Analysis of zz-www.sudokuoftheday.co.uk-20060804-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006
level: medium
position: .7.9...6226........3....7....1..9.3.....8.2.74...2....6....8..4.8.47.3....5..68.. initial
Autosolve
position: .789...6226...7..3.3...27..8217.9.353.6.8.2.74.7.2....6132.8.7498247.3.6745..682. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E1: 1,5 => CTR => E1: 3,4 * DIS # F1: 1,5 => CTR => F1: 3,4 * DIS # E3: 1,5 => CTR => E3: 4,6 * DIS # E3: 1,5 => CTR => E3: 4,6 * DIS # D6: 1,5 => CTR => D6: 3,6 * DIS # F6: 1,5 => CTR => F6: 3 * DIS # F1: 1,5 => CTR => F1: 3,4 * DIS # F6: 1,5 => CTR => F6: 3 * DIS # E9: 1,3 => CTR => E9: 9 * DIS # D6: 1,3 => CTR => D6: 5,6 * DIS # E9: 3 => CTR => E9: 1,9 * CNT 11 HDP CHAINS / 39 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # E1: 1,5 => CTR => E1: 3,4 * DIS E1: 3,4 # F1: 1,5 => CTR => F1: 3,4 * DIS E1: 3,4 + F1: 3,4 # H2: 4,9 => CTR => H2: 1,5,8 * DIS E1: 3,4 + F1: 3,4 + H2: 1,5,8 # E3: 1,5 => CTR => E3: 6 * PRF E1: 3,4 + F1: 3,4 + H2: 1,5,8 + E3: 6 # H3: 1,5 => SOL * STA E1: 3,4 + F1: 3,4 + H2: 1,5,8 + E3: 6 + H3: 1,5 * CNT 5 HDP CHAINS / 7 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .7.9...6226........3....7....1..9.3.....8.2.74...2....6....8..4.8.47.3....5..68.. | initial |
| .789...6226...7..3.3...27..8217.9.353.6.8.2.74.7.2....6132.8.7498247.3.6745..682. | autosolve |
| 178934562269517483534862719821749635396185247457623198613258974982471356745396821 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) A1: 1,5 C2: 4,9 A3: 1,5 C3: 4,9 B5: 5,9 B6: 5,9 E4: 4,6 D5: 1,5 G4: 4,6 E7: 5,9 F8: 1,5 D9: 1,3 G7: 5,9 H8: 1,5 I9: 1,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,A3: 1.. / A1 = 1 => 14 pairs (_) / A3 = 1 => 15 pairs (_) H8,I9: 1.. / H8 = 1 => 0 pairs (X) / I9 = 1 => 16 pairs (_) F8,H8: 1.. / F8 = 1 => 16 pairs (_) / H8 = 1 => 0 pairs (X) E1,F1: 3.. / E1 = 3 => 15 pairs (_) / F1 = 3 => 0 pairs (X) D6,F6: 3.. / D6 = 3 => 0 pairs (X) / F6 = 3 => 15 pairs (_) D9,E9: 3.. / D9 = 3 => 15 pairs (_) / E9 = 3 => 0 pairs (X) D6,D9: 3.. / D6 = 3 => 0 pairs (X) / D9 = 3 => 15 pairs (_) E1,E9: 3.. / E1 = 3 => 15 pairs (_) / E9 = 3 => 0 pairs (X) F1,F6: 3.. / F1 = 3 => 0 pairs (X) / F6 = 3 => 15 pairs (_) C2,C3: 4.. / C2 = 4 => 15 pairs (_) / C3 = 4 => 13 pairs (_) E4,F5: 4.. / E4 = 4 => 13 pairs (_) / F5 = 4 => 0 pairs (X) G4,H5: 4.. / G4 = 4 => 0 pairs (X) / H5 = 4 => 13 pairs (_) E4,G4: 4.. / E4 = 4 => 13 pairs (_) / G4 = 4 => 0 pairs (X) F5,H5: 4.. / F5 = 4 => 0 pairs (X) / H5 = 4 => 13 pairs (_) F1,F5: 4.. / F1 = 4 => 13 pairs (_) / F5 = 4 => 0 pairs (X) A1,A3: 5.. / A1 = 5 => 15 pairs (_) / A3 = 5 => 14 pairs (_) B5,B6: 5.. / B5 = 5 => 0 pairs (X) / B6 = 5 => 15 pairs (_) E7,F8: 5.. / E7 = 5 => 16 pairs (_) / F8 = 5 => 0 pairs (X) G7,H8: 5.. / G7 = 5 => 0 pairs (X) / H8 = 5 => 16 pairs (_) E7,G7: 5.. / E7 = 5 => 16 pairs (_) / G7 = 5 => 0 pairs (X) F8,H8: 5.. / F8 = 5 => 0 pairs (X) / H8 = 5 => 16 pairs (_) D3,E3: 6.. / D3 = 6 => 0 pairs (X) / E3 = 6 => 13 pairs (_) E4,D6: 6.. / E4 = 6 => 0 pairs (X) / D6 = 6 => 13 pairs (_) G4,G6: 6.. / G4 = 6 => 13 pairs (_) / G6 = 6 => 0 pairs (X) E4,G4: 6.. / E4 = 6 => 0 pairs (X) / G4 = 6 => 13 pairs (_) D6,G6: 6.. / D6 = 6 => 13 pairs (_) / G6 = 6 => 0 pairs (X) D3,D6: 6.. / D3 = 6 => 0 pairs (X) / D6 = 6 => 13 pairs (_) E3,E4: 6.. / E3 = 6 => 13 pairs (_) / E4 = 6 => 0 pairs (X) D2,D3: 8.. / D2 = 8 => 15 pairs (_) / D3 = 8 => 16 pairs (_) H6,I6: 8.. / H6 = 8 => 16 pairs (_) / I6 = 8 => 17 pairs (_) D2,H2: 8.. / D2 = 8 => 15 pairs (_) / H2 = 8 => 16 pairs (_) I3,I6: 8.. / I3 = 8 => 16 pairs (_) / I6 = 8 => 17 pairs (_) C2,C3: 9.. / C2 = 9 => 13 pairs (_) / C3 = 9 => 15 pairs (_) B5,B6: 9.. / B5 = 9 => 15 pairs (_) / B6 = 9 => 0 pairs (X) E7,E9: 9.. / E7 = 9 => 0 pairs (X) / E9 = 9 => 16 pairs (_) G7,I9: 9.. / G7 = 9 => 16 pairs (_) / I9 = 9 => 0 pairs (X) B5,H5: 9.. / B5 = 9 => 15 pairs (_) / H5 = 9 => 0 pairs (X) E7,G7: 9.. / E7 = 9 => 0 pairs (X) / G7 = 9 => 16 pairs (_) E9,I9: 9.. / E9 = 9 => 16 pairs (_) / I9 = 9 => 0 pairs (X) * DURATION: 0:00:50.461262 START: 01:33:20.865862 END: 01:34:11.327124 2019-05-01 * CP COUNT: (39) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B5,B6,C2,C3,D5,D9,E4,E7,F8,G4,G7,H8,I9) * .789...6226...7..3.3...27..8217.9.353.6.8.2.74.7.2....6132.8.7498247.3.6745..682. * PAIR A1: 1,5 ROW 1 E1: 1,5,3,4 # reduction candidate for 1,5 E1: 1,5 => CTR * .789.346226...7..3.3...27..8217496353.6.8.2474.7.2....6132.8.7498247.3.6745..682. E1: 3,4 # 16 pairs F1: 1,5,3,4 # reduction candidate for 1,5 F1: 1,5 => CTR * .7893.46226...7..3.3...27..8217496353.6.8.2474.7623...6132.8.7498247.3.67453.682. F1: 3,4 # 16 pairs G1: 1,5,4 # reduction candidate for 1,5 G1: 1,5 # 19 pairs * PAIR C2: 4,9 ROW 2 G2: 4,9,1,5 # reduction candidate for 4,9 G2: 4,9 # 17 pairs H2: 4,9,1,5,8 # reduction candidate for 4,9 H2: 4,9 # 18 pairs * PAIR A3: 1,5 ROW 3 D3: 1,5,6,8 # reduction candidate for 1,5 D3: 1,5 # 18 pairs E3: 1,5,4,6 # reduction candidate for 1,5 E3: 1,5 => CTR * .78943.6226.8.79.3.396.27488217694353.65842174.732.6..6132.8.7498247.3.6745136829 E3: 4,6 # 17 pairs H3: 1,5,4,8,9 # reduction candidate for 1,5 H3: 1,5 # 23 pairs * PAIR C3: 4,9 ROW 3 H3: 4,9,1,5,8 # reduction candidate for 4,9 H3: 4,9 # 17 pairs H3: 1,5,8 # 15 pairs * PAIR E4: 4,6 COL E E3: 4,6,1,5 # reduction candidate for 4,6 E3: 1,5 => CTR * .78943.6226.8.79.3.396.27488217694353.65842174.732.6..6132.8.7498247.3.6745136829 E3: 4,6 # 17 pairs * PAIR D5: 1,5 BLK 5 F5: 1,5,4 # reduction candidate for 1,5 F5: 1,5 # 13 pairs D6: 1,5,3,6 # reduction candidate for 1,5 D6: 1,5 => CTR * .789...6226...7..3.3.6.27..8217694353.6.842.74.7.236..6132.8.7498247.3.67453.682. D6: 3,6 # 16 pairs F6: 1,5,3 # reduction candidate for 1,5 F6: 1,5 => CTR * .789.3.6226...79.3.396.27..8217694353.658421745732169861329857498247.3.6745136829 F6: 3 # 15 pairs * PAIR D5: 1,5 COL D D2: 1,5,8 # reduction candidate for 1,5 D2: 1,5 # 16 pairs D3: 1,5,6,8 # reduction candidate for 1,5 D3: 1,5 # 18 pairs * PAIR F8: 1,5 COL F F1: 1,5,3,4 # reduction candidate for 1,5 F1: 1,5 => CTR * .7893.46226...7..3.3...27..8217496353.6.8.2474.7623...6132.8.7498247.3.67453.682. F1: 3,4 # 16 pairs F5: 1,5,4 # reduction candidate for 1,5 F5: 1,5 # 13 pairs F6: 1,5,3 # reduction candidate for 1,5 F6: 1,5 => CTR * .789.3.6226...79.3.396.27..8217694353.658421745732169861329857498247.3.6745136829 F6: 3 # 15 pairs * PAIR D9: 1,3 BLK 8 E9: 1,3,9 # reduction candidate for 1,3 E9: 1,3 => CTR * 57893..6226.8.71.313.6.27.88217694353.6.8.2.74.7.23.81613298574982475316745316829 E9: 9 # 16 pairs * PAIR D9: 1,3 COL D D6: 1,3,5,6 # reduction candidate for 1,3 D6: 1,3 => CTR * .78943.6226.8.7..3.3.6.27..8217694353.65842174573216..6132.8.7498247.3.6745..682. D6: 5,6 # 17 pairs * PAIR G7: 5,9 COL G G2: 5,9,1,4 # reduction candidate for 5,9 G2: 5,9 # 18 pairs G2: 1,4 # 16 pairs * PAIR H8: 1,5 COL H H2: 1,5,4,8,9 # reduction candidate for 1,5 H2: 1,5 # 19 pairs H3: 1,5,4,8,9 # reduction candidate for 1,5 H3: 1,5 # 23 pairs * PAIR I9: 1,9 ROW 9 E9: 1,9,3 # reduction candidate for 1,9 E9: 3 => CTR * .789.3.6226...7..3.3...27..8217.9.353.658.2.74.7.2....613298574982475316745136829 E9: 1,9 # 15 pairs * PAIR I9: 1,9 COL I I3: 1,9,8 # reduction candidate for 1,9 I3: 1,9 # 17 pairs I6: 1,9,8 # reduction candidate for 1,9 I6: 1,9 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060804-absurd-base-pr-000.dot * REASONING * DIS # E1: 1,5 => CTR => E1: 3,4 * DIS # F1: 1,5 => CTR => F1: 3,4 * DIS # E3: 1,5 => CTR => E3: 4,6 * DIS # E3: 1,5 => CTR => E3: 4,6 * DIS # D6: 1,5 => CTR => D6: 3,6 * DIS # F6: 1,5 => CTR => F6: 3 * DIS # F1: 1,5 => CTR => F1: 3,4 * DIS # F6: 1,5 => CTR => F6: 3 * DIS # E9: 1,3 => CTR => E9: 9 * DIS # D6: 1,3 => CTR => D6: 5,6 * DIS # E9: 3 => CTR => E9: 1,9 * CNT 11 HDP CHAINS / 39 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B5,B6,C2,C3,D5,D9,E4,E7,F8,G4,G7,H8,I9) * .789...6226...7..3.3...27..8217.9.353.6.8.2.74.7.2....6132.8.7498247.3.6745..682. * PAIR A1: 1,5 ROW 1 E1: 1,5,3,4 # reduction candidate for 1,5 E1: 1,5 => CTR * .789.346226...7..3.3...27..8217496353.6.8.2474.7.2....6132.8.7498247.3.6745..682. F1: 1,5,3,4 # reduction candidate for 1,5 F1: 1,5 => CTR * .7893.46226...7..3.3...27..8217496353.6.8.2474.7623...6132.8.7498247.3.67453.682. * RESTART * PAIR RESTART * PAIR C2: 4,9 ROW 2 G2: 4,9,1,5 # reduction candidate for 4,9 G2: 4,9 # 20 pairs H2: 4,9,1,5,8 # reduction candidate for 4,9 H2: 4,9 => CTR * .789...6226.8.7..3.3...27..8217.94353.6.842.74.7.2.6..6132589749824713567453.682. * RESTART * PAIR RESTART * PAIR A3: 1,5 ROW 3 D3: 1,5,6,8 # reduction candidate for 1,5 D3: 1,5 # 18 pairs E3: 1,5,6 # reduction candidate for 1,5 E3: 1,5 => CTR * .789431622648179531396527488217694353.6.842.74.732.68.6132985749824753167451.682. H3: 1,5,8,9 # reduction candidate for 1,5 H3: 1,5 => SOLVED * 178934562269517483534862719821749635396185247457623198613258974982471356745396821 * DURATION: 0:00:06.439316 START: 01:34:37.378939 END: 01:34:43.818255 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060804-absurd-base-pr-001.dot * REASONING * DIS # E1: 1,5 => CTR => E1: 3,4 * DIS E1: 3,4 # F1: 1,5 => CTR => F1: 3,4 * DIS E1: 3,4 + F1: 3,4 # H2: 4,9 => CTR => H2: 1,5,8 * DIS E1: 3,4 + F1: 3,4 + H2: 1,5,8 # E3: 1,5 => CTR => E3: 6 * PRF E1: 3,4 + F1: 3,4 + H2: 1,5,8 + E3: 6 # H3: 1,5 => SOL * STA E1: 3,4 + F1: 3,4 + H2: 1,5,8 + E3: 6 + H3: 1,5 * CNT 5 HDP CHAINS / 7 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006, 20060804, absurd
Solution
position: 178934562269517483534862719821749635396185247457623198613258974982471356745396821 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 # E1: 1,5 => CTR => E1: 3,4 * INC # E1: 3,4 => UNS * DIS # F1: 1,5 => CTR => F1: 3,4 * INC # F1: 3,4 => UNS * INC # G1: 1,5 => UNS * INC # G2: 4,9 => UNS * INC # H2: 4,9 => UNS * INC # D3: 1,5 => UNS * DIS # E3: 1,5 => CTR => E3: 4,6 * INC # E3: 4,6 => UNS * INC # H3: 1,5 => UNS * INC # H3: 4,9 => UNS * INC # H3: 1,5,8 => UNS * INC # E3: 4,6 => UNS * DIS # E3: 1,5 => CTR => E3: 4,6 * INC # F5: 1,5 => UNS * DIS # D6: 1,5 => CTR => D6: 3,6 * INC # D6: 3,6 => UNS * DIS # F6: 1,5 => CTR => F6: 3 * INC # F6: 3 => UNS * INC # D2: 1,5 => UNS * INC # D3: 1,5 => UNS * DIS # F1: 1,5 => CTR => F1: 3,4 * INC # F1: 3,4 => UNS * INC # F5: 1,5 => UNS * DIS # F6: 1,5 => CTR => F6: 3 * INC # F6: 3 => UNS * DIS # E9: 1,3 => CTR => E9: 9 * INC # E9: 9 => UNS * DIS # D6: 1,3 => CTR => D6: 5,6 * INC # D6: 5,6 => UNS * INC # G2: 5,9 => UNS * INC # G2: 1,4 => UNS * INC # H2: 1,5 => UNS * INC # H3: 1,5 => UNS * INC # E9: 1,9 => UNS * DIS # E9: 3 => CTR => E9: 1,9 * INC # I3: 1,9 => UNS * INC # I6: 1,9 => UNS * CNT 39 HDP CHAINS / 39 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # E1: 1,5 => CTR => E1: 3,4 * DIS E1: 3,4 # F1: 1,5 => CTR => F1: 3,4 * INC E1: 3,4 + F1: 3,4 # G2: 4,9 => UNS * DIS E1: 3,4 + F1: 3,4 # H2: 4,9 => CTR => H2: 1,5,8 * INC E1: 3,4 + F1: 3,4 + H2: 1,5,8 # D3: 1,5 => UNS * DIS E1: 3,4 + F1: 3,4 + H2: 1,5,8 # E3: 1,5 => CTR => E3: 6 * PRF E1: 3,4 + F1: 3,4 + H2: 1,5,8 + E3: 6 # H3: 1,5 => SOL * STA E1: 3,4 + F1: 3,4 + H2: 1,5,8 + E3: 6 + H3: 1,5 * CNT 7 HDP CHAINS / 7 HYP OPENED