Analysis of xx-top95-032-base.sdk
Contents
Original Sudoku
level: medium
position: ...5...........5.697.....2...48.2...25.1...3..8..3.........4.7..13.5..9..2...31.. initial
Autosolve
position: ...52..4..423..5.6975....2...48.2...25.1...3..8..35.......14.7..13.5..9..2...31.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # A1: 1,8 => SOL * DIS # B4: 9 => CTR => B4: 3,6 * PRF # A1: 1,8 => SOL * PRF # F3: 1,8 => SOL * DIS # F3: 6 => CTR => F3: 1,8 * PRF # A1: 1,8 => SOL * DIS # E5: 7,9 => CTR => E5: 4,6 * DIS # E9: 7,9 => CTR => E9: 6,8 * DIS # F5: 6 => CTR => F5: 7,9 * PRF # E3: 4,6 => SOL * DIS # E3: 8 => CTR => E3: 4,6 * DIS # G5: 7,9 => CTR => G5: 4,6,8 * DIS # G6: 7,9 => CTR => G6: 2,4,6 * DIS # I4: 7,9 => CTR => I4: 1,5 * PRF # I6: 7,9 => SOL * DIS # I3: 3 => CTR => I3: 1,8 * DIS # I3: 3,8 => CTR => I3: 1 * DIS # A6: 1,6 => CTR => A6: 7 * DIS # C9: 6,9 => CTR => C9: 7,8 * CNT 19 HDP CHAINS / 51 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # A1: 1,8 => SOL * STA A1: 1,8 * CNT 1 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...5...........5.697.....2...48.2...25.1...3..8..3.........4.7..13.5..9..2...31.. | initial |
| ...52..4..423..5.6975....2...48.2...25.1...3..8..35.......14.7..13.5..9..2...31.. | autosolve |
| 836521947142379586975648321364892715259167438781435269598214673413756892627983154 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (12) B1: 3,6 A2: 1,8 F1: 1,8 E2: 7,9 F2: 7,9 D3: 4,6 G1: 7,9 I1: 7,9 H2: 1,8 G3: 3,8 H6: 1,6 B7: 6,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F1,F3: 1.. / F1 = 1 => 22 pairs (_) / F3 = 1 => 0 pairs (X) H2,I3: 1.. / H2 = 1 => 0 pairs (X) / I3 = 1 => 22 pairs (_) A2,H2: 1.. / A2 = 1 => 22 pairs (_) / H2 = 1 => 0 pairs (X) F3,I3: 1.. / F3 = 1 => 0 pairs (X) / I3 = 1 => 22 pairs (_) C1,C6: 1.. / C1 = 1 => 0 pairs (X) / C6 = 1 => 26 pairs (_) G6,I6: 2.. / G6 = 2 => 12 pairs (_) / I6 = 2 => 13 pairs (_) D7,D8: 2.. / D7 = 2 => 13 pairs (_) / D8 = 2 => 17 pairs (_) A1,B1: 3.. / A1 = 3 => 13 pairs (_) / B1 = 3 => 18 pairs (_) G3,I3: 3.. / G3 = 3 => 12 pairs (_) / I3 = 3 => 0 pairs (X) A4,B4: 3.. / A4 = 3 => 18 pairs (_) / B4 = 3 => 13 pairs (_) G7,I7: 3.. / G7 = 3 => 0 pairs (X) / I7 = 3 => 12 pairs (_) A1,A4: 3.. / A1 = 3 => 13 pairs (_) / A4 = 3 => 18 pairs (_) B1,B4: 3.. / B1 = 3 => 18 pairs (_) / B4 = 3 => 13 pairs (_) G3,G7: 3.. / G3 = 3 => 12 pairs (_) / G7 = 3 => 0 pairs (X) I3,I7: 3.. / I3 = 3 => 0 pairs (X) / I7 = 3 => 12 pairs (_) D3,E3: 4.. / D3 = 4 => 14 pairs (_) / E3 = 4 => 0 pairs (*) E5,D6: 4.. / E5 = 4 => 14 pairs (_) / D6 = 4 => 0 pairs (*) A8,A9: 4.. / A8 = 4 => 14 pairs (_) / A9 = 4 => 13 pairs (_) A9,I9: 4.. / A9 = 4 => 13 pairs (_) / I9 = 4 => 14 pairs (_) D3,D6: 4.. / D3 = 4 => 14 pairs (_) / D6 = 4 => 0 pairs (*) E3,E5: 4.. / E3 = 4 => 0 pairs (*) / E5 = 4 => 0 pairs (X) H4,I4: 5.. / H4 = 5 => 15 pairs (_) / I4 = 5 => 22 pairs (_) A7,A9: 5.. / A7 = 5 => 12 pairs (_) / A9 = 5 => 0 pairs (X) A7,I7: 5.. / A7 = 5 => 12 pairs (_) / I7 = 5 => 0 pairs (X) H4,H9: 5.. / H4 = 5 => 15 pairs (_) / H9 = 5 => 22 pairs (_) E2,F2: 7.. / E2 = 7 => 12 pairs (_) / F2 = 7 => 13 pairs (_) G1,I1: 7.. / G1 = 7 => 11 pairs (_) / I1 = 7 => 11 pairs (_) G5,I5: 8.. / G5 = 8 => 14 pairs (_) / I5 = 8 => 15 pairs (_) F8,E9: 8.. / F8 = 8 => 0 pairs (X) / E9 = 8 => 0 pairs (_) A2,H2: 8.. / A2 = 8 => 0 pairs (X) / H2 = 8 => 22 pairs (_) E3,E9: 8.. / E3 = 8 => 0 pairs (X) / E9 = 8 => 0 pairs (_) H2,H9: 8.. / H2 = 8 => 22 pairs (_) / H9 = 8 => 0 pairs (X) E2,F2: 9.. / E2 = 9 => 13 pairs (_) / F2 = 9 => 12 pairs (_) G1,I1: 9.. / G1 = 9 => 11 pairs (_) / I1 = 9 => 11 pairs (_) B4,B7: 9.. / B4 = 9 => 0 pairs (X) / B7 = 9 => 14 pairs (_) F2,F5: 9.. / F2 = 9 => 12 pairs (_) / F5 = 9 => 13 pairs (_) * DURATION: 0:01:00.940471 START: 23:28:22.759056 END: 23:29:23.699527 2017-05-03 * CP COUNT: (36) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,B1,B7,D3,E2,F1,F2,G1,G3,H2,H6,I1) * ...52..4..423..5.6975....2...48.2...25.1...3..8..35.......14.7..13.5..9..2...31.. * PAIR B1: 3,6 BLK 1 A1: 3,6,1,8 # reduction candidate for 3,6 A1: 1,8 => SOLVED * 836521947142379586975648321364892715259167438781435269598214673413756892627983154 A1: 3,6 # 14 pairs * PAIR B1: 3,6 COL B B4: 3,6,9 # reduction candidate for 3,6 B4: 9 => CTR * 63.52.947.423..5.6975486321394862715256147839.8.935462569214.7..13.5.69..2.6.31.. B4: 3,6 # 14 pairs * PAIR A2: 1,8 BLK 1 A1: 1,8,3,6 # reduction candidate for 1,8 A1: 1,8 => SOLVED * 836521947142379586975648321364892715259167438781435269598214673413756892627983154 A1: 3,6 # 14 pairs C1: 1,8,6 # reduction candidate for 1,8 C1: 1,8 # 14 pairs * PAIR F1: 1,8 BLK 2 F3: 1,8,6 # reduction candidate for 1,8 F3: 1,8 => SOLVED * 836521947142379586975648321364892715259167438781435269598214673413756892627983154 F3: 6 => CTR * ..8521.4.142379586975486321394862715256147.3.781935.6.569214873413758692827693154 * PAIR F1: 1,8 ROW 1 A1: 1,8,3,6 # reduction candidate for 1,8 A1: 1,8 => SOLVED * 836521947142379586975648321364892715259167438781435269598214673413756892627983154 A1: 3,6 # 14 pairs C1: 1,8,6 # reduction candidate for 1,8 C1: 1,8 # 14 pairs * PAIR E2: 7,9 COL E E4: 7,9,6 # reduction candidate for 7,9 E4: 7,9 # 15 pairs E5: 7,9,4,6 # reduction candidate for 7,9 E5: 7,9 => CTR * .68521.4.1423..586975648321.3486291525.1...3..81435.6.5...14673.13.56.9..2..83154 E5: 4,6 # 13 pairs E9: 7,9,6,8 # reduction candidate for 7,9 E9: 7,9 => CTR * ..8521.4.142379586975486321394862715256147.3.781935.6.569214873413758692827693154 E9: 6,8 # 13 pairs * PAIR F2: 7,9 COL F F5: 7,9,6 # reduction candidate for 7,9 F5: 6 => CTR * ...521.4.142379586975468321..4892.1525.146.3.68.735....9..14.73.13.57.9..2.9831.. F5: 7,9 # 14 pairs * PAIR D3: 4,6 BLK 2 E3: 4,6,8 # reduction candidate for 4,6 E3: 4,6 => SOLVED * 836521947142379586975648321364892715259167438781435269598214673413756892627983154 E3: 8 => CTR * ..8521.4.142379586975486321394862715256147.3.781935.6.569214873413758692827693154 * PAIR D3: 4,6 COL D D6: 4,6,7,9 # reduction candidate for 4,6 D6: 4,6 # 19 pairs D6: 7,9 # 16 pairs * PAIR G1: 7,9 COL G G4: 7,9,6 # reduction candidate for 7,9 G4: 7,9 # 13 pairs G5: 7,9,4,6,8 # reduction candidate for 7,9 G5: 7,9 => CTR * ..1528.4.8423..5.69754...21..48.265.25.14..38.8..35.1.....14.73.13.5..9.42...3165 G5: 4,6,8 # 12 pairs G6: 7,9,2,4,6 # reduction candidate for 7,9 G6: 7,9 => CTR * ...521.4.1423..586975648321..48.2.1525.1...3..814359625...14673.13.56298.2..83154 G6: 2,4,6 # 12 pairs * PAIR I1: 7,9 COL I I4: 7,9,1,5 # reduction candidate for 7,9 I4: 7,9 => CTR * 361528.4.8423..516975..1.2.1348.2.5.25.1...3..8..35.61.9..14.7..13.5..9..2..831.. I4: 1,5 # 13 pairs I5: 7,9,4,8 # reduction candidate for 7,9 I5: 7,9 # 20 pairs I6: 7,9,1,2,4 # reduction candidate for 7,9 I6: 7,9 => SOLVED * 836521947142379586975648321364892715259167438781435269598214673413756892627983154 I6: 1,2,4 # 12 pairs * PAIR H2: 1,8 BLK 3 I3: 1,8,3 # reduction candidate for 1,8 I3: 3 => CTR * ...52..4..423..516975..1823..48.2...25.1...38.8..35.6.....1437..13.5.69..2..8315. I3: 1,8 # 12 pairs * PAIR G3: 3,8 BLK 3 I3: 3,8,1 # reduction candidate for 3,8 I3: 3,8 => CTR * ...528.4.8423..516975..1.2...48.2.5.25.1...3..8..35.6...8.14.7..13.5..9..2...318. I3: 1 # 22 pairs * PAIR G3: 3,8 COL G G7: 3,8,2,6 # reduction candidate for 3,8 G7: 3,8 # 16 pairs G7: 2,6 # 14 pairs * PAIR H6: 1,6 BLK 6 H4: 1,6,5 # reduction candidate for 1,6 H4: 1,6 # 22 pairs H4: 5 # 15 pairs * PAIR H6: 1,6 ROW 6 A6: 1,6,7 # reduction candidate for 1,6 A6: 1,6 => CTR * ..1528.4.8423..516975..1.2...48.2..125.1...3.18..35.6.....14.7..13.5..9..2..8315. A6: 7 # 16 pairs C6: 1,6,7,9 # reduction candidate for 1,6 C6: 1,6 # 20 pairs * PAIR B7: 6,9 BLK 7 C7: 6,9,8 # reduction candidate for 6,9 C7: 6,9 # 21 pairs C9: 6,9,7,8 # reduction candidate for 6,9 C9: 6,9 => CTR * ..1528.4.8423..516975..1.2...48.2..125.1...3.18..35.6.5.8.14.7..13.5..9..2..8315. C9: 7,8 # 14 pairs * PAIR B7: 6,9 ROW 7 D7: 6,9,2 # reduction candidate for 6,9 D7: 6,9 # 17 pairs D7: 2 # 13 pairs * PAIR B7: 6,9 COL B B4: 6,9,3 # reduction candidate for 6,9 B4: 6,9 # 18 pairs B4: 3 # 13 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top95-032-base-pr-000.dot * REASONING * PRF # A1: 1,8 => SOL * DIS # B4: 9 => CTR => B4: 3,6 * PRF # A1: 1,8 => SOL * PRF # F3: 1,8 => SOL * DIS # F3: 6 => CTR => F3: 1,8 * PRF # A1: 1,8 => SOL * DIS # E5: 7,9 => CTR => E5: 4,6 * DIS # E9: 7,9 => CTR => E9: 6,8 * DIS # F5: 6 => CTR => F5: 7,9 * PRF # E3: 4,6 => SOL * DIS # E3: 8 => CTR => E3: 4,6 * DIS # G5: 7,9 => CTR => G5: 4,6,8 * DIS # G6: 7,9 => CTR => G6: 2,4,6 * DIS # I4: 7,9 => CTR => I4: 1,5 * PRF # I6: 7,9 => SOL * DIS # I3: 3 => CTR => I3: 1,8 * DIS # I3: 3,8 => CTR => I3: 1 * DIS # A6: 1,6 => CTR => A6: 7 * DIS # C9: 6,9 => CTR => C9: 7,8 * CNT 19 HDP CHAINS / 51 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,B1,B7,D3,E2,F1,F2,G1,G3,H2,H6,I1) * ...52..4..423..5.6975....2...48.2...25.1...3..8..35.......14.7..13.5..9..2...31.. * PAIR B1: 3,6 BLK 1 A1: 3,6,1,8 # reduction candidate for 3,6 A1: 1,8 => SOLVED * 836521947142379586975648321364892715259167438781435269598214673413756892627983154 * DURATION: 0:00:03.321742 START: 23:30:13.210508 END: 23:30:16.532250 2017-05-03 * SOLUTION FOUND * SAVE PR GRAPH xx-top95-032-base-pr-001.dot * REASONING * PRF # A1: 1,8 => SOL * STA A1: 1,8 * CNT 1 HDP CHAINS / 2 HYP OPENED
Header Info
Top 95 Sudokus 032 [sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt
Solution
position: 836521947142379586975648321364892715259167438781435269598214673413756892627983154 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:
* INC # A1: 3,6 => UNS * PRF # A1: 1,8 => SOL * INC # B4: 3,6 => UNS * DIS # B4: 9 => CTR => B4: 3,6 * PRF # A1: 1,8 => SOL * INC # A1: 3,6 => UNS * INC # C1: 1,8 => UNS * PRF # F3: 1,8 => SOL * DIS # F3: 6 => CTR => F3: 1,8 * PRF # A1: 1,8 => SOL * INC # A1: 3,6 => UNS * INC # C1: 1,8 => UNS * INC # E4: 7,9 => UNS * DIS # E5: 7,9 => CTR => E5: 4,6 * INC # E5: 4,6 => UNS * DIS # E9: 7,9 => CTR => E9: 6,8 * INC # E9: 6,8 => UNS * INC # F5: 7,9 => UNS * DIS # F5: 6 => CTR => F5: 7,9 * PRF # E3: 4,6 => SOL * DIS # E3: 8 => CTR => E3: 4,6 * INC # D6: 4,6 => UNS * INC # D6: 7,9 => UNS * INC # G4: 7,9 => UNS * DIS # G5: 7,9 => CTR => G5: 4,6,8 * INC # G5: 4,6,8 => UNS * DIS # G6: 7,9 => CTR => G6: 2,4,6 * INC # G6: 2,4,6 => UNS * DIS # I4: 7,9 => CTR => I4: 1,5 * INC # I4: 1,5 => UNS * INC # I5: 7,9 => UNS * PRF # I6: 7,9 => SOL * INC # I6: 1,2,4 => UNS * INC # I3: 1,8 => UNS * DIS # I3: 3 => CTR => I3: 1,8 * DIS # I3: 3,8 => CTR => I3: 1 * INC # I3: 1 => UNS * INC # G7: 3,8 => UNS * INC # G7: 2,6 => UNS * INC # H4: 1,6 => UNS * INC # H4: 5 => UNS * DIS # A6: 1,6 => CTR => A6: 7 * INC # A6: 7 => UNS * INC # C6: 1,6 => UNS * INC # C7: 6,9 => UNS * DIS # C9: 6,9 => CTR => C9: 7,8 * INC # C9: 7,8 => UNS * INC # D7: 6,9 => UNS * INC # D7: 2 => UNS * INC # B4: 6,9 => UNS * INC # B4: 3 => UNS * CNT 51 HDP CHAINS / 51 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A1: 3,6 => UNS * PRF # A1: 1,8 => SOL * STA A1: 1,8 * CNT 2 HDP CHAINS / 2 HYP OPENED