Analysis of zz-www.sudokuoftheday.co.uk-20190124-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019
level: medium
position: .......71....6..3..7....6.......3...2.9.4......1...5.9.6.3.....5.34.6...91..582.. initial
Autosolve
position: ..62...71....67.3..7....6.......3.262.964.3.7631872549.6.32....5234.67.8914758263 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A1: 4 => CTR => A1: 3,8 * DIS # A3: 3,8 => CTR => A3: 1,4 * DIS # B4: 5,8 => CTR => B4: 4 * DIS # B2: 5,8 => CTR => B2: 4,9 * PRF # D4: 1,9 => SOL * DIS # D4: 5 => CTR => D4: 1,9 * DIS # D4: 9 => CTR => D4: 1,5 * PRF # F3: 1,5 => SOL * DIS # A4: 4 => CTR => A4: 7,8 * DIS # C4: 7,8 => CTR => C4: 5 * PRF # C4: 5 => SOL * DIS # H7: 1,9 => CTR => H7: 5 * PRF # F3: 1,9 => SOL * DIS # H7: 1,9 => CTR => H7: 5 * CNT 14 HDP CHAINS / 30 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A1: 4 => CTR => A1: 3,8 * DIS A1: 3,8 # A3: 3,8 => CTR => A3: 1,4 * DIS A1: 3,8 + A3: 1,4 # B4: 5,8 => CTR => B4: 4 * DIS A1: 3,8 + A3: 1,4 + B4: 4 # C4: 7 => CTR => C4: 5,8 * DIS A1: 3,8 + A3: 1,4 + B4: 4 + C4: 5,8 # B2: 5,8 => CTR => B2: 9 * PRF A1: 3,8 + A3: 1,4 + B4: 4 + C4: 5,8 + B2: 9 => SOL * STA A1: 3,8 + A3: 1,4 + B4: 4 + C4: 5,8 + B2: 9 * CNT 6 HDP CHAINS / 8 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .......71....6..3..7....6.......3...2.9.4......1...5.9.6.3.....5.34.6...91..582.. | initial |
| ..62...71....67.3..7....6.......3.262.964.3.7631872549.6.32....5234.67.8914758263 | autosolve |
| 356284971198567432472931685745193826289645317631872549867329154523416798914758263 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) E1: 3,8 E3: 3,8 B5: 5,8 E4: 1,9 F5: 1,5 G4: 1,8 H5: 1,8 A7: 7,8 C7: 7,8 F7: 1,9 E8: 1,9 I7: 4,5 H8: 1,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A2,A3: 1.. / A2 = 1 => 14 pairs (_) / A3 = 1 => 15 pairs (_) G4,H5: 1.. / G4 = 1 => 0 pairs (X) / H5 = 1 => 0 pairs (_) F7,E8: 1.. / F7 = 1 => 0 pairs (X) / E8 = 1 => 15 pairs (_) A2,D2: 1.. / A2 = 1 => 14 pairs (_) / D2 = 1 => 15 pairs (_) F5,H5: 1.. / F5 = 1 => 0 pairs (X) / H5 = 1 => 0 pairs (_) E8,H8: 1.. / E8 = 1 => 15 pairs (_) / H8 = 1 => 0 pairs (X) E4,E8: 1.. / E4 = 1 => 0 pairs (X) / E8 = 1 => 15 pairs (_) G4,G7: 1.. / G4 = 1 => 0 pairs (X) / G7 = 1 => 0 pairs (_) C2,C3: 2.. / C2 = 2 => 15 pairs (_) / C3 = 2 => 16 pairs (_) I2,I3: 2.. / I2 = 2 => 16 pairs (_) / I3 = 2 => 15 pairs (_) C2,I2: 2.. / C2 = 2 => 15 pairs (_) / I2 = 2 => 16 pairs (_) C3,I3: 2.. / C3 = 2 => 16 pairs (_) / I3 = 2 => 15 pairs (_) A1,A3: 3.. / A1 = 3 => 12 pairs (_) / A3 = 3 => 0 pairs (X) E1,E3: 3.. / E1 = 3 => 0 pairs (X) / E3 = 3 => 12 pairs (_) A1,E1: 3.. / A1 = 3 => 12 pairs (_) / E1 = 3 => 0 pairs (X) A3,E3: 3.. / A3 = 3 => 0 pairs (X) / E3 = 3 => 12 pairs (_) F1,F3: 4.. / F1 = 4 => 0 pairs (*) / F3 = 4 => 0 pairs (X) A4,B4: 4.. / A4 = 4 => 0 pairs (X) / B4 = 4 => 16 pairs (_) G7,I7: 4.. / G7 = 4 => 0 pairs (X) / I7 = 4 => 16 pairs (_) D4,F5: 5.. / D4 = 5 => 0 pairs (X) / F5 = 5 => 0 pairs (_) H7,I7: 5.. / H7 = 5 => 16 pairs (_) / I7 = 5 => 0 pairs (X) B1,F1: 5.. / B1 = 5 => 0 pairs (*) / F1 = 5 => 0 pairs (X) B5,F5: 5.. / B5 = 5 => 0 pairs (X) / F5 = 5 => 0 pairs (_) H3,H7: 5.. / H3 = 5 => 0 pairs (X) / H7 = 5 => 16 pairs (_) A4,C4: 7.. / A4 = 7 => 14 pairs (_) / C4 = 7 => 0 pairs (X) A7,C7: 7.. / A7 = 7 => 0 pairs (X) / C7 = 7 => 14 pairs (_) A4,A7: 7.. / A4 = 7 => 14 pairs (_) / A7 = 7 => 0 pairs (X) C4,C7: 7.. / C4 = 7 => 0 pairs (X) / C7 = 7 => 14 pairs (_) E1,E3: 8.. / E1 = 8 => 12 pairs (_) / E3 = 8 => 0 pairs (X) G4,H5: 8.. / G4 = 8 => 0 pairs (*) / H5 = 8 => 0 pairs (X) A7,C7: 8.. / A7 = 8 => 14 pairs (_) / C7 = 8 => 0 pairs (X) B5,H5: 8.. / B5 = 8 => 0 pairs (*) / H5 = 8 => 0 pairs (X) H3,H5: 8.. / H3 = 8 => 0 pairs (*) / H5 = 8 => 0 pairs (X) B1,B2: 9.. / B1 = 9 => 0 pairs (X) / B2 = 9 => 15 pairs (_) D4,E4: 9.. / D4 = 9 => 0 pairs (X) / E4 = 9 => 15 pairs (_) F7,E8: 9.. / F7 = 9 => 15 pairs (_) / E8 = 9 => 0 pairs (X) E8,H8: 9.. / E8 = 9 => 0 pairs (X) / H8 = 9 => 15 pairs (_) E4,E8: 9.. / E4 = 9 => 15 pairs (_) / E8 = 9 => 0 pairs (X) * DURATION: 0:00:42.851351 START: 03:10:39.312082 END: 03:11:22.163433 2019-05-01 * CP COUNT: (38) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B5,C7,E1,E3,E4,E8,F5,F7,G4,H5,H8,I7) * ..62...71....67.3..7....6.......3.262.964.3.7631872549.6.32....5234.67.8914758263 * PAIR E1: 3,8 ROW 1 A1: 3,8,4 # reduction candidate for 3,8 A1: 4 => CTR * 4.623..711...67.3.37.18469..4...3126259641387631872549.6.329...5234.67.8914758263 A1: 3,8 # 15 pairs * PAIR E3: 3,8 ROW 3 A3: 3,8,1,4 # reduction candidate for 3,8 A3: 3,8 => CTR * ..62...711...67.3..7....6.......3126259641387631872549.6.329415523416798914758263 A3: 1,4 # 13 pairs * PAIR B5: 5,8 BLK 4 B4: 5,8,4 # reduction candidate for 5,8 B4: 5,8 => CTR * .462.5971.95167.3..7...46..4.7593126259641387631872549768329415523416798914758263 B4: 4 # 16 pairs C4: 5,8,7 # reduction candidate for 5,8 C4: 5,8 # 14 pairs * PAIR B5: 5,8 COL B B1: 5,8,4,9 # reduction candidate for 5,8 B1: 5,8 # 19 pairs B2: 5,8,4,9 # reduction candidate for 5,8 B2: 5,8 => CTR * 496235871.85.6793..7...46...4.593126259641387631872549.6.329415523416798914758263 B2: 4,9 # 14 pairs * PAIR E4: 1,9 BLK 5 D4: 1,9,5 # reduction candidate for 1,9 D4: 1,9 => SOLVED * 356284971198567432472931685745193826289645317631872549867329154523416798914758263 D4: 5 => CTR * ..62.5.71..5.67.32.729.46.....593126259641387631872549.6.329415523416798914758263 * PAIR F5: 1,5 BLK 5 D4: 1,5,9 # reduction candidate for 1,5 D4: 9 => CTR * ..62...71....67.3..7....6.....913826289645317631872549.6.321...5234967.8914758263 D4: 1,5 # 15 pairs * PAIR F5: 1,5 COL F F3: 1,5,4,9 # reduction candidate for 1,5 F3: 1,5 => SOLVED * 356284971198567432472931685745193826289645317631872549867329154523416798914758263 F3: 4,9 # 15 pairs * PAIR A7: 7,8 COL A A4: 7,8,4 # reduction candidate for 7,8 A4: 4 => CTR * .462.5971.95167.3..7...46..4.7593126259641387631872549768329415523416798914758263 A4: 7,8 # 16 pairs * PAIR C7: 7,8 COL C C4: 7,8,5 # reduction candidate for 7,8 C4: 7,8 => CTR * ..62.5.71..5.67.3..7...46.....593126259641387631872549.6.329415523416798914758263 C4: 5 => SOLVED * 356284971198567432472931685745193826289645317631872549867329154523416798914758263 * PAIR F7: 1,9 ROW 7 G7: 1,9,4 # reduction candidate for 1,9 G7: 1,9 # 16 pairs H7: 1,9,5 # reduction candidate for 1,9 H7: 1,9 => CTR * ..62.5.71..5.67.32.729.465......3126259641387631872549.6.329415523416798914758263 H7: 5 # 16 pairs * PAIR F7: 1,9 COL F F3: 1,9,4,5 # reduction candidate for 1,9 F3: 1,9 => SOLVED * 356284971198567432472931685745193826289645317631872549867329154523416798914758263 F3: 4,5 # 15 pairs * PAIR I7: 4,5 COL I I2: 4,5,2 # reduction candidate for 4,5 I2: 4,5 # 15 pairs I3: 4,5,2 # reduction candidate for 4,5 I3: 4,5 # 16 pairs * PAIR H8: 1,9 BLK 9 G7: 1,9,4 # reduction candidate for 1,9 G7: 1,9 # 16 pairs H7: 1,9,5 # reduction candidate for 1,9 H7: 1,9 => CTR * ..62.5.71..5.67.32.729.465......3126259641387631872549.6.329415523416798914758263 H7: 5 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190124-absurd-base-pr-000.dot * REASONING * DIS # A1: 4 => CTR => A1: 3,8 * DIS # A3: 3,8 => CTR => A3: 1,4 * DIS # B4: 5,8 => CTR => B4: 4 * DIS # B2: 5,8 => CTR => B2: 4,9 * PRF # D4: 1,9 => SOL * DIS # D4: 5 => CTR => D4: 1,9 * DIS # D4: 9 => CTR => D4: 1,5 * PRF # F3: 1,5 => SOL * DIS # A4: 4 => CTR => A4: 7,8 * DIS # C4: 7,8 => CTR => C4: 5 * PRF # C4: 5 => SOL * DIS # H7: 1,9 => CTR => H7: 5 * PRF # F3: 1,9 => SOL * DIS # H7: 1,9 => CTR => H7: 5 * CNT 14 HDP CHAINS / 30 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B5,C7,E1,E3,E4,E8,F5,F7,G4,H5,H8,I7) * ..62...71....67.3..7....6.......3.262.964.3.7631872549.6.32....5234.67.8914758263 * PAIR E1: 3,8 ROW 1 A1: 3,8,4 # reduction candidate for 3,8 A1: 4 => CTR * 4.623..711...67.3.37.18469..4...3126259641387631872549.6.329...5234.67.8914758263 * PAIR RESTART * PAIR E3: 3,8 ROW 3 A3: 3,8,1,4 # reduction candidate for 3,8 A3: 3,8 => CTR * ..62.5.711..96783..7.1.469.48759312625964138763187254976832....5234.67.8914758263 * PAIR RESTART * PAIR B5: 5,8 BLK 4 B4: 5,8,4 # reduction candidate for 5,8 B4: 5,8 => CTR * 3.628..718..167.3.17..3.68.4.7..3826289645317631872549768321.545234967.8914758263 C4: 5,8,7 # reduction candidate for 5,8 C4: 5,8 # 14 pairs * RESTART * PAIR B5: 5,8 BLK 4 C4: 5,8,7 # reduction candidate for 5,8 C4: 7 => CTR * 3.628..71....67.3..7..3.6...47593126259641387631872549768329415523416798914758263 * PAIR B5: 5,8 COL B B2: 5,8,9 # reduction candidate for 5,8 B2: 5,8 => CTR * 3962854714..16793.17.93468.74.593.262.964.3.763187254986732....5234.67.8914758263 B2: 9 => SOLVED * 356284971198567432472931685745193826289645317631872549867329154523416798914758263 * DURATION: 0:00:07.697423 START: 03:11:41.813437 END: 03:11:49.510860 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190124-absurd-base-pr-001.dot * REASONING * DIS # A1: 4 => CTR => A1: 3,8 * DIS A1: 3,8 # A3: 3,8 => CTR => A3: 1,4 * DIS A1: 3,8 + A3: 1,4 # B4: 5,8 => CTR => B4: 4 * DIS A1: 3,8 + A3: 1,4 + B4: 4 # C4: 7 => CTR => C4: 5,8 * DIS A1: 3,8 + A3: 1,4 + B4: 4 + C4: 5,8 # B2: 5,8 => CTR => B2: 9 * PRF A1: 3,8 + A3: 1,4 + B4: 4 + C4: 5,8 + B2: 9 => SOL * STA A1: 3,8 + A3: 1,4 + B4: 4 + C4: 5,8 + B2: 9 * CNT 6 HDP CHAINS / 8 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019, 20190124, absurd
Solution
position: 356284971198567432472931685745193826289645317631872549867329154523416798914758263 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: 3,8 => UNS * DIS # A1: 4 => CTR => A1: 3,8 * DIS # A3: 3,8 => CTR => A3: 1,4 * INC # A3: 1,4 => UNS * DIS # B4: 5,8 => CTR => B4: 4 * INC # B4: 4 => UNS * INC # C4: 5,8 => UNS * INC # B1: 5,8 => UNS * DIS # B2: 5,8 => CTR => B2: 4,9 * INC # B2: 4,9 => UNS * PRF # D4: 1,9 => SOL * DIS # D4: 5 => CTR => D4: 1,9 * INC # D4: 1,5 => UNS * DIS # D4: 9 => CTR => D4: 1,5 * PRF # F3: 1,5 => SOL * INC # F3: 4,9 => UNS * INC # A4: 7,8 => UNS * DIS # A4: 4 => CTR => A4: 7,8 * DIS # C4: 7,8 => CTR => C4: 5 * PRF # C4: 5 => SOL * INC # G7: 1,9 => UNS * DIS # H7: 1,9 => CTR => H7: 5 * INC # H7: 5 => UNS * PRF # F3: 1,9 => SOL * INC # F3: 4,5 => UNS * INC # I2: 4,5 => UNS * INC # I3: 4,5 => UNS * INC # G7: 1,9 => UNS * DIS # H7: 1,9 => CTR => H7: 5 * INC # H7: 5 => UNS * CNT 30 HDP CHAINS / 30 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A1: 3,8 => UNS * DIS # A1: 4 => CTR => A1: 3,8 * DIS A1: 3,8 # A3: 3,8 => CTR => A3: 1,4 * DIS A1: 3,8 + A3: 1,4 # B4: 5,8 => CTR => B4: 4 * INC A1: 3,8 + A3: 1,4 + B4: 4 # C4: 5,8 => UNS * INC A1: 3,8 + A3: 1,4 + B4: 4 # C4: 5,8 => UNS * DIS A1: 3,8 + A3: 1,4 + B4: 4 # C4: 7 => CTR => C4: 5,8 * DIS A1: 3,8 + A3: 1,4 + B4: 4 + C4: 5,8 # B2: 5,8 => CTR => B2: 9 * PRF A1: 3,8 + A3: 1,4 + B4: 4 + C4: 5,8 + B2: 9 => SOL * STA A1: 3,8 + A3: 1,4 + B4: 4 + C4: 5,8 + B2: 9 * CNT 9 HDP CHAINS / 8 HYP OPENED