Analysis of zz-www.sudokuoftheday.co.uk-20060712-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006
level: medium
position: 64.5.........1.....25..9.6..8.7...96...3.....91..2...73...6..2..54.........15..48 initial
Autosolve
position: 64.5......3..1.....25..9.6.58.741.964..39....91..2.4.73...6..2..54...6..2..15..48 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A3: 1 => CTR => A3: 7,8 * DIS # F2: 7,8 => CTR => F2: 2,4,6 * DIS # C1: 8,9 => CTR => C1: 1 * PRF # D2: 4,8 => SOL * DIS # F2: 4,8 => CTR => F2: 2,6,7 * DIS # D7: 4,8 => CTR => D7: 9 * DIS # C5: 2 => CTR => C5: 6,7 * DIS # B9: 6,7 => CTR => B9: 9 * DIS # B9: 6 => CTR => B9: 7,9 * DIS # G7: 7,9 => CTR => G7: 1,5 * DIS # C1: 9 => CTR => C1: 1,8 * DIS # B9: 6,7 => CTR => B9: 9 * DIS # C5: 2 => CTR => C5: 6,7 * DIS # G9: 9 => CTR => G9: 3,7 * CNT 14 HDP CHAINS / 44 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A3: 1 => CTR => A3: 7,8 * DIS A3: 7,8 # F2: 7,8 => CTR => F2: 2,4,6 * PRF A3: 7,8 + F2: 2,4,6 # D2: 4,8 => SOL * STA A3: 7,8 + F2: 2,4,6 + D2: 4,8 * CNT 3 HDP CHAINS / 8 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 64.5.........1.....25..9.6..8.7...96...3.....91..2...73...6..2..54.........15..48 | initial |
| 64.5......3..1.....25..9.6.58.741.964..39....91..2.4.73...6..2..54...6..2..15..48 | autosolve |
| 641572983839416275725839164582741396467395812913628457378964521154287639296153748 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) A2: 7,8 C2: 8,9 D3: 4,8 C4: 2,3 B5: 6,7 C6: 3,6 D6: 6,8 G4: 2,3 B7: 7,9 C7: 1,8 A8: 1,8 C9: 6,7 F9: 3,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C1,A3: 1.. / C1 = 1 => 18 pairs (_) / A3 = 1 => 0 pairs (X) C7,A8: 1.. / C7 = 1 => 0 pairs (X) / A8 = 1 => 18 pairs (_) A3,A8: 1.. / A3 = 1 => 0 pairs (X) / A8 = 1 => 18 pairs (_) C1,C7: 1.. / C1 = 1 => 18 pairs (_) / C7 = 1 => 0 pairs (X) C4,C5: 2.. / C4 = 2 => 14 pairs (_) / C5 = 2 => 0 pairs (X) D8,F8: 2.. / D8 = 2 => 14 pairs (_) / F8 = 2 => 0 pairs (X) C4,G4: 2.. / C4 = 2 => 14 pairs (_) / G4 = 2 => 0 pairs (X) D2,D8: 2.. / D2 = 2 => 0 pairs (X) / D8 = 2 => 14 pairs (_) C4,C6: 3.. / C4 = 3 => 0 pairs (X) / C6 = 3 => 14 pairs (_) G4,H6: 3.. / G4 = 3 => 14 pairs (_) / H6 = 3 => 0 pairs (X) C4,G4: 3.. / C4 = 3 => 0 pairs (X) / G4 = 3 => 14 pairs (_) C6,H6: 3.. / C6 = 3 => 14 pairs (_) / H6 = 3 => 0 pairs (X) F9,G9: 3.. / F9 = 3 => 14 pairs (_) / G9 = 3 => 0 pairs (X) I2,I3: 4.. / I2 = 4 => 14 pairs (_) / I3 = 4 => 0 pairs (*) D7,F7: 4.. / D7 = 4 => 0 pairs (X) / F7 = 4 => 14 pairs (_) D3,I3: 4.. / D3 = 4 => 14 pairs (_) / I3 = 4 => 0 pairs (*) F2,F7: 4.. / F2 = 4 => 0 pairs (X) / F7 = 4 => 14 pairs (_) F5,F6: 5.. / F5 = 5 => 17 pairs (_) / F6 = 5 => 15 pairs (_) G7,I7: 5.. / G7 = 5 => 14 pairs (_) / I7 = 5 => 14 pairs (_) F6,H6: 5.. / F6 = 5 => 15 pairs (_) / H6 = 5 => 17 pairs (_) D2,F2: 6.. / D2 = 6 => 0 pairs (X) / F2 = 6 => 19 pairs (_) B9,C9: 6.. / B9 = 6 => 0 pairs (X) / C9 = 6 => 12 pairs (_) B5,B9: 6.. / B5 = 6 => 12 pairs (_) / B9 = 6 => 0 pairs (X) D2,D6: 6.. / D2 = 6 => 0 pairs (X) / D6 = 6 => 19 pairs (_) A2,A3: 7.. / A2 = 7 => 14 pairs (_) / A3 = 7 => 18 pairs (_) B5,C5: 7.. / B5 = 7 => 0 pairs (X) / C5 = 7 => 12 pairs (_) C5,C9: 7.. / C5 = 7 => 12 pairs (_) / C9 = 7 => 0 pairs (X) C7,A8: 8.. / C7 = 8 => 18 pairs (_) / A8 = 8 => 0 pairs (X) C1,C2: 9.. / C1 = 9 => 0 pairs (X) / C2 = 9 => 13 pairs (_) B7,B9: 9.. / B7 = 9 => 0 pairs (X) / B9 = 9 => 12 pairs (_) D7,D8: 9.. / D7 = 9 => 14 pairs (_) / D8 = 9 => 0 pairs (X) D8,I8: 9.. / D8 = 9 => 0 pairs (X) / I8 = 9 => 14 pairs (_) B9,G9: 9.. / B9 = 9 => 12 pairs (_) / G9 = 9 => 0 pairs (X) * DURATION: 0:00:37.677887 START: 00:37:57.927225 END: 00:38:35.605112 2019-05-01 * CP COUNT: (33) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A8,B5,B7,C2,C4,C6,C7,C9,D3,D6,F9,G4) * 64.5......3..1.....25..9.6.58.741.964..39....91..2.4.73...6..2..54...6..2..15..48 * PAIR A2: 7,8 BLK 1 A3: 7,8,1 # reduction candidate for 7,8 A3: 1 => CTR * 64.537...73.216..41254897635827413964..39....91362.4.7371864.2.85497263129.153.48 A3: 7,8 # 18 pairs * PAIR A2: 7,8 ROW 2 F2: 7,8,2,4,6 # reduction candidate for 7,8 F2: 7,8 => CTR * 64.5.2....3.61.254.254.9.6.5827413964..39....91.82.4.73..964.2..542..6.929615..48 F2: 2,4,6 # 13 pairs G2: 7,8,2,5,9 # reduction candidate for 7,8 G2: 7,8 # 18 pairs H2: 7,8,5 # reduction candidate for 7,8 H2: 7,8 # 16 pairs * PAIR C2: 8,9 BLK 1 C1: 8,9,1 # reduction candidate for 8,9 C1: 8,9 => CTR * 64.537...73.216..41254897635827413964..39....91362.4.7371864.2.85497263129.153.48 C1: 1 # 18 pairs * PAIR C2: 8,9 ROW 2 G2: 8,9,2,5,7 # reduction candidate for 8,9 G2: 8,9 # 18 pairs G2: 2,5,7 # 13 pairs * PAIR D3: 4,8 BLK 2 D2: 4,8,2,6 # reduction candidate for 4,8 D2: 4,8 => SOLVED * 641572983839416275725839164582741396467395812913628457378964521154287639296153748 D2: 2,6 # 14 pairs F2: 4,8,2,6,7 # reduction candidate for 4,8 F2: 4,8 => CTR * 64.5.2....3.618.7..254.9.6.58.741.96467395...91382645737.964.2..542..6.929615..48 F2: 2,6,7 # 14 pairs * PAIR D3: 4,8 COL D D7: 4,8,9 # reduction candidate for 4,8 D7: 4,8 => CTR * 64.537...73.216..41254897635827413964..39....91362.4.7371864.2.85497263129.153.48 D7: 9 # 14 pairs * PAIR B5: 6,7 BLK 4 C5: 6,7,2 # reduction candidate for 6,7 C5: 2 => CTR * 64.5......3..1.....25..9.6.58.741.96472396...91682543739.46..2..54...6..2..15..48 C5: 6,7 # 14 pairs * PAIR B5: 6,7 COL B B9: 6,7,9 # reduction candidate for 6,7 B9: 6,7 => CTR * 64.5......3.216..4.254.9.6.58.741.964..39....91.62.4.739.8647258549726..2..153948 B9: 9 # 12 pairs * PAIR D6: 6,8 BLK 5 F5: 6,8,5 # reduction candidate for 6,8 F5: 6,8 # 15 pairs F6: 6,8,5 # reduction candidate for 6,8 F6: 6,8 # 17 pairs * PAIR D6: 6,8 COL D D2: 6,8,2,4 # reduction candidate for 6,8 D2: 2,4 # 20 pairs D2: 6,8 # 15 pairs * PAIR G4: 2,3 COL G G1: 2,3,1,7,8,9 # reduction candidate for 2,3 G1: 2,3 # 16 pairs G1: 1,7,8,9 # 13 pairs * PAIR B7: 7,9 BLK 7 B9: 7,9,6 # reduction candidate for 7,9 B9: 6 => CTR * 64.5......3.216..4.254.9.6.58.741.9647639....91362.4.739.8647258549726..267153948 B9: 7,9 # 12 pairs * PAIR B7: 7,9 ROW 7 G7: 7,9,1,5 # reduction candidate for 7,9 G7: 7,9 => CTR * 6485..219739216..41254897635827413964..39.1.291362.4.73718649258549.26.12..15..48 G7: 1,5 # 14 pairs * PAIR C7: 1,8 COL C C1: 1,8,9 # reduction candidate for 1,8 C1: 9 => CTR * 6495.....738.1..541254.9.6358.741.964..398.1.91.6254873.1864.2.8549.26312..153.48 C1: 1,8 # 13 pairs * PAIR A8: 1,8 COL A A3: 1,8,7 # reduction candidate for 1,8 A3: 7 # 18 pairs A3: 1,8 # 14 pairs * PAIR C9: 6,7 BLK 7 B9: 6,7,9 # reduction candidate for 6,7 B9: 6,7 => CTR * 64.5......3.216..4.254.9.6.58.741.964..39....91.62.4.739.8647258549726..2..153948 B9: 9 # 12 pairs * PAIR C9: 6,7 COL C C5: 6,7,2 # reduction candidate for 6,7 C5: 2 => CTR * 64.5......3..1.....25..9.6.58.741.96472396...91682543739.46..2..54...6..2..15..48 C5: 6,7 # 14 pairs * PAIR F9: 3,7 BLK 8 E8: 3,7,8 # reduction candidate for 3,7 E8: 3,7 # 17 pairs F8: 3,7,2,8 # reduction candidate for 3,7 F8: 3,7 # 15 pairs * PAIR F9: 3,7 ROW 9 G9: 3,7,9 # reduction candidate for 3,7 G9: 9 => CTR * 64.5......3.216..4.254.9.6.58.741.964..39....91.62.4.739.8647258549726..2..153948 G9: 3,7 # 12 pairs * PAIR F9: 3,7 COL F F1: 3,7,2,8 # reduction candidate for 3,7 F1: 3,7 # 19 pairs F1: 2,8 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060712-absurd-base-pr-000.dot * REASONING * DIS # A3: 1 => CTR => A3: 7,8 * DIS # F2: 7,8 => CTR => F2: 2,4,6 * DIS # C1: 8,9 => CTR => C1: 1 * PRF # D2: 4,8 => SOL * DIS # F2: 4,8 => CTR => F2: 2,6,7 * DIS # D7: 4,8 => CTR => D7: 9 * DIS # C5: 2 => CTR => C5: 6,7 * DIS # B9: 6,7 => CTR => B9: 9 * DIS # B9: 6 => CTR => B9: 7,9 * DIS # G7: 7,9 => CTR => G7: 1,5 * DIS # C1: 9 => CTR => C1: 1,8 * DIS # B9: 6,7 => CTR => B9: 9 * DIS # C5: 2 => CTR => C5: 6,7 * DIS # G9: 9 => CTR => G9: 3,7 * CNT 14 HDP CHAINS / 44 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A8,B5,B7,C2,C4,C6,C7,C9,D3,D6,F9,G4) * 64.5......3..1.....25..9.6.58.741.964..39....91..2.4.73...6..2..54...6..2..15..48 * PAIR A2: 7,8 BLK 1 A3: 7,8,1 # reduction candidate for 7,8 A3: 1 => CTR * 64.537...73.216..41254897635827413964..39....91362.4.7371864.2.85497263129.153.48 * PAIR A2: 7,8 ROW 2 F2: 7,8,2,4,6 # reduction candidate for 7,8 F2: 7,8 => CTR * 6415.29.3.3961.254.25439.615827413964..39..1.91.82.4.73.8964.2.1542..6.929615..48 G2: 7,8,2,5 # reduction candidate for 7,8 G2: 7,8 # 22 pairs H2: 7,8,5 # reduction candidate for 7,8 H2: 7,8 # 26 pairs * PAIR RESTART * PAIR A2: 7,8 ROW 2 G2: 7,8,2,5 # reduction candidate for 7,8 G2: 7,8 # 22 pairs H2: 7,8,5 # reduction candidate for 7,8 H2: 7,8 # 26 pairs * PAIR D3: 4,8 BLK 2 D2: 4,8,2,6 # reduction candidate for 4,8 D2: 4,8 => SOLVED * 641572983839416275725839164582741396467395812913628457378964521154287639296153748 * DURATION: 0:00:06.928404 START: 00:39:01.982624 END: 00:39:08.911028 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060712-absurd-base-pr-001.dot * REASONING * DIS # A3: 1 => CTR => A3: 7,8 * DIS A3: 7,8 # F2: 7,8 => CTR => F2: 2,4,6 * PRF A3: 7,8 + F2: 2,4,6 # D2: 4,8 => SOL * STA A3: 7,8 + F2: 2,4,6 + D2: 4,8 * CNT 3 HDP CHAINS / 8 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006, 20060712, absurd
Solution
position: 641572983839416275725839164582741396467395812913628457378964521154287639296153748 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 # A3: 7,8 => UNS * DIS # A3: 1 => CTR => A3: 7,8 * DIS # F2: 7,8 => CTR => F2: 2,4,6 * INC # F2: 2,4,6 => UNS * INC # G2: 7,8 => UNS * INC # H2: 7,8 => UNS * DIS # C1: 8,9 => CTR => C1: 1 * INC # C1: 1 => UNS * INC # G2: 8,9 => UNS * INC # G2: 2,5,7 => UNS * PRF # D2: 4,8 => SOL * INC # D2: 2,6 => UNS * DIS # F2: 4,8 => CTR => F2: 2,6,7 * INC # F2: 2,6,7 => UNS * DIS # D7: 4,8 => CTR => D7: 9 * INC # D7: 9 => UNS * INC # C5: 6,7 => UNS * DIS # C5: 2 => CTR => C5: 6,7 * DIS # B9: 6,7 => CTR => B9: 9 * INC # B9: 9 => UNS * INC # F5: 6,8 => UNS * INC # F6: 6,8 => UNS * INC # D2: 6,8 => UNS * INC # D2: 2,4 => UNS * INC # G1: 2,3 => UNS * INC # G1: 1,7,8,9 => UNS * INC # B9: 7,9 => UNS * DIS # B9: 6 => CTR => B9: 7,9 * DIS # G7: 7,9 => CTR => G7: 1,5 * INC # G7: 1,5 => UNS * INC # C1: 1,8 => UNS * DIS # C1: 9 => CTR => C1: 1,8 * INC # A3: 1,8 => UNS * INC # A3: 7 => UNS * DIS # B9: 6,7 => CTR => B9: 9 * INC # B9: 9 => UNS * INC # C5: 6,7 => UNS * DIS # C5: 2 => CTR => C5: 6,7 * INC # E8: 3,7 => UNS * INC # F8: 3,7 => UNS * INC # G9: 3,7 => UNS * DIS # G9: 9 => CTR => G9: 3,7 * INC # F1: 3,7 => UNS * INC # F1: 2,8 => UNS * CNT 44 HDP CHAINS / 44 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A3: 7,8 => UNS * DIS # A3: 1 => CTR => A3: 7,8 * DIS A3: 7,8 # F2: 7,8 => CTR => F2: 2,4,6 * INC A3: 7,8 + F2: 2,4,6 # G2: 7,8 => UNS * INC A3: 7,8 + F2: 2,4,6 # H2: 7,8 => UNS * INC A3: 7,8 + F2: 2,4,6 # G2: 7,8 => UNS * INC A3: 7,8 + F2: 2,4,6 # H2: 7,8 => UNS * PRF A3: 7,8 + F2: 2,4,6 # D2: 4,8 => SOL * STA A3: 7,8 + F2: 2,4,6 + D2: 4,8 * CNT 8 HDP CHAINS / 8 HYP OPENED