Analysis of zz-www.sudokuoftheday.co.uk-20190221-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Feb&YEAR=2019
level: medium
position: .3..4......6278....2.....761...9....2..6....3.....2519.....5.4..93............7.2 initial
Autosolve
position: .3..46.....6278..4.2.....761...9...72.96..48336..82519..2..5.4..93.2..........7.2 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A1: 5,9 => CTR => A1: 7,8 * DIS # A3: 5,9 => CTR => A3: 4,8 * PRF # C1: 1,5 => SOL * DIS # B9: 1,5 => CTR => B9: 4,8 * DIS # D4: 3,4 => CTR => D4: 5 * PRF # D4: 5 => SOL * DIS # E3: 3 => CTR => E3: 1,5 * DIS # F8: 4 => CTR => F8: 1,7 * DIS # G2: 1 => CTR => G2: 3,9 * DIS # B7: 1,8 => CTR => B7: 7 * PRF # B7: 7 => SOL * PRF # D7: 1,8 => SOL * CNT 12 HDP CHAINS / 37 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A1: 5,9 => CTR => A1: 7,8 * DIS A1: 7,8 # A3: 5,9 => CTR => A3: 4,8 * PRF A1: 7,8 + A3: 4,8 # C1: 1,5 => SOL * STA A1: 7,8 + A3: 4,8 + C1: 1,5 * CNT 3 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .3..4......6278....2.....761...9....2..6....3.....2519.....5.4..93............7.2 | initial |
| .3..46.....6278..4.2.....761...9...72.96..48336..82519..2..5.4..93.2..........7.2 | autosolve |
| 735146298916278354824359176148593627259617483367482519672835941493721865581964732 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) A2: 5,9 B2: 1,5 B5: 5,7 C6: 4,7 F4: 3,4 E5: 1,5 F5: 1,7 D6: 4,7 G4: 2,6 H4: 2,6 G7: 3,9 I7: 1,8 H8: 5,6 H9: 3,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E5,F5: 1.. / E5 = 1 => 0 pairs (*) / F5 = 1 => 0 pairs (X) B2,G2: 1.. / B2 = 1 => 17 pairs (_) / G2 = 1 => 0 pairs (X) G1,H1: 2.. / G1 = 2 => 14 pairs (_) / H1 = 2 => 14 pairs (_) G4,H4: 2.. / G4 = 2 => 14 pairs (_) / H4 = 2 => 14 pairs (_) G1,G4: 2.. / G1 = 2 => 14 pairs (_) / G4 = 2 => 14 pairs (_) H1,H4: 2.. / H1 = 2 => 14 pairs (_) / H4 = 2 => 14 pairs (_) G2,H2: 3.. / G2 = 3 => 16 pairs (_) / H2 = 3 => 26 pairs (_) D4,F4: 3.. / D4 = 3 => 0 pairs (X) / F4 = 3 => 15 pairs (_) G7,H9: 3.. / G7 = 3 => 26 pairs (_) / H9 = 3 => 16 pairs (_) G2,G7: 3.. / G2 = 3 => 16 pairs (_) / G7 = 3 => 26 pairs (_) H2,H9: 3.. / H2 = 3 => 26 pairs (_) / H9 = 3 => 16 pairs (_) A3,C3: 4.. / A3 = 4 => 15 pairs (_) / C3 = 4 => 0 pairs (*) C6,D6: 4.. / C6 = 4 => 0 pairs (X) / D6 = 4 => 0 pairs (_) B4,B9: 4.. / B4 = 4 => 0 pairs (*) / B9 = 4 => 0 pairs (X) D4,E5: 5.. / D4 = 5 => 0 pairs (*) / E5 = 5 => 0 pairs (X) H8,I8: 5.. / H8 = 5 => 14 pairs (_) / I8 = 5 => 14 pairs (_) B5,E5: 5.. / B5 = 5 => 0 pairs (*) / E5 = 5 => 0 pairs (X) E3,E5: 5.. / E3 = 5 => 0 pairs (*) / E5 = 5 => 0 pairs (X) I1,I8: 5.. / I1 = 5 => 14 pairs (_) / I8 = 5 => 14 pairs (_) G4,H4: 6.. / G4 = 6 => 14 pairs (_) / H4 = 6 => 14 pairs (_) A7,A9: 6.. / A7 = 6 => 15 pairs (_) / A9 = 6 => 0 pairs (X) E7,E9: 6.. / E7 = 6 => 0 pairs (X) / E9 = 6 => 15 pairs (_) G8,H8: 6.. / G8 = 6 => 14 pairs (_) / H8 = 6 => 14 pairs (_) A7,E7: 6.. / A7 = 6 => 15 pairs (_) / E7 = 6 => 0 pairs (X) A9,E9: 6.. / A9 = 6 => 0 pairs (X) / E9 = 6 => 15 pairs (_) G4,G8: 6.. / G4 = 6 => 14 pairs (_) / G8 = 6 => 14 pairs (_) H4,H8: 6.. / H4 = 6 => 14 pairs (_) / H8 = 6 => 14 pairs (_) A1,C1: 7.. / A1 = 7 => 0 pairs (*) / C1 = 7 => 0 pairs (X) B5,C6: 7.. / B5 = 7 => 0 pairs (X) / C6 = 7 => 0 pairs (_) F5,D6: 7.. / F5 = 7 => 0 pairs (*) / D6 = 7 => 0 pairs (X) B5,F5: 7.. / B5 = 7 => 0 pairs (X) / F5 = 7 => 0 pairs (_) C6,D6: 7.. / C6 = 7 => 0 pairs (*) / D6 = 7 => 0 pairs (X) B5,B7: 7.. / B5 = 7 => 0 pairs (X) / B7 = 7 => 0 pairs (_) C1,C6: 7.. / C1 = 7 => 0 pairs (X) / C6 = 7 => 0 pairs (_) F5,F8: 7.. / F5 = 7 => 0 pairs (*) / F8 = 7 => 0 pairs (X) B4,C4: 8.. / B4 = 8 => 17 pairs (_) / C4 = 8 => 21 pairs (_) G7,H9: 9.. / G7 = 9 => 16 pairs (_) / H9 = 9 => 26 pairs (_) D7,G7: 9.. / D7 = 9 => 26 pairs (_) / G7 = 9 => 16 pairs (_) F3,F9: 9.. / F3 = 9 => 16 pairs (_) / F9 = 9 => 17 pairs (_) * DURATION: 0:00:55.325425 START: 03:53:43.302611 END: 03:54:38.628036 2019-05-01 * CP COUNT: (39) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,B2,B5,C6,D6,E5,F4,F5,G4,G7,H4,H8,H9,I7) * .3..46.....6278..4.2.....761...9...72.96..48336..82519..2..5.4..93.2..........7.2 * PAIR A2: 5,9 BLK 1 A1: 5,9,7,8 # reduction candidate for 5,9 A1: 5,9 => CTR * .37.46.....6278..442.....761...9...72796514833647825197.2.65.4..93.27...64581.7.2 A1: 7,8 # 15 pairs A3: 5,9,4,8 # reduction candidate for 5,9 A3: 5,9 => CTR * .3..46.....6278..4.24...876148593..7259617483367482519.72..5.4..9372.....81...7.2 A3: 4,8 # 15 pairs * PAIR A2: 5,9 ROW 2 H2: 5,9,3 # reduction candidate for 5,9 H2: 3 # 26 pairs H2: 5,9 # 16 pairs * PAIR B2: 1,5 BLK 1 C1: 1,5,7,8 # reduction candidate for 1,5 C1: 1,5 => SOLVED * 735146298916278354824359176148593627259617483367482519672835941493721865581964732 C1: 7,8 # 15 pairs C3: 1,5,4,8 # reduction candidate for 1,5 C3: 1,5 # 25 pairs * PAIR B2: 1,5 COL B B9: 1,5,4,8 # reduction candidate for 1,5 B9: 1,5 => CTR * .3..46.....6278..4.2.....76148593..7259617483367482519..2..5.4..93.2..........7.2 B9: 4,8 # 15 pairs * PAIR F4: 3,4 BLK 5 D4: 3,4,5 # reduction candidate for 3,4 D4: 3,4 => CTR * .37.46.....6278..442153987615..9...72796514833647825197.2.65.4..93.27...64581.7.2 D4: 5 => SOLVED * 735146298916278354824359176148593627259617483367482519672835941493721865581964732 * PAIR F4: 3,4 COL F F9: 3,4,1,9 # reduction candidate for 3,4 F9: 3,4 # 18 pairs F9: 1,9 # 15 pairs * PAIR E5: 1,5 COL E E3: 1,5,3 # reduction candidate for 1,5 E3: 3 => CTR * .37.46.....6278.3442153987615..9...72796514833647825197.2.65.4..93.27...645813792 E3: 1,5 # 17 pairs * PAIR F5: 1,7 COL F F8: 1,7,4 # reduction candidate for 1,7 F8: 4 => CTR * 735.46821.16278..4.2..5..76184593..7259617483367482519672.35948893724....41869732 F8: 1,7 # 16 pairs * PAIR D6: 4,7 COL D D8: 4,7,1,8 # reduction candidate for 4,7 D8: 4,7 # 17 pairs D8: 1,8 # 17 pairs * PAIR G7: 3,9 ROW 7 D7: 3,9,1,7,8 # reduction candidate for 3,9 D7: 3,9 # 17 pairs D7: 1,7,8 # 16 pairs * PAIR G7: 3,9 COL G G2: 3,9,1 # reduction candidate for 3,9 G2: 1 => CTR * .3..46...956278134.2...98761.5.9...72796514833647825197.296534..93.2765.......792 G2: 3,9 # 17 pairs * PAIR I7: 1,8 BLK 9 G8: 1,8,6 # reduction candidate for 1,8 G8: 1,8 # 14 pairs I8: 1,8,5 # reduction candidate for 1,8 I8: 1,8 # 14 pairs * PAIR I7: 1,8 ROW 7 B7: 1,8,7 # reduction candidate for 1,8 B7: 1,8 => CTR * .37.46.....6278..442153987615..9...72796514833647825197.2.65.4..93.27...64581.7.2 B7: 7 => SOLVED * 735146298916278354824359176148593627259617483367482519672835941493721865581964732 D7: 1,8,3,7,9 # reduction candidate for 1,8 D7: 1,8 => SOLVED * 735146298916278354824359176148593627259617483367482519672835941493721865581964732 D7: 3,7,9 # 14 pairs * PAIR I7: 1,8 COL I I1: 1,8,5 # reduction candidate for 1,8 I1: 5 # 14 pairs I1: 1,8 # 14 pairs * PAIR H9: 3,9 ROW 9 D9: 3,9,1,4,8 # reduction candidate for 3,9 D9: 3,9 # 24 pairs F9: 3,9,1,4 # reduction candidate for 3,9 F9: 3,9 # 16 pairs * PAIR H9: 3,9 COL H H2: 3,9,5 # reduction candidate for 3,9 H2: 3,9 # 17 pairs H2: 5 # 14 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190221-absurd-base-pr-000.dot * REASONING * DIS # A1: 5,9 => CTR => A1: 7,8 * DIS # A3: 5,9 => CTR => A3: 4,8 * PRF # C1: 1,5 => SOL * DIS # B9: 1,5 => CTR => B9: 4,8 * DIS # D4: 3,4 => CTR => D4: 5 * PRF # D4: 5 => SOL * DIS # E3: 3 => CTR => E3: 1,5 * DIS # F8: 4 => CTR => F8: 1,7 * DIS # G2: 1 => CTR => G2: 3,9 * DIS # B7: 1,8 => CTR => B7: 7 * PRF # B7: 7 => SOL * PRF # D7: 1,8 => SOL * CNT 12 HDP CHAINS / 37 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,B2,B5,C6,D6,E5,F4,F5,G4,G7,H4,H8,H9,I7) * .3..46.....6278..4.2.....761...9...72.96..48336..82519..2..5.4..93.2..........7.2 * PAIR A2: 5,9 BLK 1 A1: 5,9,7,8 # reduction candidate for 5,9 A1: 5,9 => CTR * .37.46.....6278..442.....761...9...72796514833647825197.2.65.4..93.27...64581.7.2 A3: 5,9,4,8 # reduction candidate for 5,9 A3: 5,9 => CTR * .3..46.....6278..4.24...876148593..7259617483367482519.72..5.4..9372.....81...7.2 * PAIR B2: 1,5 BLK 1 C1: 1,5,7,8 # reduction candidate for 1,5 C1: 1,5 => SOLVED * 735146298916278354824359176148593627259617483367482519672835941493721865581964732 * DURATION: 0:00:04.023906 START: 03:55:06.812050 END: 03:55:10.835956 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190221-absurd-base-pr-001.dot * REASONING * DIS # A1: 5,9 => CTR => A1: 7,8 * DIS A1: 7,8 # A3: 5,9 => CTR => A3: 4,8 * PRF A1: 7,8 + A3: 4,8 # C1: 1,5 => SOL * STA A1: 7,8 + A3: 4,8 + C1: 1,5 * CNT 3 HDP CHAINS / 3 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Feb&YEAR=2019, 20190221, absurd
Solution
position: 735146298916278354824359176148593627259617483367482519672835941493721865581964732 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:
* DIS # A1: 5,9 => CTR => A1: 7,8 * INC # A1: 7,8 => UNS * DIS # A3: 5,9 => CTR => A3: 4,8 * INC # A3: 4,8 => UNS * INC # H2: 5,9 => UNS * INC # H2: 3 => UNS * PRF # C1: 1,5 => SOL * INC # C1: 7,8 => UNS * INC # C3: 1,5 => UNS * DIS # B9: 1,5 => CTR => B9: 4,8 * INC # B9: 4,8 => UNS * DIS # D4: 3,4 => CTR => D4: 5 * PRF # D4: 5 => SOL * INC # F9: 3,4 => UNS * INC # F9: 1,9 => UNS * INC # E3: 1,5 => UNS * DIS # E3: 3 => CTR => E3: 1,5 * INC # F8: 1,7 => UNS * DIS # F8: 4 => CTR => F8: 1,7 * INC # D8: 4,7 => UNS * INC # D8: 1,8 => UNS * INC # D7: 3,9 => UNS * INC # D7: 1,7,8 => UNS * INC # G2: 3,9 => UNS * DIS # G2: 1 => CTR => G2: 3,9 * INC # G8: 1,8 => UNS * INC # I8: 1,8 => UNS * DIS # B7: 1,8 => CTR => B7: 7 * PRF # B7: 7 => SOL * PRF # D7: 1,8 => SOL * INC # D7: 3,7,9 => UNS * INC # I1: 1,8 => UNS * INC # I1: 5 => UNS * INC # D9: 3,9 => UNS * INC # F9: 3,9 => UNS * INC # H2: 3,9 => UNS * INC # H2: 5 => UNS * CNT 37 HDP CHAINS / 37 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A1: 5,9 => CTR => A1: 7,8 * DIS A1: 7,8 # A3: 5,9 => CTR => A3: 4,8 * PRF A1: 7,8 + A3: 4,8 # C1: 1,5 => SOL * STA A1: 7,8 + A3: 4,8 + C1: 1,5 * CNT 3 HDP CHAINS / 3 HYP OPENED