candidate for 2,4
F5: 2,4                                  #  8 pairs
F5: 5,8                                  #  7 pairs
* PAIR H1: 6,7 BLK 3
I1: 6,7,5                                # reduction candidate for 6,7
I1: 5 => SOLVED
* 748392165369514728125876943932147856687235419514689372853461297476923581291758634
* DURATION: 0:00:17.542048  START: 23:31:37.692018  END: 23:31:55.234066 2017-05-03
* SOLUTION FOUND
* SAVE PR GRAPH xx-top95-035-base-pr-001.dot
* REASONING
* DIS # A3: 5,7 => CTR => A3: 1,3,9
* DIS A3: 1,3,9 # A5: 5,7 => CTR => A5: 1,6,8
* DIS A3: 1,3,9 + A5: 1,6,8 # E3: 2,4 => CTR => E3: 1,7,8
* PRF A3: 1,3,9 + A5: 1,6,8 + E3: 1,7,8 # I1: 5 => SOL
* STA A3: 1,3,9 + A5: 1,6,8 + E3: 1,7,8 + I1: 5
* CNT   4 HDP CHAINS /  21 HYP OPENED

Header Info

Top 95 Sudokus 035
[sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt

Solution

position: 748392165369514728125876943932147856687235419514689372853461297476923581291758634 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 # A3: 5,7 => CTR => A3: 1,3,9
* INC # A3: 1,3,9 => UNS
* INC # C3: 5,7 => UNS
* INC # I1: 5,7 => UNS
* INC # I1: 6 => UNS
* DIS # A5: 5,7 => CTR => A5: 1,6,8
* INC # A5: 1,6,8 => UNS
* INC # A6: 5,7 => UNS
* INC # B3: 2,4 => UNS
* INC # B3: 1,9 => UNS
* INC # D3: 2,4 => UNS
* DIS # E3: 2,4 => CTR => E3: 1,7,8
* INC # E3: 1,7,8 => UNS
* INC # F5: 2,4 => UNS
* INC # F5: 5,8 => UNS
* INC # I1: 6,7 => UNS
* PRF # I1: 5 => SOL
* DIS # H5: 6,7 => CTR => H5: 1,4
* INC # H5: 1,4 => UNS
* INC # H6: 6,7 => UNS
* INC # H7: 6,7 => UNS
* CNT  21 HDP CHAINS /  21 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # A3: 5,7 => CTR => A3: 1,3,9
* INC A3: 1,3,9 # C3: 5,7 => UNS
* INC A3: 1,3,9 # C3: 5,7 => UNS
* INC A3: 1,3,9 # C3: 1,2,3,9 => UNS
* INC A3: 1,3,9 # I1: 5,7 => UNS
* INC A3: 1,3,9 # I1: 6 => UNS
* DIS A3: 1,3,9 # A5: 5,7 => CTR => A5: 1,6,8
* INC A3: 1,3,9 + A5: 1,6,8 # C3: 5,7 => UNS
* INC A3: 1,3,9 + A5: 1,6,8 # C3: 1,2,3,9 => UNS
* INC A3: 1,3,9 + A5: 1,6,8 # I1: 5,7 => UNS
* INC A3: 1,3,9 + A5: 1,6,8 # I1: 6 => UNS
* INC A3: 1,3,9 + A5: 1,6,8 # B3: 2,4 => UNS
* INC A3: 1,3,9 + A5: 1,6,8 # B3: 1,9 => UNS
* INC A3: 1,3,9 + A5: 1,6,8 # D3: 2,4 => UNS
* DIS A3: 1,3,9 + A5: 1,6,8 # E3: 2,4 => CTR => E3: 1,7,8
* INC A3: 1,3,9 + A5: 1,6,8 + E3: 1,7,8 # D3: 2,4 => UNS
* INC A3: 1,3,9 + A5: 1,6,8 + E3: 1,7,8 # D3: 8 => UNS
* INC A3: 1,3,9 + A5: 1,6,8 + E3: 1,7,8 # F5: 2,4 => UNS
* INC A3: 1,3,9 + A5: 1,6,8 + E3: 1,7,8 # F5: 5,8 => UNS
* INC A3: 1,3,9 + A5: 1,6,8 + E3: 1,7,8 # I1: 6,7 => UNS
* PRF A3: 1,3,9 + A5: 1,6,8 + E3: 1,7,8 # I1: 5 => SOL
* STA A3: 1,3,9 + A5: 1,6,8 + E3: 1,7,8 + I1: 5
* CNT  21 HDP CHAINS /  21 HYP OPENED