Analysis of zz-www.sudokuoftheday.co.uk-20060613-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: .....2.4..8971....7....392.16.3........2..5.........968..5.92.35.7.2............. initial
Autosolve
position: ...9.2.4.289714..57....392.16.39...2...2..5.........968..5.92.3537.2...9....3..5. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C1: 1 => CTR => C1: 3,6 * DIS # D8: 6,8 => CTR => D8: 1,4 * DIS # I9: 1,8 => CTR => I9: 4,7 * DIS # C5: 3,4 => CTR => C5: 8 * DIS # C6: 3,4 => CTR => C6: 2,5,8 * DIS # G4: 7,8 => CTR => G4: 4 * DIS # H5: 7,8 => CTR => H5: 1,3 * PRF # G6: 7,8 => SOL * PRF # C9: 1,4 => SOL * CNT 9 HDP CHAINS / 35 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C1: 1 => CTR => C1: 3,6 * DIS C1: 3,6 # D8: 6,8 => CTR => D8: 1,4 * DIS C1: 3,6 + D8: 1,4 # I9: 1,8 => CTR => I9: 4,7 * DIS C1: 3,6 + D8: 1,4 + I9: 4,7 # C5: 3,4 => CTR => C5: 8 * DIS C1: 3,6 + D8: 1,4 + I9: 4,7 + C5: 8 # C6: 3,4 => CTR => C6: 2,5 * DIS C1: 3,6 + D8: 1,4 + I9: 4,7 + C5: 8 + C6: 2,5 # A5: 9 => CTR => A5: 3,4 * DIS C1: 3,6 + D8: 1,4 + I9: 4,7 + C5: 8 + C6: 2,5 + A5: 3,4 # C7: 1,4 => CTR => C7: 6 * PRF C1: 3,6 + D8: 1,4 + I9: 4,7 + C5: 8 + C6: 2,5 + A5: 3,4 + C7: 6 => SOL * STA C1: 3,6 + D8: 1,4 + I9: 4,7 + C5: 8 + C6: 2,5 + A5: 3,4 + C7: 6 * CNT 8 HDP CHAINS / 30 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .....2.4..8971....7....392.16.3........2..5.........968..5.92.35.7.2............. | initial |
| ...9.2.4.289714..57....392.16.39...2...2..5.........968..5.92.3537.2...9....3..5. | autosolve |
| 653982147289714365714653928165398472498267531372145896846579213537421689921836754 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (12) A1: 3,6 B1: 1,5 D3: 6,8 G2: 3,6 H2: 3,6 I3: 1,8 B5: 7,9 A6: 3,4 B6: 2,7 H4: 7,8 B7: 1,4 B9: 2,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B6,C6: 2.. / B6 = 2 => 11 pairs (_) / C6 = 2 => 18 pairs (_) B9,C9: 2.. / B9 = 2 => 18 pairs (_) / C9 = 2 => 11 pairs (_) B6,B9: 2.. / B6 = 2 => 11 pairs (_) / B9 = 2 => 18 pairs (_) C6,C9: 2.. / C6 = 2 => 18 pairs (_) / C9 = 2 => 11 pairs (_) A1,C1: 3.. / A1 = 3 => 0 pairs (X) / C1 = 3 => 15 pairs (_) G2,H2: 3.. / G2 = 3 => 14 pairs (_) / H2 = 3 => 21 pairs (_) H5,G6: 3.. / H5 = 3 => 14 pairs (_) / G6 = 3 => 21 pairs (_) G2,G6: 3.. / G2 = 3 => 14 pairs (_) / G6 = 3 => 21 pairs (_) H2,H5: 3.. / H2 = 3 => 21 pairs (_) / H5 = 3 => 14 pairs (_) B3,C3: 4.. / B3 = 4 => 14 pairs (_) / C3 = 4 => 20 pairs (_) C4,G4: 4.. / C4 = 4 => 0 pairs (X) / G4 = 4 => 17 pairs (_) D8,G8: 4.. / D8 = 4 => 17 pairs (_) / G8 = 4 => 0 pairs (X) B3,B7: 4.. / B3 = 4 => 14 pairs (_) / B7 = 4 => 20 pairs (_) I5,I9: 4.. / I5 = 4 => 0 pairs (X) / I9 = 4 => 17 pairs (_) B1,B3: 5.. / B1 = 5 => 13 pairs (_) / B3 = 5 => 22 pairs (_) E1,E3: 5.. / E1 = 5 => 22 pairs (_) / E3 = 5 => 13 pairs (_) C4,C6: 5.. / C4 = 5 => 17 pairs (_) / C6 = 5 => 12 pairs (_) F4,F6: 5.. / F4 = 5 => 12 pairs (_) / F6 = 5 => 17 pairs (_) B1,E1: 5.. / B1 = 5 => 13 pairs (_) / E1 = 5 => 22 pairs (_) B3,E3: 5.. / B3 = 5 => 22 pairs (_) / E3 = 5 => 13 pairs (_) C4,F4: 5.. / C4 = 5 => 17 pairs (_) / F4 = 5 => 12 pairs (_) C6,F6: 5.. / C6 = 5 => 12 pairs (_) / F6 = 5 => 17 pairs (_) G2,H2: 6.. / G2 = 6 => 21 pairs (_) / H2 = 6 => 14 pairs (_) E5,F5: 6.. / E5 = 6 => 17 pairs (_) / F5 = 6 => 13 pairs (_) A1,A9: 6.. / A1 = 6 => 15 pairs (_) / A9 = 6 => 0 pairs (X) G1,I1: 7.. / G1 = 7 => 20 pairs (_) / I1 = 7 => 13 pairs (_) B5,B6: 7.. / B5 = 7 => 11 pairs (_) / B6 = 7 => 18 pairs (_) E7,F9: 7.. / E7 = 7 => 23 pairs (_) / F9 = 7 => 0 pairs (X) E7,H7: 7.. / E7 = 7 => 23 pairs (_) / H7 = 7 => 0 pairs (X) A5,B5: 9.. / A5 = 9 => 11 pairs (_) / B5 = 9 => 18 pairs (_) A9,B9: 9.. / A9 = 9 => 18 pairs (_) / B9 = 9 => 11 pairs (_) A5,A9: 9.. / A5 = 9 => 11 pairs (_) / A9 = 9 => 18 pairs (_) B5,B9: 9.. / B5 = 9 => 18 pairs (_) / B9 = 9 => 11 pairs (_) * DURATION: 0:00:35.966504 START: 23:48:40.885929 END: 23:49:16.852433 2019-04-30 * CP COUNT: (33) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A6,B1,B5,B6,B7,B9,D3,G2,H2,H4,I3) * ...9.2.4.289714..57....392.16.39...2...2..5.........968..5.92.3537.2...9....3..5. * PAIR A1: 3,6 BLK 1 C1: 3,6,1 # reduction candidate for 3,6 C1: 1 => CTR * 3.1962.4.289714..57.685392116.39...2...2.651.4..1..39681457926353762.489692438157 C1: 3,6 # 15 pairs * PAIR B1: 1,5 BLK 1 B3: 1,5,4 # reduction candidate for 1,5 B3: 1,5 # 20 pairs B3: 4 # 14 pairs * PAIR D3: 6,8 BLK 2 E1: 6,8,5 # reduction candidate for 6,8 E1: 6,8 # 13 pairs E3: 6,8,5 # reduction candidate for 6,8 E3: 6,8 # 22 pairs * PAIR D3: 6,8 COL D D8: 6,8,1,4 # reduction candidate for 6,8 D8: 6,8 => CTR * 6.39.2.4.289714365741.53928164395..29782615343254..196816549273537.2.419492.3..5. D8: 1,4 # 13 pairs D9: 6,8,1,4 # reduction candidate for 6,8 D9: 6,8 # 15 pairs * PAIR I3: 1,8 BLK 3 G1: 1,8,7 # reduction candidate for 1,8 G1: 1,8 # 13 pairs I1: 1,8,7 # reduction candidate for 1,8 I1: 1,8 # 20 pairs * PAIR I3: 1,8 COL I I5: 1,8,4,7 # reduction candidate for 1,8 I5: 1,8 # 19 pairs I9: 1,8,4,7 # reduction candidate for 1,8 I9: 1,8 => CTR * 6.39.2.47289714365741.53928164395..2978261534325...1968..5.92.3537.2...9492.3..5. I9: 4,7 # 13 pairs * PAIR A6: 3,4 BLK 4 A5: 3,4,9 # reduction candidate for 3,4 A5: 3,4 # 18 pairs C5: 3,4,8 # reduction candidate for 3,4 C5: 3,4 => CTR * 3..9.2.472897146357..6.392.16.39.4729732465..42...73968..5.92.353742...9692.3.754 C5: 8 # 13 pairs C6: 3,4,2,5,8 # reduction candidate for 3,4 C6: 3,4 => CTR * 3..9.21472897143657..6.3928165398472978246531423175.968..5.92.353742...969283..54 C6: 2,5,8 # 12 pairs * PAIR A6: 3,4 ROW 6 G6: 3,4,1,7,8 # reduction candidate for 3,4 G6: 3,4 # 21 pairs G6: 1,7,8 # 14 pairs * PAIR H4: 7,8 BLK 6 G4: 7,8,4 # reduction candidate for 7,8 G4: 7,8 => CTR * 6.39.2.4.289714365741.53928164395..29782..534325...196816549273537.2.419492.3..5. G4: 4 # 17 pairs H5: 7,8,1,3 # reduction candidate for 7,8 H5: 7,8 => CTR * .5.9821472897146357..65392816.39.4.2...2465.14.....3968..5.92.353742.869....3.754 H5: 1,3 # 13 pairs I5: 7,8,1,4 # reduction candidate for 7,8 I5: 7,8 # 21 pairs G6: 7,8,1,3,4 # reduction candidate for 7,8 G6: 7,8 => SOLVED * 653982147289714365714653928165398472498267531372145896846579213537421689921836754 G6: 1,3,4 # 12 pairs * PAIR H4: 7,8 ROW 4 F4: 7,8,5 # reduction candidate for 7,8 F4: 7,8 # 17 pairs F4: 5 # 12 pairs * PAIR B7: 1,4 BLK 7 C7: 1,4,6 # reduction candidate for 1,4 C7: 1,4 # 25 pairs C9: 1,4,2,6 # reduction candidate for 1,4 C9: 1,4 => SOLVED * 653982147289714365714653928165398472498267531372145896846579213537421689921836754 C9: 2,6 # 14 pairs * PAIR B7: 1,4 COL B B3: 1,4,5 # reduction candidate for 1,4 B3: 5 # 22 pairs B3: 1,4 # 13 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060613-absurd-base-pr-000.dot * REASONING * DIS # C1: 1 => CTR => C1: 3,6 * DIS # D8: 6,8 => CTR => D8: 1,4 * DIS # I9: 1,8 => CTR => I9: 4,7 * DIS # C5: 3,4 => CTR => C5: 8 * DIS # C6: 3,4 => CTR => C6: 2,5,8 * DIS # G4: 7,8 => CTR => G4: 4 * DIS # H5: 7,8 => CTR => H5: 1,3 * PRF # G6: 7,8 => SOL * PRF # C9: 1,4 => SOL * CNT 9 HDP CHAINS / 35 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A6,B1,B5,B6,B7,B9,D3,G2,H2,H4,I3) * ...9.2.4.289714..57....392.16.39...2...2..5.........968..5.92.3537.2...9....3..5. * PAIR A1: 3,6 BLK 1 C1: 3,6,1 # reduction candidate for 3,6 C1: 1 => CTR * 3.1962.4.289714..57.685392116.39...2...2.651.4..1..39681457926353762.489692438157 * PAIR B1: 1,5 BLK 1 B3: 1,5,4 # reduction candidate for 1,5 B3: 1,5 # 20 pairs B3: 4 # 14 pairs * PAIR D3: 6,8 BLK 2 E3: 6,8,5 # reduction candidate for 6,8 E3: 6,8 # 22 pairs E3: 5 # 15 pairs * PAIR D3: 6,8 COL D D8: 6,8,1,4 # reduction candidate for 6,8 D8: 6,8 => CTR * 6.39.2.4.289714365741.53928164395..29782615343254..196816549273537.2.419492.3..5. D9: 6,8,1,4 # reduction candidate for 6,8 D9: 6,8 # 18 pairs * RESTART * PAIR D3: 6,8 COL D D9: 6,8,1,4 # reduction candidate for 6,8 D9: 1,4 # 27 pairs D9: 6,8 # 18 pairs * PAIR RESTART * PAIR D3: 6,8 BLK 2 E3: 6,8,5 # reduction candidate for 6,8 E3: 6,8 # 22 pairs E3: 5 # 16 pairs * PAIR D3: 6,8 COL D D9: 6,8,1,4 # reduction candidate for 6,8 D9: 1,4 # 27 pairs D9: 6,8 # 18 pairs * PAIR I3: 1,8 BLK 3 G1: 1,8,7 # reduction candidate for 1,8 G1: 1,8 # 17 pairs I1: 1,8,7 # reduction candidate for 1,8 I1: 1,8 # 24 pairs * PAIR I3: 1,8 COL I I5: 1,8,4,7 # reduction candidate for 1,8 I5: 1,8 # 22 pairs I9: 1,8,4,7 # reduction candidate for 1,8 I9: 1,8 => CTR * 6.39.2.47289714365741.53928164395..2978261534325...1968..5.92.3537.2...9492.3..5. * RESTART * PAIR I3: 1,8 COL I I5: 1,8,4,7 # reduction candidate for 1,8 I5: 4,7 # 24 pairs I5: 1,8 # 22 pairs * PAIR RESTART * PAIR I3: 1,8 BLK 3 G1: 1,8,7 # reduction candidate for 1,8 G1: 1,8 # 22 pairs I1: 1,8,7 # reduction candidate for 1,8 I1: 1,8 # 24 pairs * PAIR I3: 1,8 COL I I5: 1,8,4,7 # reduction candidate for 1,8 I5: 4,7 # 24 pairs I5: 1,8 # 22 pairs * PAIR A6: 3,4 BLK 4 A5: 3,4,9 # reduction candidate for 3,4 A5: 3,4 # 18 pairs C5: 3,4,8 # reduction candidate for 3,4 C5: 3,4 => CTR * 3.69.2.472897146357..6.392.16.39.4729732465..42...73968..5.92.353742...9692.3.754 C6: 3,4,2,5 # reduction candidate for 3,4 C6: 3,4 => CTR * 3.69.21472897143657..6.3928165398472978246531423175.968..5.92.353742...969283..54 * RESTART * PAIR A6: 3,4 BLK 4 A5: 3,4,9 # reduction candidate for 3,4 A5: 9 => CTR * 6.39.2.4.289714..57....392.16.39...29782..53.325....968..5.92.3537.2...9492.3..57 * PAIR B7: 1,4 BLK 7 C7: 1,4,6 # reduction candidate for 1,4 C7: 1,4 => CTR * 6.39.2.4.2897143657..6.392.16539.4824982..5373728451968..5.92.353742..19926.3..54 C7: 6 => SOLVED * 653982147289714365714653928165398472498267531372145896846579213537421689921836754 * DURATION: 0:00:21.248268 START: 23:49:38.378154 END: 23:49:59.626422 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060613-absurd-base-pr-001.dot * REASONING * DIS # C1: 1 => CTR => C1: 3,6 * DIS C1: 3,6 # D8: 6,8 => CTR => D8: 1,4 * DIS C1: 3,6 + D8: 1,4 # I9: 1,8 => CTR => I9: 4,7 * DIS C1: 3,6 + D8: 1,4 + I9: 4,7 # C5: 3,4 => CTR => C5: 8 * DIS C1: 3,6 + D8: 1,4 + I9: 4,7 + C5: 8 # C6: 3,4 => CTR => C6: 2,5 * DIS C1: 3,6 + D8: 1,4 + I9: 4,7 + C5: 8 + C6: 2,5 # A5: 9 => CTR => A5: 3,4 * DIS C1: 3,6 + D8: 1,4 + I9: 4,7 + C5: 8 + C6: 2,5 + A5: 3,4 # C7: 1,4 => CTR => C7: 6 * PRF C1: 3,6 + D8: 1,4 + I9: 4,7 + C5: 8 + C6: 2,5 + A5: 3,4 + C7: 6 => SOL * STA C1: 3,6 + D8: 1,4 + I9: 4,7 + C5: 8 + C6: 2,5 + A5: 3,4 + C7: 6 * CNT 8 HDP CHAINS / 30 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006, 20060613, absurd
Solution
position: 653982147289714365714653928165398472498267531372145896846579213537421689921836754 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 # C1: 3,6 => UNS * DIS # C1: 1 => CTR => C1: 3,6 * INC # B3: 1,5 => UNS * INC # B3: 4 => UNS * INC # E1: 6,8 => UNS * INC # E3: 6,8 => UNS * DIS # D8: 6,8 => CTR => D8: 1,4 * INC # D8: 1,4 => UNS * INC # D9: 6,8 => UNS * INC # G1: 1,8 => UNS * INC # I1: 1,8 => UNS * INC # I5: 1,8 => UNS * DIS # I9: 1,8 => CTR => I9: 4,7 * INC # I9: 4,7 => UNS * INC # A5: 3,4 => UNS * DIS # C5: 3,4 => CTR => C5: 8 * INC # C5: 8 => UNS * DIS # C6: 3,4 => CTR => C6: 2,5,8 * INC # C6: 2,5,8 => UNS * INC # G6: 3,4 => UNS * INC # G6: 1,7,8 => UNS * DIS # G4: 7,8 => CTR => G4: 4 * INC # G4: 4 => UNS * DIS # H5: 7,8 => CTR => H5: 1,3 * INC # H5: 1,3 => UNS * INC # I5: 7,8 => UNS * PRF # G6: 7,8 => SOL * INC # G6: 1,3,4 => UNS * INC # F4: 7,8 => UNS * INC # F4: 5 => UNS * INC # C7: 1,4 => UNS * PRF # C9: 1,4 => SOL * INC # C9: 2,6 => UNS * INC # B3: 1,4 => UNS * INC # B3: 5 => UNS * CNT 35 HDP CHAINS / 35 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C1: 3,6 => UNS * DIS # C1: 1 => CTR => C1: 3,6 * INC C1: 3,6 # B3: 1,5 => UNS * INC C1: 3,6 # B3: 4 => UNS * INC C1: 3,6 # E3: 6,8 => UNS * INC C1: 3,6 # E3: 5 => UNS * DIS C1: 3,6 # D8: 6,8 => CTR => D8: 1,4 * INC C1: 3,6 + D8: 1,4 # D9: 6,8 => UNS * INC C1: 3,6 + D8: 1,4 # D9: 6,8 => UNS * INC C1: 3,6 + D8: 1,4 # D9: 1,4 => UNS * INC C1: 3,6 + D8: 1,4 # E3: 6,8 => UNS * INC C1: 3,6 + D8: 1,4 # E3: 5 => UNS * INC C1: 3,6 + D8: 1,4 # D9: 6,8 => UNS * INC C1: 3,6 + D8: 1,4 # D9: 1,4 => UNS * INC C1: 3,6 + D8: 1,4 # G1: 1,8 => UNS * INC C1: 3,6 + D8: 1,4 # I1: 1,8 => UNS * INC C1: 3,6 + D8: 1,4 # I5: 1,8 => UNS * DIS C1: 3,6 + D8: 1,4 # I9: 1,8 => CTR => I9: 4,7 * INC C1: 3,6 + D8: 1,4 + I9: 4,7 # I5: 1,8 => UNS * INC C1: 3,6 + D8: 1,4 + I9: 4,7 # I5: 4,7 => UNS * INC C1: 3,6 + D8: 1,4 + I9: 4,7 # G1: 1,8 => UNS * INC C1: 3,6 + D8: 1,4 + I9: 4,7 # I1: 1,8 => UNS * INC C1: 3,6 + D8: 1,4 + I9: 4,7 # I5: 1,8 => UNS * INC C1: 3,6 + D8: 1,4 + I9: 4,7 # I5: 4,7 => UNS * INC C1: 3,6 + D8: 1,4 + I9: 4,7 # A5: 3,4 => UNS * DIS C1: 3,6 + D8: 1,4 + I9: 4,7 # C5: 3,4 => CTR => C5: 8 * DIS C1: 3,6 + D8: 1,4 + I9: 4,7 + C5: 8 # C6: 3,4 => CTR => C6: 2,5 * INC C1: 3,6 + D8: 1,4 + I9: 4,7 + C5: 8 + C6: 2,5 # A5: 3,4 => UNS * DIS C1: 3,6 + D8: 1,4 + I9: 4,7 + C5: 8 + C6: 2,5 # A5: 9 => CTR => A5: 3,4 * DIS C1: 3,6 + D8: 1,4 + I9: 4,7 + C5: 8 + C6: 2,5 + A5: 3,4 # C7: 1,4 => CTR => C7: 6 * PRF C1: 3,6 + D8: 1,4 + I9: 4,7 + C5: 8 + C6: 2,5 + A5: 3,4 + C7: 6 => SOL * STA C1: 3,6 + D8: 1,4 + I9: 4,7 + C5: 8 + C6: 2,5 + A5: 3,4 + C7: 6 * CNT 31 HDP CHAINS / 30 HYP OPENED