Analysis of zz-www.sudokuoftheday.co.uk-20190428-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019
level: medium
position: .1.3..5....7.9..62.3.8...7...3.5...9.....41.....7...3....5..64.85.....2.6........ initial
Autosolve
position: .1.3..598.87.9.362.3.8..471.43.5.7897.8.34156.6.7..2343..5..64785....92367...3815 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # C3: 2,6 => SOL * DIS # C3: 5,9 => CTR => C3: 2,6 * DIS # E1: 2,6 => CTR => E1: 4,7 * DIS # E1: 2,6 => CTR => E1: 4,7 * DIS # F3: 2,6 => CTR => F3: 5 * PRF # C3: 2,6 => SOL * DIS # C3: 5,9 => CTR => C3: 2,6 * DIS # A6: 5,9 => CTR => A6: 1 * PRF # A6: 1 => SOL * DIS # C3: 5,9 => CTR => C3: 2,6 * PRF # C3: 2,6 => SOL * DIS # D9: 4 => CTR => D9: 2,9 * DIS # E7: 2 => CTR => E7: 1,8 * PRF # C7: 2,9 => SOL * PRF # E8: 1,4 => SOL * DIS # D9: 2,4 => CTR => D9: 9 * PRF # D9: 9 => SOL * PRF # C9: 2,4 => SOL * DIS # C9: 9 => CTR => C9: 2,4 * CNT 19 HDP CHAINS / 38 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # C3: 2,6 => SOL * STA C3: 2,6 * CNT 1 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .1.3..5....7.9..62.3.8...7...3.5...9.....41.....7...3....5..64.85.....2.6........ | initial |
| .1.3..598.87.9.362.3.8..471.43.5.7897.8.34156.6.7..2343..5..64785....92367...3815 | autosolve |
| 416372598587491362932865471243156789798234156165789234329518647851647923674923815 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) A1: 2,4 C1: 2,6 A2: 4,5 D2: 1,4 F2: 1,5 E3: 2,6 A4: 1,2 B5: 2,9 C6: 5,9 D5: 2,9 E6: 1,8 F6: 8,9 B7: 2,9 C8: 1,4 F7: 8,9 E9: 2,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D2,F2: 1.. / D2 = 1 => 0 pairs (X) / F2 = 1 => 18 pairs (_) A4,A6: 1.. / A4 = 1 => 0 pairs (X) / A6 = 1 => 0 pairs (_) C7,C8: 1.. / C7 = 1 => 18 pairs (_) / C8 = 1 => 0 pairs (*) A6,E6: 1.. / A6 = 1 => 0 pairs (*) / E6 = 1 => 0 pairs (X) C7,E7: 1.. / C7 = 1 => 18 pairs (_) / E7 = 1 => 0 pairs (*) A4,B5: 2.. / A4 = 2 => 0 pairs (*) / B5 = 2 => 0 pairs (X) B5,D5: 2.. / B5 = 2 => 0 pairs (X) / D5 = 2 => 0 pairs (_) B5,B7: 2.. / B5 = 2 => 0 pairs (X) / B7 = 2 => 0 pairs (_) A1,A2: 4.. / A1 = 4 => 18 pairs (_) / A2 = 4 => 0 pairs (X) E1,D2: 4.. / E1 = 4 => 0 pairs (X) / D2 = 4 => 18 pairs (_) C8,C9: 4.. / C8 = 4 => 18 pairs (_) / C9 = 4 => 0 pairs (*) A1,E1: 4.. / A1 = 4 => 18 pairs (_) / E1 = 4 => 0 pairs (X) A2,D2: 4.. / A2 = 4 => 0 pairs (X) / D2 = 4 => 18 pairs (_) F2,F3: 5.. / F2 = 5 => 0 pairs (X) / F3 = 5 => 18 pairs (_) A6,C6: 5.. / A6 = 5 => 0 pairs (X) / C6 = 5 => 16 pairs (_) A2,F2: 5.. / A2 = 5 => 18 pairs (_) / F2 = 5 => 0 pairs (X) C3,C6: 5.. / C3 = 5 => 0 pairs (X) / C6 = 5 => 16 pairs (_) C1,C3: 6.. / C1 = 6 => 16 pairs (_) / C3 = 6 => 0 pairs (X) D4,F4: 6.. / D4 = 6 => 23 pairs (_) / F4 = 6 => 20 pairs (_) D4,D8: 6.. / D4 = 6 => 23 pairs (_) / D8 = 6 => 20 pairs (_) E1,F1: 7.. / E1 = 7 => 18 pairs (_) / F1 = 7 => 20 pairs (_) E8,F8: 7.. / E8 = 7 => 20 pairs (_) / F8 = 7 => 18 pairs (_) E1,E8: 7.. / E1 = 7 => 18 pairs (_) / E8 = 7 => 20 pairs (_) F1,F8: 7.. / F1 = 7 => 20 pairs (_) / F8 = 7 => 18 pairs (_) E6,F6: 8.. / E6 = 8 => 0 pairs (*) / F6 = 8 => 0 pairs (X) E7,F7: 8.. / E7 = 8 => 0 pairs (X) / F7 = 8 => 0 pairs (_) E6,E7: 8.. / E6 = 8 => 0 pairs (*) / E7 = 8 => 0 pairs (X) F6,F7: 8.. / F6 = 8 => 0 pairs (X) / F7 = 8 => 0 pairs (_) A3,C3: 9.. / A3 = 9 => 17 pairs (_) / C3 = 9 => 0 pairs (X) D5,F6: 9.. / D5 = 9 => 0 pairs (X) / F6 = 9 => 0 pairs (_) F7,D9: 9.. / F7 = 9 => 0 pairs (X) / D9 = 9 => 0 pairs (_) B5,D5: 9.. / B5 = 9 => 0 pairs (*) / D5 = 9 => 0 pairs (X) C9,D9: 9.. / C9 = 9 => 0 pairs (X) / D9 = 9 => 0 pairs (_) A3,A6: 9.. / A3 = 9 => 17 pairs (_) / A6 = 9 => 0 pairs (X) B5,B7: 9.. / B5 = 9 => 0 pairs (*) / B7 = 9 => 0 pairs (X) D5,D9: 9.. / D5 = 9 => 0 pairs (X) / D9 = 9 => 0 pairs (_) F6,F7: 9.. / F6 = 9 => 0 pairs (*) / F7 = 9 => 0 pairs (X) * DURATION: 0:00:45.550153 START: 05:39:34.065838 END: 05:40:19.615991 2019-05-01 * CP COUNT: (37) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A2,A4,B5,B7,C1,C6,C8,D2,D5,E3,E6,E9,F2,F6,F7) * .1.3..598.87.9.362.3.8..471.43.5.7897.8.34156.6.7..2343..5..64785....92367...3815 * PAIR A1: 2,4 ROW 1 E1: 2,4,6,7 # reduction candidate for 2,4 E1: 6,7 # 19 pairs E1: 2,4 # 19 pairs * PAIR C1: 2,6 BLK 1 C3: 2,6,5,9 # reduction candidate for 2,6 C3: 2,6 => SOLVED * 416372598587491362932865471243156789798234156165789234329518647851647923674923815 C3: 5,9 => CTR * .163..598.87.9.362.3.8..471143.5.789728934156.6.71823439.5..64785....92367...3815 * PAIR C1: 2,6 ROW 1 E1: 2,6,4,7 # reduction candidate for 2,6 E1: 2,6 => CTR * 41.3.7598587491362.3.8.5471.43.52789728934156.657.823439.5..64785....92367...3815 E1: 4,7 # 17 pairs F1: 2,6,7 # reduction candidate for 2,6 F1: 2,6 # 18 pairs * PAIR D2: 1,4 COL D D8: 1,4,6 # reduction candidate for 1,4 D8: 1,4 # 23 pairs D8: 6 # 20 pairs * PAIR E3: 2,6 BLK 2 E1: 2,6,4,7 # reduction candidate for 2,6 E1: 2,6 => CTR * 41.3.7598587491362.3.8.5471.43.52789728934156.657.823439.5..64785....92367...3815 E1: 4,7 # 17 pairs F1: 2,6,7 # reduction candidate for 2,6 F1: 2,6 # 18 pairs F3: 2,6,5 # reduction candidate for 2,6 F3: 2,6 => CTR * 216347598487195362.3.8..471143.5.789728934156.6.71823439.5..64785....92367...3815 F3: 5 # 18 pairs * PAIR E3: 2,6 ROW 3 C3: 2,6,5,9 # reduction candidate for 2,6 C3: 2,6 => SOLVED * 416372598587491362932865471243156789798234156165789234329518647851647923674923815 C3: 5,9 => CTR * .163..598.87.9.362.3.8..471143.5.789728934156.6.71823439.5..64785....92367...3815 * PAIR A4: 1,2 ROW 4 D4: 1,2,6 # reduction candidate for 1,2 D4: 1,2 # 20 pairs F4: 1,2,6 # reduction candidate for 1,2 F4: 1,2 # 23 pairs * PAIR C6: 5,9 BLK 4 A6: 5,9,1 # reduction candidate for 5,9 A6: 5,9 => CTR * .1.3..598.87.9.362.3.8..471143.5.789728934156.6.71823439.5..64785....92367...3815 A6: 1 => SOLVED * 416372598587491362932865471243156789798234156165789234329518647851647923674923815 * PAIR C6: 5,9 COL C C3: 5,9,2,6 # reduction candidate for 5,9 C3: 5,9 => CTR * .163..598.87.9.362.3.8..471143.5.789728934156.6.71823439.5..64785....92367...3815 C3: 2,6 => SOLVED * 416372598587491362932865471243156789798234156165789234329518647851647923674923815 * PAIR D5: 2,9 COL D D9: 2,9,4 # reduction candidate for 2,9 D9: 4 => CTR * .1.3..598.87.9.362.3.8..471.43.5.7897.8934156.6.7.823439.5..64785....92367...3815 D9: 2,9 # 18 pairs * PAIR E6: 1,8 COL E E7: 1,8,2 # reduction candidate for 1,8 E7: 2 => CTR * .1.3..598.87.9.362.3.8..471.43.5.7897.8.34156.6.7892343.1528647854.17923672943815 E7: 1,8 # 18 pairs * PAIR B7: 2,9 BLK 7 C7: 2,9,1 # reduction candidate for 2,9 C7: 2,9 => SOLVED * 416372598587491362932865471243156789798234156165789234329518647851647923674923815 C7: 1 # 18 pairs C9: 2,9,4 # reduction candidate for 2,9 C9: 2,9 # 18 pairs * PAIR C8: 1,4 ROW 8 D8: 1,4,6 # reduction candidate for 1,4 D8: 1,4 # 23 pairs E8: 1,4,6,7 # reduction candidate for 1,4 E8: 1,4 => SOLVED * 416372598587491362932865471243156789798234156165789234329518647851647923674923815 E8: 6,7 # 19 pairs * PAIR E9: 2,4 BLK 8 D9: 2,4,9 # reduction candidate for 2,4 D9: 2,4 => CTR * .1.3..598.87.9.362.3.8..471.43.5.7897.8934156.6.7.823439.5..64785....92367...3815 D9: 9 => SOLVED * 416372598587491362932865471243156789798234156165789234329518647851647923674923815 * PAIR E9: 2,4 ROW 9 C9: 2,4,9 # reduction candidate for 2,4 C9: 2,4 => SOLVED * 416372598587491362932865471243156789798234156165789234329518647851647923674923815 C9: 9 => CTR * .1.3..598.87.9.36293.8..471.43.5.789798234156.657.923432158.647854...923679..3815 * PAIR E9: 2,4 COL E E1: 2,4,6,7 # reduction candidate for 2,4 E1: 6,7 # 19 pairs E1: 2,4 # 19 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190428-absurd-base-pr-000.dot * REASONING * PRF # C3: 2,6 => SOL * DIS # C3: 5,9 => CTR => C3: 2,6 * DIS # E1: 2,6 => CTR => E1: 4,7 * DIS # E1: 2,6 => CTR => E1: 4,7 * DIS # F3: 2,6 => CTR => F3: 5 * PRF # C3: 2,6 => SOL * DIS # C3: 5,9 => CTR => C3: 2,6 * DIS # A6: 5,9 => CTR => A6: 1 * PRF # A6: 1 => SOL * DIS # C3: 5,9 => CTR => C3: 2,6 * PRF # C3: 2,6 => SOL * DIS # D9: 4 => CTR => D9: 2,9 * DIS # E7: 2 => CTR => E7: 1,8 * PRF # C7: 2,9 => SOL * PRF # E8: 1,4 => SOL * DIS # D9: 2,4 => CTR => D9: 9 * PRF # D9: 9 => SOL * PRF # C9: 2,4 => SOL * DIS # C9: 9 => CTR => C9: 2,4 * CNT 19 HDP CHAINS / 38 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A2,A4,B5,B7,C1,C6,C8,D2,D5,E3,E6,E9,F2,F6,F7) * .1.3..598.87.9.362.3.8..471.43.5.7897.8.34156.6.7..2343..5..64785....92367...3815 * PAIR A1: 2,4 ROW 1 E1: 2,4,6,7 # reduction candidate for 2,4 E1: 6,7 # 19 pairs E1: 2,4 # 19 pairs * PAIR C1: 2,6 BLK 1 C3: 2,6,5,9 # reduction candidate for 2,6 C3: 2,6 => SOLVED * 416372598587491362932865471243156789798234156165789234329518647851647923674923815 * DURATION: 0:00:02.942974 START: 05:40:46.470804 END: 05:40:49.413778 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190428-absurd-base-pr-001.dot * REASONING * PRF # C3: 2,6 => SOL * STA C3: 2,6 * CNT 1 HDP CHAINS / 3 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019, 20190428, absurd
Solution
position: 416372598587491362932865471243156789798234156165789234329518647851647923674923815 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 # E1: 2,4 => UNS * INC # E1: 6,7 => UNS * PRF # C3: 2,6 => SOL * DIS # C3: 5,9 => CTR => C3: 2,6 * DIS # E1: 2,6 => CTR => E1: 4,7 * INC # E1: 4,7 => UNS * INC # F1: 2,6 => UNS * INC # D8: 1,4 => UNS * INC # D8: 6 => UNS * DIS # E1: 2,6 => CTR => E1: 4,7 * INC # E1: 4,7 => UNS * INC # F1: 2,6 => UNS * DIS # F3: 2,6 => CTR => F3: 5 * INC # F3: 5 => UNS * PRF # C3: 2,6 => SOL * DIS # C3: 5,9 => CTR => C3: 2,6 * INC # D4: 1,2 => UNS * INC # F4: 1,2 => UNS * DIS # A6: 5,9 => CTR => A6: 1 * PRF # A6: 1 => SOL * DIS # C3: 5,9 => CTR => C3: 2,6 * PRF # C3: 2,6 => SOL * INC # D9: 2,9 => UNS * DIS # D9: 4 => CTR => D9: 2,9 * INC # E7: 1,8 => UNS * DIS # E7: 2 => CTR => E7: 1,8 * PRF # C7: 2,9 => SOL * INC # C7: 1 => UNS * INC # C9: 2,9 => UNS * INC # D8: 1,4 => UNS * PRF # E8: 1,4 => SOL * INC # E8: 6,7 => UNS * DIS # D9: 2,4 => CTR => D9: 9 * PRF # D9: 9 => SOL * PRF # C9: 2,4 => SOL * DIS # C9: 9 => CTR => C9: 2,4 * INC # E1: 2,4 => UNS * INC # E1: 6,7 => UNS * CNT 38 HDP CHAINS / 38 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # E1: 2,4 => UNS * INC # E1: 6,7 => UNS * PRF # C3: 2,6 => SOL * STA C3: 2,6 * CNT 3 HDP CHAINS / 3 HYP OPENED