Analysis of zz-www.sudokuoftheday.co.uk-20060612-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006
level: medium
position: 3.......4..7..43959...1..7.29..3.........5.8956....2.......74..7...6...8.5...3.6. initial
Autosolve
position: 3....9..4..7..439594531..7.29..3.....73..5.8956....2.......74..7...6...8.5...3.6. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # B2: 2,8 => SOL * DIS # B2: 1 => CTR => B2: 2,8 * DIS # B7: 2,8 => CTR => B7: 1,3 * PRF # C7: 1,9 => SOL * DIS # D2: 2,8 => CTR => D2: 6 * PRF # D2: 6 => SOL * PRF # F3: 2,8 => SOL * DIS # F3: 6 => CTR => F3: 2,8 * PRF # B2: 2,8 => SOL * DIS # B2: 1 => CTR => B2: 2,8 * DIS # E7: 2,8 => CTR => E7: 5,9 * DIS # E9: 2,8 => CTR => E9: 4,9 * DIS # G1: 6,8 => CTR => G1: 1 * PRF # G1: 1 => SOL * DIS # F3: 6,8 => CTR => F3: 2 * PRF # F3: 2 => SOL * DIS # F3: 8 => CTR => F3: 2,6 * DIS # C4: 1,4 => CTR => C4: 8 * PRF # D5: 1,4 => SOL * DIS # A9: 1,4 => CTR => A9: 8 * DIS # D5: 2,4 => CTR => D5: 1,6 * DIS # D4: 1,8 => CTR => D4: 4,6,7 * DIS # F4: 1,8 => CTR => F4: 6 * PRF # F4: 6 => SOL * DIS # D6: 1,8 => CTR => D6: 4,7,9 * DIS # C6: 4 => CTR => C6: 1,8 * PRF # I4: 7 => SOL * DIS # D5: 2,4 => CTR => D5: 1,6 * DIS # G1: 8 => CTR => G1: 1,6 * CNT 29 HDP CHAINS / 57 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # B2: 2,8 => SOL * STA B2: 2,8 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 3.......4..7..43959...1..7.29..3.........5.8956....2.......74..7...6...8.5...3.6. | initial |
| 3....9..4..7..439594531..7.29..3.....73..5.8956....2.......74..7...6...8.5...3.6. | autosolve |
| 386579124127684395945312876298436517473125689561798243619857432734261958852943761 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) B1: 2,8 C1: 2,6 D1: 5,7 E1: 5,7 E2: 2,8 H1: 1,2 G3: 6,8 I3: 2,6 A5: 1,4 E5: 2,4 F6: 1,8 G4: 5,7 G5: 1,6 F8: 1,2 G8: 5,9 G9: 7,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A2,B2: 1.. / A2 = 1 => 0 pairs (*) / B2 = 1 => 0 pairs (X) G1,H1: 1.. / G1 = 1 => 0 pairs (*) / H1 = 1 => 0 pairs (X) G1,G5: 1.. / G1 = 1 => 0 pairs (*) / G5 = 1 => 0 pairs (X) H1,I3: 2.. / H1 = 2 => 0 pairs (*) / I3 = 2 => 0 pairs (X) D5,E5: 2.. / D5 = 2 => 0 pairs (X) / E5 = 2 => 19 pairs (_) F3,I3: 2.. / F3 = 2 => 0 pairs (*) / I3 = 2 => 0 pairs (X) F3,F8: 2.. / F3 = 2 => 0 pairs (*) / F8 = 2 => 0 pairs (X) H6,I6: 3.. / H6 = 3 => 16 pairs (_) / I6 = 3 => 20 pairs (_) B7,B8: 3.. / B7 = 3 => 23 pairs (_) / B8 = 3 => 16 pairs (_) B8,H8: 3.. / B8 = 3 => 16 pairs (_) / H8 = 3 => 23 pairs (_) I6,I7: 3.. / I6 = 3 => 20 pairs (_) / I7 = 3 => 16 pairs (_) H4,H6: 4.. / H4 = 4 => 16 pairs (_) / H6 = 4 => 21 pairs (_) C8,D8: 4.. / C8 = 4 => 26 pairs (_) / D8 = 4 => 16 pairs (_) A5,A9: 4.. / A5 = 4 => 25 pairs (_) / A9 = 4 => 0 pairs (X) D1,E1: 5.. / D1 = 5 => 14 pairs (_) / E1 = 5 => 15 pairs (_) G4,H4: 5.. / G4 = 5 => 15 pairs (_) / H4 = 5 => 21 pairs (_) E1,E7: 5.. / E1 = 5 => 15 pairs (_) / E7 = 5 => 14 pairs (_) G4,G8: 5.. / G4 = 5 => 15 pairs (_) / G8 = 5 => 21 pairs (_) C1,A2: 6.. / C1 = 6 => 0 pairs (*) / A2 = 6 => 0 pairs (X) D2,F3: 6.. / D2 = 6 => 0 pairs (*) / F3 = 6 => 0 pairs (X) I4,G5: 6.. / I4 = 6 => 0 pairs (X) / G5 = 6 => 0 pairs (_) A7,C7: 6.. / A7 = 6 => 0 pairs (*) / C7 = 6 => 0 pairs (X) C1,G1: 6.. / C1 = 6 => 0 pairs (*) / G1 = 6 => 0 pairs (X) A2,D2: 6.. / A2 = 6 => 0 pairs (X) / D2 = 6 => 0 pairs (_) D5,G5: 6.. / D5 = 6 => 0 pairs (X) / G5 = 6 => 0 pairs (_) A2,A7: 6.. / A2 = 6 => 0 pairs (X) / A7 = 6 => 0 pairs (_) C1,C7: 6.. / C1 = 6 => 0 pairs (*) / C7 = 6 => 0 pairs (X) F3,F4: 6.. / F3 = 6 => 0 pairs (X) / F4 = 6 => 0 pairs (_) I3,I4: 6.. / I3 = 6 => 0 pairs (*) / I4 = 6 => 0 pairs (X) D1,E1: 7.. / D1 = 7 => 15 pairs (_) / E1 = 7 => 14 pairs (_) G9,I9: 7.. / G9 = 7 => 15 pairs (_) / I9 = 7 => 21 pairs (_) E1,E6: 7.. / E1 = 7 => 14 pairs (_) / E6 = 7 => 15 pairs (_) G4,G9: 7.. / G4 = 7 => 21 pairs (_) / G9 = 7 => 15 pairs (_) G1,G3: 8.. / G1 = 8 => 0 pairs (X) / G3 = 8 => 18 pairs (_) C4,C6: 8.. / C4 = 8 => 18 pairs (_) / C6 = 8 => 0 pairs (X) B1,G1: 8.. / B1 = 8 => 18 pairs (_) / G1 = 8 => 0 pairs (X) F3,G3: 8.. / F3 = 8 => 0 pairs (X) / G3 = 8 => 18 pairs (_) D6,E6: 9.. / D6 = 9 => 16 pairs (_) / E6 = 9 => 14 pairs (_) G8,G9: 9.. / G8 = 9 => 15 pairs (_) / G9 = 9 => 21 pairs (_) * DURATION: 0:00:43.373571 START: 23:47:07.056513 END: 23:47:50.430084 2019-04-30 * CP COUNT: (39) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,B1,C1,D1,E1,E2,E5,F6,F8,G3,G4,G5,G8,G9,H1,I3) * 3....9..4..7..439594531..7.29..3.....73..5.8956....2.......74..7...6...8.5...3.6. * PAIR B1: 2,8 BLK 1 B2: 2,8,1 # reduction candidate for 2,8 B2: 2,8 => SOLVED * 386579124127684395945312876298436517473125689561798243619857432734261958852943761 B2: 1 => CTR * 326..9.14.17..439594531..7229..3...6.7362518956....2.......74..7...62..8.52..3.6. * PAIR B1: 2,8 COL B B7: 2,8,1,3 # reduction candidate for 2,8 B7: 2,8 => CTR * 326..9.14.17..439594531..7229..3...6.7362518956....2.......74..73..62.58.52..3.6. B7: 1,3 # 18 pairs * PAIR C1: 2,6 COL C C7: 2,6,1,9 # reduction candidate for 2,6 C7: 1,9 => SOLVED * 386579124127684395945312876298436517473125689561798243619857432734261958852943761 C7: 2,6 # 19 pairs * PAIR E2: 2,8 BLK 2 D2: 2,8,6 # reduction candidate for 2,8 D2: 2,8 => CTR * 3....9..4617..439594531687229..3...6.7362518956....2....6..74..7...62..8.52..3.6. D2: 6 => SOLVED * 386579124127684395945312876298436517473125689561798243619857432734261958852943761 F3: 2,8,6 # reduction candidate for 2,8 F3: 2,8 => SOLVED * 386579124127684395945312876298436517473125689561798243619857432734261958852943761 F3: 6 => CTR * 3....9..4..7..439594531687229..3...6.7362518956....2.......74..7...62..8.52..3.6. * PAIR E2: 2,8 ROW 2 B2: 2,8,1 # reduction candidate for 2,8 B2: 2,8 => SOLVED * 386579124127684395945312876298436517473125689561798243619857432734261958852943761 B2: 1 => CTR * 326..9.14.17..439594531..7229..3...6.7362518956....2.......74..7...62..8.52..3.6. * PAIR E2: 2,8 COL E E7: 2,8,5,9 # reduction candidate for 2,8 E7: 2,8 => CTR * 3.6759124.2768439594531287629.136547173.4568956.97.2....9..74..7...6.9.845.89376. E7: 5,9 # 17 pairs E9: 2,8,4,9 # reduction candidate for 2,8 E9: 2,8 => CTR * 3.6..9124.2768439594531287629..36...17324568956....2.......74..7...6...845...3.6. E9: 4,9 # 17 pairs * PAIR H1: 1,2 COL H H7: 1,2,3,5 # reduction candidate for 1,2 H7: 1,2 # 20 pairs H8: 1,2,3,5 # reduction candidate for 1,2 H8: 1,2 # 21 pairs * PAIR G3: 6,8 BLK 3 G1: 6,8,1 # reduction candidate for 6,8 G1: 6,8 => CTR * 326..9814..72.439594531..7229..3...6.7362518956....2.......74..7...62..8.52..3.6. G1: 1 => SOLVED * 386579124127684395945312876298436517473125689561798243619857432734261958852943761 * PAIR G3: 6,8 ROW 3 F3: 6,8,2 # reduction candidate for 6,8 F3: 6,8 => CTR * 326..9814..72.439594531..7229..3...6.7362518956....2.......74..7...62..8.52..3.6. F3: 2 => SOLVED * 386579124127684395945312876298436517473125689561798243619857432734261958852943761 * PAIR I3: 2,6 ROW 3 F3: 2,6,8 # reduction candidate for 2,6 F3: 8 => CTR * 3....9..4..762439594531867229..36....7324518956....2.......74..7...6...8.5...3.6. F3: 2,6 # 18 pairs * PAIR A5: 1,4 BLK 4 C4: 1,4,8 # reduction candidate for 1,4 C4: 1,4 => CTR * 326..9814..72.439594531..7229..3...6.73625189568..12.......742.7...62..8.52..3.6. C4: 8 # 18 pairs C6: 1,4,8 # reduction candidate for 1,4 C6: 1,4 # 18 pairs * PAIR A5: 1,4 ROW 5 D5: 1,4,2,6 # reduction candidate for 1,4 D5: 1,4 => SOLVED * 386579124127684395945312876298436517473125689561798243619857432734261958852943761 D5: 2,6 # 17 pairs * PAIR A5: 1,4 COL A A9: 1,4,8 # reduction candidate for 1,4 A9: 1,4 => CTR * 326..9.14.17..439594531..7229..3...6.7362518956....2.......74..7...62..8152..3.67 A9: 8 # 25 pairs * PAIR E5: 2,4 BLK 5 D5: 2,4,1,6 # reduction candidate for 2,4 D5: 2,4 => CTR * 3.6..9124.2768439594531287629..36...173..568956....2.......74..7...6...8.5...3.6. D5: 1,6 # 25 pairs * PAIR E5: 2,4 COL E E9: 2,4,8,9 # reduction candidate for 2,4 E9: 2,4 # 21 pairs E9: 8,9 # 17 pairs * PAIR F6: 1,8 BLK 5 D4: 1,8,4,6,7 # reduction candidate for 1,8 D4: 1,8 => CTR * 3.6..91248.76.439594531..7.29..36...173..568956....2..6....74..7...6...845...3.6. D4: 4,6,7 # 16 pairs F4: 1,8,6 # reduction candidate for 1,8 F4: 1,8 => CTR * 3....9..4..7..439594531687229..3...6.7362518956....2.......74..7...62..8.52..3.6. F4: 6 => SOLVED * 386579124127684395945312876298436517473125689561798243619857432734261958852943761 D6: 1,8,4,7,9 # reduction candidate for 1,8 D6: 1,8 => CTR * 3.65791248.7..439594531..7.29873.54.173.45689564.9.237....574.373.46.95845...376. D6: 4,7,9 # 16 pairs * PAIR F6: 1,8 ROW 6 C6: 1,8,4 # reduction candidate for 1,8 C6: 4 => CTR * 3.6..91248.7..439594531..7.298.3....173..5689564...2.......74..7..46...845...3.6. C6: 1,8 # 19 pairs * PAIR G5: 1,6 BLK 6 I4: 1,6,7 # reduction candidate for 1,6 I4: 7 => SOLVED * 386579124127684395945312876298436517473125689561798243619857432734261958852943761 I4: 1,6 # 20 pairs * PAIR G5: 1,6 ROW 5 D5: 1,6,2,4 # reduction candidate for 1,6 D5: 2,4 => CTR * 3.6..9124.2768439594531287629..36...173..568956....2.......74..7...6...8.5...3.6. D5: 1,6 # 25 pairs * PAIR G5: 1,6 COL G G1: 1,6,8 # reduction candidate for 1,6 G1: 8 => CTR * 3.6..9814..76.439594531867.29..3.....73..5.8956....2.......74..7...6...8.5...3.6. G1: 1,6 # 18 pairs * PAIR F8: 1,2 BLK 8 D7: 1,2,5,8,9 # reduction candidate for 1,2 D7: 1,2 # 17 pairs D8: 1,2,4,5,9 # reduction candidate for 1,2 D8: 1,2 # 27 pairs D9: 1,2,4,8,9 # reduction candidate for 1,2 D9: 1,2 # 17 pairs * PAIR F8: 1,2 ROW 8 B8: 1,2,3 # reduction candidate for 1,2 B8: 1,2 # 23 pairs C8: 1,2,4,9 # reduction candidate for 1,2 C8: 1,2 # 16 pairs H8: 1,2,3,5 # reduction candidate for 1,2 H8: 1,2 # 21 pairs * PAIR G8: 5,9 ROW 8 D8: 5,9,1,2,4 # reduction candidate for 5,9 D8: 5,9 # 27 pairs D8: 1,2,4 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060612-absurd-base-pr-000.dot * REASONING * PRF # B2: 2,8 => SOL * DIS # B2: 1 => CTR => B2: 2,8 * DIS # B7: 2,8 => CTR => B7: 1,3 * PRF # C7: 1,9 => SOL * DIS # D2: 2,8 => CTR => D2: 6 * PRF # D2: 6 => SOL * PRF # F3: 2,8 => SOL * DIS # F3: 6 => CTR => F3: 2,8 * PRF # B2: 2,8 => SOL * DIS # B2: 1 => CTR => B2: 2,8 * DIS # E7: 2,8 => CTR => E7: 5,9 * DIS # E9: 2,8 => CTR => E9: 4,9 * DIS # G1: 6,8 => CTR => G1: 1 * PRF # G1: 1 => SOL * DIS # F3: 6,8 => CTR => F3: 2 * PRF # F3: 2 => SOL * DIS # F3: 8 => CTR => F3: 2,6 * DIS # C4: 1,4 => CTR => C4: 8 * PRF # D5: 1,4 => SOL * DIS # A9: 1,4 => CTR => A9: 8 * DIS # D5: 2,4 => CTR => D5: 1,6 * DIS # D4: 1,8 => CTR => D4: 4,6,7 * DIS # F4: 1,8 => CTR => F4: 6 * PRF # F4: 6 => SOL * DIS # D6: 1,8 => CTR => D6: 4,7,9 * DIS # C6: 4 => CTR => C6: 1,8 * PRF # I4: 7 => SOL * DIS # D5: 2,4 => CTR => D5: 1,6 * DIS # G1: 8 => CTR => G1: 1,6 * CNT 29 HDP CHAINS / 57 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,B1,C1,D1,E1,E2,E5,F6,F8,G3,G4,G5,G8,G9,H1,I3) * 3....9..4..7..439594531..7.29..3.....73..5.8956....2.......74..7...6...8.5...3.6. * PAIR B1: 2,8 BLK 1 B2: 2,8,1 # reduction candidate for 2,8 B2: 2,8 => SOLVED * 386579124127684395945312876298436517473125689561798243619857432734261958852943761 * DURATION: 0:00:01.845342 START: 23:48:29.971006 END: 23:48:31.816348 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060612-absurd-base-pr-001.dot * REASONING * PRF # B2: 2,8 => SOL * STA B2: 2,8 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006, 20060612, absurd
Solution
position: 386579124127684395945312876298436517473125689561798243619857432734261958852943761 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 # B2: 2,8 => SOL * DIS # B2: 1 => CTR => B2: 2,8 * DIS # B7: 2,8 => CTR => B7: 1,3 * INC # B7: 1,3 => UNS * INC # C7: 2,6 => UNS * PRF # C7: 1,9 => SOL * DIS # D2: 2,8 => CTR => D2: 6 * PRF # D2: 6 => SOL * PRF # F3: 2,8 => SOL * DIS # F3: 6 => CTR => F3: 2,8 * PRF # B2: 2,8 => SOL * DIS # B2: 1 => CTR => B2: 2,8 * DIS # E7: 2,8 => CTR => E7: 5,9 * INC # E7: 5,9 => UNS * DIS # E9: 2,8 => CTR => E9: 4,9 * INC # E9: 4,9 => UNS * INC # H7: 1,2 => UNS * INC # H8: 1,2 => UNS * DIS # G1: 6,8 => CTR => G1: 1 * PRF # G1: 1 => SOL * DIS # F3: 6,8 => CTR => F3: 2 * PRF # F3: 2 => SOL * INC # F3: 2,6 => UNS * DIS # F3: 8 => CTR => F3: 2,6 * DIS # C4: 1,4 => CTR => C4: 8 * INC # C4: 8 => UNS * INC # C6: 1,4 => UNS * PRF # D5: 1,4 => SOL * INC # D5: 2,6 => UNS * DIS # A9: 1,4 => CTR => A9: 8 * INC # A9: 8 => UNS * DIS # D5: 2,4 => CTR => D5: 1,6 * INC # D5: 1,6 => UNS * INC # E9: 2,4 => UNS * INC # E9: 8,9 => UNS * DIS # D4: 1,8 => CTR => D4: 4,6,7 * INC # D4: 4,6,7 => UNS * DIS # F4: 1,8 => CTR => F4: 6 * PRF # F4: 6 => SOL * DIS # D6: 1,8 => CTR => D6: 4,7,9 * INC # D6: 4,7,9 => UNS * INC # C6: 1,8 => UNS * DIS # C6: 4 => CTR => C6: 1,8 * INC # I4: 1,6 => UNS * PRF # I4: 7 => SOL * INC # D5: 1,6 => UNS * DIS # D5: 2,4 => CTR => D5: 1,6 * INC # G1: 1,6 => UNS * DIS # G1: 8 => CTR => G1: 1,6 * INC # D7: 1,2 => UNS * INC # D8: 1,2 => UNS * INC # D9: 1,2 => UNS * INC # B8: 1,2 => UNS * INC # C8: 1,2 => UNS * INC # H8: 1,2 => UNS * INC # D8: 5,9 => UNS * INC # D8: 1,2,4 => UNS * CNT 57 HDP CHAINS / 57 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # B2: 2,8 => SOL * STA B2: 2,8 * CNT 1 HDP CHAINS / 1 HYP OPENED