Analysis of xx-top95-046-base.sdk
Contents
Original Sudoku
level: medium
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
Pair Reduction Variants
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
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
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