Analysis of zz-www.sudokuoftheday.co.uk-20060528-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006
level: medium
position: .1.8..2....729..639....3..8.....7..9.....4.8..96.3..2...5.........4...3..7..69.4. initial
Autosolve
position: .1.8.629...729..63962..3..8...6.7..9...9.4.8..96.3..2...5...9....94...3..7..69.4. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A1: 5 => CTR => A1: 3,4 * DIS # E3: 1,5 => CTR => E3: 4,7 * DIS # G2: 1,5 => CTR => G2: 4 * DIS # F6: 1,5 => CTR => F6: 8 * DIS # C4: 1,3 => CTR => C4: 4,8 * DIS # A5: 1,3 => CTR => A5: 2,5,7 * DIS # G5: 1,3 => CTR => G5: 5,6,7 * DIS # F6: 1,5 => CTR => F6: 8 * PRF # G6: 1,5 => SOL * DIS # I6: 1,5 => CTR => I6: 4,7 * DIS # G4: 1,5 => CTR => G4: 3,4 * DIS # G5: 1,5 => CTR => G5: 3,6,7 * PRF # G6: 1,5 => SOL * DIS # I6: 1,5 => CTR => I6: 4,7 * DIS # A7: 2,8 => CTR => A7: 1,3,4,6 * DIS # B7: 2,8 => CTR => B7: 3,4 * DIS # A8: 2,8 => CTR => A8: 1,6 * DIS # F8: 2,8 => CTR => F8: 1,5 * DIS # G8: 1,7 => CTR => G8: 5,6,8 * DIS # E7: 1,7 => CTR => E7: 8 * CNT 20 HDP CHAINS / 65 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A1: 5 => CTR => A1: 3,4 * DIS A1: 3,4 # C4: 3,4 => CTR => C4: 1,8 * DIS A1: 3,4 + C4: 1,8 # G5: 1,3 => CTR => G5: 5,6,7 * DIS A1: 3,4 + C4: 1,8 + G5: 5,6,7 # C9: 8 => CTR => C9: 1,3 * PRF A1: 3,4 + C4: 1,8 + G5: 5,6,7 + C9: 1,3 # G6: 1,5 => SOL * STA A1: 3,4 + C4: 1,8 + G5: 5,6,7 + C9: 1,3 + G6: 1,5 * CNT 5 HDP CHAINS / 10 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .1.8..2....729..639....3..8.....7..9.....4.8..96.3..2...5.........4...3..7..69.4. | initial |
| .1.8.629...729..63962..3..8...6.7..9...9.4.8..96.3..2...5...9....94...3..7..69.4. | autosolve |
| 314856297857291463962743518428617359531924786796538124645382971189475632273169845 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (7) C1: 3,4 F2: 1,5 C5: 1,3 D6: 1,5 H4: 1,5 B8: 2,8 H7: 1,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F2,G2: 1.. / F2 = 1 => 10 pairs (_) / G2 = 1 => 0 pairs (X) E4,E5: 2.. / E4 = 2 => 9 pairs (_) / E5 = 2 => 8 pairs (_) F7,F8: 2.. / F7 = 2 => 7 pairs (_) / F8 = 2 => 0 pairs (X) A9,I9: 2.. / A9 = 2 => 0 pairs (*) / I9 = 2 => 0 pairs (X) A1,C1: 3.. / A1 = 3 => 12 pairs (_) / C1 = 3 => 15 pairs (_) G4,G5: 3.. / G4 = 3 => 7 pairs (_) / G5 = 3 => 0 pairs (X) D7,D9: 3.. / D7 = 3 => 14 pairs (_) / D9 = 3 => 14 pairs (_) E1,E3: 4.. / E1 = 4 => 0 pairs (X) / E3 = 4 => 8 pairs (_) A7,B7: 4.. / A7 = 4 => 12 pairs (_) / B7 = 4 => 10 pairs (_) E3,G3: 4.. / E3 = 4 => 8 pairs (_) / G3 = 4 => 0 pairs (X) C1,C4: 4.. / C1 = 4 => 12 pairs (_) / C4 = 4 => 15 pairs (_) I1,I6: 4.. / I1 = 4 => 0 pairs (X) / I6 = 4 => 8 pairs (_) H3,H4: 5.. / H3 = 5 => 15 pairs (_) / H4 = 5 => 7 pairs (_) G5,I5: 6.. / G5 = 6 => 7 pairs (_) / I5 = 6 => 0 pairs (*) A7,A8: 6.. / A7 = 6 => 16 pairs (_) / A8 = 6 => 7 pairs (_) A7,I7: 6.. / A7 = 6 => 16 pairs (_) / I7 = 6 => 7 pairs (_) G5,G8: 6.. / G5 = 6 => 7 pairs (_) / G8 = 6 => 0 pairs (*) A5,A6: 7.. / A5 = 7 => 7 pairs (_) / A6 = 7 => 10 pairs (_) E1,I1: 7.. / E1 = 7 => 20 pairs (_) / I1 = 7 => 10 pairs (_) D3,D7: 7.. / D3 = 7 => 10 pairs (_) / D7 = 7 => 20 pairs (_) H3,H7: 7.. / H3 = 7 => 20 pairs (_) / H7 = 7 => 10 pairs (_) A2,B2: 8.. / A2 = 8 => 9 pairs (_) / B2 = 8 => 9 pairs (_) E4,F6: 8.. / E4 = 8 => 0 pairs (X) / F6 = 8 => 8 pairs (_) G8,G9: 8.. / G8 = 8 => 11 pairs (_) / G9 = 8 => 0 pairs (*) A6,F6: 8.. / A6 = 8 => 0 pairs (X) / F6 = 8 => 8 pairs (_) C4,C9: 8.. / C4 = 8 => 18 pairs (_) / C9 = 8 => 14 pairs (_) * DURATION: 0:00:25.170992 START: 23:27:33.136743 END: 23:27:58.307735 2019-04-30 * CP COUNT: (26) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B8,C1,C5,D6,F2,H4,H7) * .1.8.629...729..63962..3..8...6.7..9...9.4.8..96.3..2...5...9....94...3..7..69.4. * PAIR C1: 3,4 BLK 1 A1: 3,4,5 # reduction candidate for 3,4 A1: 5 => CTR * 5138.629...729..63962..37.8..46.73.9..19.4687796.38.2...57829166294..835.78.69.42 A1: 3,4 # 14 pairs * PAIR C1: 3,4 COL C C4: 3,4,1,8 # reduction candidate for 3,4 C4: 3,4 # 15 pairs C4: 1,8 # 13 pairs * PAIR F2: 1,5 BLK 2 D3: 1,5,7 # reduction candidate for 1,5 D3: 1,5 # 20 pairs E3: 1,5,4,7 # reduction candidate for 1,5 E3: 1,5 => CTR * 513846297..729..639627.34.8..46.7..9..19.4685.96.3.724..5..297..2947583..78.69542 E3: 4,7 # 8 pairs * PAIR F2: 1,5 ROW 2 G2: 1,5,4 # reduction candidate for 1,5 G2: 1,5 => CTR * 5138.629...729..63962..37.8..46.73.9..19.4687796.3842...57829166294..835.78.69.42 G2: 4 # 14 pairs * PAIR F2: 1,5 COL F F6: 1,5,8 # reduction candidate for 1,5 F6: 1,5 => CTR * .1.8.629..8729..63962..3..8...687..97..924.8.896.3..2...5..89...294..83..78.69.42 F6: 8 # 8 pairs F8: 1,5,2,8 # reduction candidate for 1,5 F8: 1,5 # 8 pairs * PAIR C5: 1,3 BLK 4 A4: 1,3,2,4,5,8 # reduction candidate for 1,3 A4: 1,3 # 19 pairs C4: 1,3,4,8 # reduction candidate for 1,3 C4: 1,3 => CTR * 3148.6295587291463962543..8.4.6573.9.5.9.468..96.3..24435..29.66294.583.178369542 C4: 4,8 # 8 pairs A5: 1,3,2,5,7 # reduction candidate for 1,3 A5: 1,3 => CTR * 51387629484729..63962.43.782..6.73.9...9.4687796.38.2.4357829166.94..73..7.369845 A5: 2,5,7 # 7 pairs * PAIR C5: 1,3 ROW 5 G5: 1,3,5,6,7 # reduction candidate for 1,3 G5: 1,3 => CTR * .14856297..7291463962743..84.86.7..975.924.86196.3872.64538.97...947.63..7..6984. G5: 5,6,7 # 7 pairs * PAIR C5: 1,3 COL C C9: 1,3,8 # reduction candidate for 1,3 C9: 1,3 # 18 pairs C9: 8 # 14 pairs * PAIR D6: 1,5 BLK 5 E4: 1,5,2,8 # reduction candidate for 1,5 E4: 1,5 # 11 pairs E5: 1,5,2 # reduction candidate for 1,5 E5: 1,5 # 9 pairs F6: 1,5,8 # reduction candidate for 1,5 F6: 1,5 => CTR * .1.8.629..8729..63962..3..8...687..97..924.8.896.3..2...5..89...294..83..78.69.42 F6: 8 # 8 pairs * PAIR D6: 1,5 ROW 6 A6: 1,5,4,7,8 # reduction candidate for 1,5 A6: 1,5 # 11 pairs G6: 1,5,4,7 # reduction candidate for 1,5 G6: 1,5 => SOLVED * 314856297857291463962743518428617359531924786796538124645382971189475632273169845 G6: 4,7 # 8 pairs I6: 1,5,4,7 # reduction candidate for 1,5 I6: 1,5 => CTR * .13876294..729..63962.43..8..46.7..9..19.4.8.796.3842...578.91..294..837.7836954. I6: 4,7 # 8 pairs * PAIR D6: 1,5 COL D D3: 1,5,7 # reduction candidate for 1,5 D3: 1,5 # 20 pairs D9: 1,5,3 # reduction candidate for 1,5 D9: 1,5 # 14 pairs * PAIR H4: 1,5 BLK 6 G4: 1,5,3,4 # reduction candidate for 1,5 G4: 1,5 => CTR * 314856297..7291463962743..84386.7..97.19.4386.96.3872464538.97...947.63..73.6984. G4: 3,4 # 8 pairs G5: 1,5,3,6,7 # reduction candidate for 1,5 G5: 1,5 => CTR * 314856297..72914639627431584.86.73.9731924586.96.3872464538.97...947.63..73.6984. G5: 3,6,7 # 7 pairs I5: 1,5,6,7 # reduction candidate for 1,5 I5: 1,5 # 10 pairs G6: 1,5,4,7 # reduction candidate for 1,5 G6: 1,5 => SOLVED * 314856297857291463962743518428617359531924786796538124645382971189475632273169845 G6: 4,7 # 8 pairs I6: 1,5,4,7 # reduction candidate for 1,5 I6: 1,5 => CTR * .13876294..729..63962.43..8..46.7..9..19.4.8.796.3842...578.91..294..837.7836954. I6: 4,7 # 8 pairs * PAIR H4: 1,5 ROW 4 A4: 1,5,2,3,4,8 # reduction candidate for 1,5 A4: 1,5 # 10 pairs E4: 1,5,2,8 # reduction candidate for 1,5 E4: 1,5 # 11 pairs * PAIR H4: 1,5 COL H H3: 1,5,7 # reduction candidate for 1,5 H3: 7 # 20 pairs H3: 1,5 # 10 pairs * PAIR B8: 2,8 BLK 7 A7: 2,8,1,3,4,6 # reduction candidate for 2,8 A7: 2,8 => CTR * 314856297..7291463962743.584..6.73.9731924685.96.3.724.453..9766.947..3.173569842 A7: 1,3,4,6 # 7 pairs B7: 2,8,3,4 # reduction candidate for 2,8 B7: 2,8 => CTR * 314856297..7291463962743.582..6.73.9731924685.96.3.7244.53..9766.947..3.173569842 B7: 3,4 # 8 pairs A8: 2,8,1,6 # reduction candidate for 2,8 A8: 2,8 => CTR * 314856297..7291463962743..84.8627..9..19.4.8..9613..246453..97...947..3.173569842 A8: 1,6 # 8 pairs A9: 2,8,1,3 # reduction candidate for 2,8 A9: 2,8 # 18 pairs * PAIR B8: 2,8 ROW 8 F8: 2,8,1,5 # reduction candidate for 2,8 F8: 2,8 => CTR * .148.629.857291.63962..3..8..86.7..9...9.4.8..96.38.2...5.8.9...894.2.3..7..6984. F8: 1,5 # 8 pairs * PAIR B8: 2,8 COL B B4: 2,8,3,4,5 # reduction candidate for 2,8 B4: 2,8 # 12 pairs B4: 3,4,5 # 7 pairs * PAIR H7: 1,7 BLK 9 I7: 1,7,2,6 # reduction candidate for 1,7 I7: 1,7 # 17 pairs G8: 1,7,5,6,8 # reduction candidate for 1,7 G8: 1,7 => CTR * 314856297..7291463962743..8..86.73.9753924681196538724.351.29766.9475132271369845 G8: 5,6,8 # 7 pairs I8: 1,7,2,5,6 # reduction candidate for 1,7 I8: 1,7 # 11 pairs * PAIR H7: 1,7 ROW 7 D7: 1,7,3 # reduction candidate for 1,7 D7: 1,7 # 14 pairs E7: 1,7,8 # reduction candidate for 1,7 E7: 1,7 => CTR * .1.8.6297.87291.639627.3.18...687.5975.924.81896135724..5318976..947..3..78569142 E7: 8 # 8 pairs * PAIR H7: 1,7 COL H H3: 1,7,5 # reduction candidate for 1,7 H3: 5 # 15 pairs H3: 1,7 # 7 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060528-absurd-base-pr-000.dot * REASONING * DIS # A1: 5 => CTR => A1: 3,4 * DIS # E3: 1,5 => CTR => E3: 4,7 * DIS # G2: 1,5 => CTR => G2: 4 * DIS # F6: 1,5 => CTR => F6: 8 * DIS # C4: 1,3 => CTR => C4: 4,8 * DIS # A5: 1,3 => CTR => A5: 2,5,7 * DIS # G5: 1,3 => CTR => G5: 5,6,7 * DIS # F6: 1,5 => CTR => F6: 8 * PRF # G6: 1,5 => SOL * DIS # I6: 1,5 => CTR => I6: 4,7 * DIS # G4: 1,5 => CTR => G4: 3,4 * DIS # G5: 1,5 => CTR => G5: 3,6,7 * PRF # G6: 1,5 => SOL * DIS # I6: 1,5 => CTR => I6: 4,7 * DIS # A7: 2,8 => CTR => A7: 1,3,4,6 * DIS # B7: 2,8 => CTR => B7: 3,4 * DIS # A8: 2,8 => CTR => A8: 1,6 * DIS # F8: 2,8 => CTR => F8: 1,5 * DIS # G8: 1,7 => CTR => G8: 5,6,8 * DIS # E7: 1,7 => CTR => E7: 8 * CNT 20 HDP CHAINS / 65 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B8,C1,C5,D6,F2,H4,H7) * .1.8.629...729..63962..3..8...6.7..9...9.4.8..96.3..2...5...9....94...3..7..69.4. * PAIR C1: 3,4 BLK 1 A1: 3,4,5 # reduction candidate for 3,4 A1: 5 => CTR * 5138.629...729..63962..37.8..46.73.9..19.4687796.38.2...57829166294..835.78.69.42 * PAIR C1: 3,4 COL C C4: 3,4,1,8 # reduction candidate for 3,4 C4: 3,4 => CTR * 413856297..7291463962743158..46173.9.319.468..96.38.24.45.8297..2947583..78.69542 * PAIR RESTART * PAIR C5: 1,3 ROW 5 G5: 1,3,5,6,7 # reduction candidate for 1,3 G5: 1,3 => CTR * 3148.629...7291463962743..84.86.7..97.19.43865961387246453829....94..63..73.6984. * PAIR C5: 1,3 COL C C9: 1,3,8 # reduction candidate for 1,3 C9: 8 => CTR * 3148.6295.87291463962543..8.416.7359.539.468..96135.24435...9.66294..83.178369542 * PAIR RESTART * PAIR D6: 1,5 BLK 5 E4: 1,5,2 # reduction candidate for 1,5 E4: 1,5 # 22 pairs E5: 1,5,2 # reduction candidate for 1,5 E5: 1,5 # 20 pairs * PAIR D6: 1,5 ROW 6 A6: 1,5,7 # reduction candidate for 1,5 A6: 1,5 # 21 pairs G6: 1,5,7 # reduction candidate for 1,5 G6: 1,5 => SOLVED * 314856297857291463962743518428617359531924786796538124645382971189475632273169845 * DURATION: 0:00:09.162657 START: 23:28:32.643529 END: 23:28:41.806186 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060528-absurd-base-pr-001.dot * REASONING * DIS # A1: 5 => CTR => A1: 3,4 * DIS A1: 3,4 # C4: 3,4 => CTR => C4: 1,8 * DIS A1: 3,4 + C4: 1,8 # G5: 1,3 => CTR => G5: 5,6,7 * DIS A1: 3,4 + C4: 1,8 + G5: 5,6,7 # C9: 8 => CTR => C9: 1,3 * PRF A1: 3,4 + C4: 1,8 + G5: 5,6,7 + C9: 1,3 # G6: 1,5 => SOL * STA A1: 3,4 + C4: 1,8 + G5: 5,6,7 + C9: 1,3 + G6: 1,5 * CNT 5 HDP CHAINS / 10 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006, 20060528, absurd
Solution
position: 314856297857291463962743518428617359531924786796538124645382971189475632273169845 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 # A1: 3,4 => UNS * DIS # A1: 5 => CTR => A1: 3,4 * INC # C4: 3,4 => UNS * INC # C4: 1,8 => UNS * INC # D3: 1,5 => UNS * DIS # E3: 1,5 => CTR => E3: 4,7 * INC # E3: 4,7 => UNS * DIS # G2: 1,5 => CTR => G2: 4 * INC # G2: 4 => UNS * DIS # F6: 1,5 => CTR => F6: 8 * INC # F6: 8 => UNS * INC # F8: 1,5 => UNS * INC # A4: 1,3 => UNS * DIS # C4: 1,3 => CTR => C4: 4,8 * INC # C4: 4,8 => UNS * DIS # A5: 1,3 => CTR => A5: 2,5,7 * INC # A5: 2,5,7 => UNS * DIS # G5: 1,3 => CTR => G5: 5,6,7 * INC # G5: 5,6,7 => UNS * INC # C9: 1,3 => UNS * INC # C9: 8 => UNS * INC # E4: 1,5 => UNS * INC # E5: 1,5 => UNS * DIS # F6: 1,5 => CTR => F6: 8 * INC # F6: 8 => UNS * INC # A6: 1,5 => UNS * PRF # G6: 1,5 => SOL * INC # G6: 4,7 => UNS * DIS # I6: 1,5 => CTR => I6: 4,7 * INC # I6: 4,7 => UNS * INC # D3: 1,5 => UNS * INC # D9: 1,5 => UNS * DIS # G4: 1,5 => CTR => G4: 3,4 * INC # G4: 3,4 => UNS * DIS # G5: 1,5 => CTR => G5: 3,6,7 * INC # G5: 3,6,7 => UNS * INC # I5: 1,5 => UNS * PRF # G6: 1,5 => SOL * INC # G6: 4,7 => UNS * DIS # I6: 1,5 => CTR => I6: 4,7 * INC # I6: 4,7 => UNS * INC # A4: 1,5 => UNS * INC # E4: 1,5 => UNS * INC # H3: 1,5 => UNS * INC # H3: 7 => UNS * DIS # A7: 2,8 => CTR => A7: 1,3,4,6 * INC # A7: 1,3,4,6 => UNS * DIS # B7: 2,8 => CTR => B7: 3,4 * INC # B7: 3,4 => UNS * DIS # A8: 2,8 => CTR => A8: 1,6 * INC # A8: 1,6 => UNS * INC # A9: 2,8 => UNS * DIS # F8: 2,8 => CTR => F8: 1,5 * INC # F8: 1,5 => UNS * INC # B4: 2,8 => UNS * INC # B4: 3,4,5 => UNS * INC # I7: 1,7 => UNS * DIS # G8: 1,7 => CTR => G8: 5,6,8 * INC # G8: 5,6,8 => UNS * INC # I8: 1,7 => UNS * INC # D7: 1,7 => UNS * DIS # E7: 1,7 => CTR => E7: 8 * INC # E7: 8 => UNS * INC # H3: 1,7 => UNS * INC # H3: 5 => UNS * CNT 65 HDP CHAINS / 65 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A1: 3,4 => UNS * DIS # A1: 5 => CTR => A1: 3,4 * DIS A1: 3,4 # C4: 3,4 => CTR => C4: 1,8 * DIS A1: 3,4 + C4: 1,8 # G5: 1,3 => CTR => G5: 5,6,7 * INC A1: 3,4 + C4: 1,8 + G5: 5,6,7 # C9: 1,3 => UNS * DIS A1: 3,4 + C4: 1,8 + G5: 5,6,7 # C9: 8 => CTR => C9: 1,3 * INC A1: 3,4 + C4: 1,8 + G5: 5,6,7 + C9: 1,3 # E4: 1,5 => UNS * INC A1: 3,4 + C4: 1,8 + G5: 5,6,7 + C9: 1,3 # E5: 1,5 => UNS * INC A1: 3,4 + C4: 1,8 + G5: 5,6,7 + C9: 1,3 # A6: 1,5 => UNS * PRF A1: 3,4 + C4: 1,8 + G5: 5,6,7 + C9: 1,3 # G6: 1,5 => SOL * STA A1: 3,4 + C4: 1,8 + G5: 5,6,7 + C9: 1,3 + G6: 1,5 * CNT 10 HDP CHAINS / 10 HYP OPENED