Analysis of zz-www.sudokuoftheday.co.uk-20060315-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2006
level: medium
position: .7..........926....2.7...3.8..16.52.....4.....36....8.2.4....78.1.87........1.25. initial
Autosolve
position: .7......2...926....2.7...3.8..16.52...2.48....362...8.2.4...178.1.872.......1.25. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C3: 5,8 => CTR => C3: 1,9 * DIS # I3: 1,4 => CTR => I3: 5,6,9 * DIS # A6: 4,9 => CTR => A6: 1,5,7 * DIS # I4: 4,9 => CTR => I4: 3,7 * DIS # A5: 7,9 => CTR => A5: 1,5 * DIS # A6: 7,9 => CTR => A6: 1,4,5 * PRF # F4: 7,9 => SOL * DIS # F4: 3 => CTR => F4: 7,9 * DIS # I4: 7,9 => CTR => I4: 3,4 * DIS # C9: 7,9 => CTR => C9: 3,8 * PRF # A5: 5,9 => SOL * DIS # D1: 3,5 => CTR => D1: 4 * DIS # F6: 5,9 => CTR => F6: 7 * PRF # A6: 1,4,7 => SOL * DIS # B9: 6,9 => CTR => B9: 8 * DIS # I8: 3,9 => CTR => I8: 4,6 * DIS # A9: 3,9 => CTR => A9: 7 * DIS # I5: 3,9 => CTR => I5: 1,6,7 * CNT 18 HDP CHAINS / 45 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C3: 5,8 => CTR => C3: 1,9 * DIS C3: 1,9 # I3: 1,4 => CTR => I3: 5,6,9 * DIS C3: 1,9 + I3: 5,6,9 # A6: 4,9 => CTR => A6: 1,5,7 * DIS C3: 1,9 + I3: 5,6,9 + A6: 1,5,7 # A5: 7,9 => CTR => A5: 1,5 * PRF C3: 1,9 + I3: 5,6,9 + A6: 1,5,7 + A5: 1,5 # F4: 7,9 => SOL * STA C3: 1,9 + I3: 5,6,9 + A6: 1,5,7 + A5: 1,5 + F4: 7,9 * CNT 5 HDP CHAINS / 13 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .7..........926....2.7...3.8..16.52.....4.....36....8.2.4....78.1.87........1.25. | initial |
| .7......2...926....2.7...3.8..16.52...2.48....362...8.2.4...178.1.872.......1.25. | autosolve |
| 671435892358926417429781635847169523592348761136257984264593178915872346783614259 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (11) E3: 5,8 H2: 1,4 B4: 4,9 C4: 7,9 B5: 5,9 D5: 3,5 E6: 5,9 B7: 6,9 D9: 4,6 F9: 4,9 I9: 3,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F1,F3: 1.. / F1 = 1 => 12 pairs (_) / F3 = 1 => 11 pairs (_) A5,A6: 1.. / A5 = 1 => 13 pairs (_) / A6 = 1 => 0 pairs (*) A6,I6: 1.. / A6 = 1 => 0 pairs (*) / I6 = 1 => 0 pairs (X) A2,C2: 3.. / A2 = 3 => 13 pairs (_) / C2 = 3 => 13 pairs (_) F4,D5: 3.. / F4 = 3 => 0 pairs (X) / D5 = 3 => 0 pairs (_) F4,I4: 3.. / F4 = 3 => 0 pairs (X) / I4 = 3 => 0 pairs (_) E1,E7: 3.. / E1 = 3 => 12 pairs (_) / E7 = 3 => 18 pairs (_) G5,G8: 3.. / G5 = 3 => 0 pairs (X) / G8 = 3 => 18 pairs (_) B4,A6: 4.. / B4 = 4 => 11 pairs (_) / A6 = 4 => 0 pairs (X) D9,F9: 4.. / D9 = 4 => 0 pairs (X) / F9 = 4 => 11 pairs (_) B4,I4: 4.. / B4 = 4 => 11 pairs (_) / I4 = 4 => 0 pairs (X) B2,B4: 4.. / B2 = 4 => 0 pairs (X) / B4 = 4 => 11 pairs (_) D1,D9: 4.. / D1 = 4 => 11 pairs (_) / D9 = 4 => 0 pairs (X) I2,I3: 5.. / I2 = 5 => 0 pairs (X) / I3 = 5 => 13 pairs (_) A8,C8: 5.. / A8 = 5 => 0 pairs (X) / C8 = 5 => 12 pairs (_) B2,B5: 5.. / B2 = 5 => 0 pairs (*) / B5 = 5 => 0 pairs (X) A1,A3: 6.. / A1 = 6 => 11 pairs (_) / A3 = 6 => 11 pairs (_) B7,B9: 6.. / B7 = 6 => 11 pairs (_) / B9 = 6 => 0 pairs (X) D7,D9: 6.. / D7 = 6 => 0 pairs (X) / D9 = 6 => 11 pairs (_) B7,D7: 6.. / B7 = 6 => 11 pairs (_) / D7 = 6 => 0 pairs (X) B9,D9: 6.. / B9 = 6 => 0 pairs (X) / D9 = 6 => 11 pairs (_) G2,I2: 7.. / G2 = 7 => 12 pairs (_) / I2 = 7 => 15 pairs (_) F4,F6: 7.. / F4 = 7 => 0 pairs (X) / F6 = 7 => 13 pairs (_) A9,C9: 7.. / A9 = 7 => 12 pairs (_) / C9 = 7 => 0 pairs (X) C4,C9: 7.. / C4 = 7 => 12 pairs (_) / C9 = 7 => 0 pairs (X) E1,E3: 8.. / E1 = 8 => 0 pairs (X) / E3 = 8 => 11 pairs (_) B9,C9: 8.. / B9 = 8 => 14 pairs (_) / C9 = 8 => 0 pairs (X) B2,B9: 8.. / B2 = 8 => 0 pairs (X) / B9 = 8 => 14 pairs (_) E6,E7: 9.. / E6 = 9 => 14 pairs (_) / E7 = 9 => 0 pairs (*) * DURATION: 0:00:29.563514 START: 19:49:10.087354 END: 19:49:39.650868 2019-04-30 * CP COUNT: (29) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,B5,B7,C4,D5,D9,E3,E6,F9,H2,I9) * .7......2...926....2.7...3.8..16.52...2.48....362...8.2.4...178.1.872.......1.25. * PAIR E3: 5,8 BLK 2 E1: 5,8,3 # reduction candidate for 5,8 E1: 5,8 # 18 pairs E1: 3 # 12 pairs * PAIR E3: 5,8 ROW 3 C3: 5,8,1,9 # reduction candidate for 5,8 C3: 5,8 => CTR * .7.4..8.2...9267.5.2.781.3.84.16.523.52348....362...8.294...178.1.8723......14259 C3: 1,9 # 12 pairs * PAIR H2: 1,4 BLK 3 H1: 1,4,6,9 # reduction candidate for 1,4 H1: 1,4 # 16 pairs I2: 1,4,5,7 # reduction candidate for 1,4 I2: 1,4 # 26 pairs I3: 1,4,5,6,9 # reduction candidate for 1,4 I3: 1,4 => CTR * .7.4....2...9267.5.2.7...3.84.16.523.52348....362...8.294...178.1.8723......14259 I3: 5,6,9 # 11 pairs * PAIR B4: 4,9 BLK 4 A6: 4,9,1,5,7 # reduction candidate for 4,9 A6: 4,9 => CTR * .7......23..926....2.7...3.8.7169523152348...93625748129463517851.8723..7.3.1.259 A6: 1,5,7 # 11 pairs * PAIR B4: 4,9 ROW 4 I4: 4,9,3,7 # reduction candidate for 4,9 I4: 4,9 => CTR * .7.435..2.5392681..2.7...35847163529192548.6.536297481264359178.15872..6789614253 I4: 3,7 # 12 pairs * PAIR C4: 7,9 BLK 4 A5: 7,9,1,5 # reduction candidate for 7,9 A5: 7,9 => CTR * .7......2.8.926....2.7...3.84.16.523.52348...1362...8.2946..17851.8723......1.259 A5: 1,5 # 13 pairs A6: 7,9,1,4,5 # reduction candidate for 7,9 A6: 7,9 => CTR * .7......2.8.926....2.7...3.84.16.523152348....362..4812946..17851.8723......1.259 A6: 1,4,5 # 11 pairs * PAIR C4: 7,9 ROW 4 F4: 7,9,3 # reduction candidate for 7,9 F4: 7,9 => SOLVED * 671435892358926417429781635847169523592348761136257984264593178915872346783614259 F4: 3 => CTR * .7.435..2.5.926..442.781635847163529192548.67536297481264359178.15872.4678961425. I4: 7,9,3,4 # reduction candidate for 7,9 I4: 7,9 => CTR * .7.435..2.5.926..442.781635847163529192548.67536297481264359178.15872.4678961425. I4: 3,4 # 12 pairs * PAIR C4: 7,9 COL C C9: 7,9,3,8 # reduction candidate for 7,9 C9: 7,9 => CTR * .7.435..245.926....2.7...3.8.716352...25483.7536297481264359178315872...789614253 C9: 3,8 # 13 pairs * PAIR B5: 5,9 BLK 4 A5: 5,9,1,7 # reduction candidate for 5,9 A5: 5,9 => SOLVED * 671435892358926417429781635847169523592348761136257984264593178915872346783614259 A5: 1,7 # 12 pairs A6: 5,9,1,4,7 # reduction candidate for 5,9 A6: 5,9 # 17 pairs * PAIR D5: 3,5 COL D D1: 3,5,4 # reduction candidate for 3,5 D1: 3,5 => CTR * .7......2...926....2.7...3.8..16352...25483..536297481294...178.1.872......419253 D1: 4 # 11 pairs D7: 3,5,6 # reduction candidate for 3,5 D7: 3,5 # 11 pairs * PAIR E6: 5,9 BLK 5 F6: 5,9,7 # reduction candidate for 5,9 F6: 5,9 => CTR * .7......2..3926....2.7...3.849167523.52348....362...8.2946..17851.8723....7.1.259 F6: 7 # 13 pairs * PAIR E6: 5,9 ROW 6 A6: 5,9,1,4,7 # reduction candidate for 5,9 A6: 1,4,7 => SOLVED * 671435892358926417429781635847169523592348761136257984264593178915872346783614259 A6: 5,9 # 17 pairs * PAIR E6: 5,9 COL E E7: 5,9,3 # reduction candidate for 5,9 E7: 3 # 18 pairs E7: 5,9 # 12 pairs * PAIR B7: 6,9 BLK 7 B9: 6,9,8 # reduction candidate for 6,9 B9: 6,9 => CTR * .7......2.8.926....2.7...3.84.16.52..52348....362...8.2.4...178.1.8723....8.1.259 B9: 8 # 14 pairs * PAIR I9: 3,9 BLK 9 G8: 3,9,4,6 # reduction candidate for 3,9 G8: 3,9 # 14 pairs I8: 3,9,4,6 # reduction candidate for 3,9 I8: 3,9 => CTR * .7......2.5.926714.2.7...3584916352...25483..5362974812.4...178.1587264.....1.25. I8: 4,6 # 12 pairs * PAIR I9: 3,9 ROW 9 A9: 3,9,7 # reduction candidate for 3,9 A9: 3,9 => CTR * .7......2...926....2.7...3.8.916.52..52348....362...8.2.4...178.1.8723..387614259 A9: 7 # 12 pairs C9: 3,9,7,8 # reduction candidate for 3,9 C9: 3,9 # 14 pairs * PAIR I9: 3,9 COL I I4: 3,9,4,7 # reduction candidate for 3,9 I4: 3,9 # 13 pairs I5: 3,9,1,6,7 # reduction candidate for 3,9 I5: 3,9 => CTR * .7......2...926....2.7...3.8..16352...2548..35362974812.4...178.158723......1.259 I5: 1,6,7 # 11 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060315-absurd-base-pr-000.dot * REASONING * DIS # C3: 5,8 => CTR => C3: 1,9 * DIS # I3: 1,4 => CTR => I3: 5,6,9 * DIS # A6: 4,9 => CTR => A6: 1,5,7 * DIS # I4: 4,9 => CTR => I4: 3,7 * DIS # A5: 7,9 => CTR => A5: 1,5 * DIS # A6: 7,9 => CTR => A6: 1,4,5 * PRF # F4: 7,9 => SOL * DIS # F4: 3 => CTR => F4: 7,9 * DIS # I4: 7,9 => CTR => I4: 3,4 * DIS # C9: 7,9 => CTR => C9: 3,8 * PRF # A5: 5,9 => SOL * DIS # D1: 3,5 => CTR => D1: 4 * DIS # F6: 5,9 => CTR => F6: 7 * PRF # A6: 1,4,7 => SOL * DIS # B9: 6,9 => CTR => B9: 8 * DIS # I8: 3,9 => CTR => I8: 4,6 * DIS # A9: 3,9 => CTR => A9: 7 * DIS # I5: 3,9 => CTR => I5: 1,6,7 * CNT 18 HDP CHAINS / 45 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,B5,B7,C4,D5,D9,E3,E6,F9,H2,I9) * .7......2...926....2.7...3.8..16.52...2.48....362...8.2.4...178.1.872.......1.25. * PAIR E3: 5,8 BLK 2 E1: 5,8,3 # reduction candidate for 5,8 E1: 5,8 # 18 pairs E1: 3 # 12 pairs * PAIR E3: 5,8 ROW 3 C3: 5,8,1,9 # reduction candidate for 5,8 C3: 5,8 => CTR * .7.4..8.2...9267.5.2.781.3.84.16.523.52348....362...8.294...178.1.8723......14259 * PAIR RESTART * PAIR E3: 5,8 BLK 2 E1: 5,8,3 # reduction candidate for 5,8 E1: 5,8 # 19 pairs E1: 3 # 13 pairs * PAIR H2: 1,4 BLK 3 H1: 1,4,6,9 # reduction candidate for 1,4 H1: 1,4 # 17 pairs I2: 1,4,5,7 # reduction candidate for 1,4 I2: 1,4 # 26 pairs I3: 1,4,5,6,9 # reduction candidate for 1,4 I3: 1,4 => CTR * .7.4....2...9267.5.2.7...3.84.16.523.52348....362...8.294...178.1.8723......14259 * PAIR RESTART * PAIR H2: 1,4 BLK 3 H1: 1,4,6,9 # reduction candidate for 1,4 H1: 1,4 # 17 pairs I2: 1,4,5,7 # reduction candidate for 1,4 I2: 1,4 # 26 pairs * PAIR B4: 4,9 BLK 4 A6: 4,9,1,5,7 # reduction candidate for 4,9 A6: 4,9 => CTR * .7......23..926....2.7...3.8.7169523152348...93625748129463517851.8723..7.3.1.259 * PAIR C4: 7,9 BLK 4 A5: 7,9,1,5 # reduction candidate for 7,9 A5: 7,9 => CTR * .7......2.8.926....2.7...3.84.16.523.52348...1362...8.2946..17851.8723......1.259 * PAIR C4: 7,9 ROW 4 F4: 7,9,3 # reduction candidate for 7,9 F4: 7,9 => SOLVED * 671435892358926417429781635847169523592348761136257984264593178915872346783614259 * DURATION: 0:00:10.339725 START: 19:50:05.586199 END: 19:50:15.925924 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060315-absurd-base-pr-001.dot * REASONING * DIS # C3: 5,8 => CTR => C3: 1,9 * DIS C3: 1,9 # I3: 1,4 => CTR => I3: 5,6,9 * DIS C3: 1,9 + I3: 5,6,9 # A6: 4,9 => CTR => A6: 1,5,7 * DIS C3: 1,9 + I3: 5,6,9 + A6: 1,5,7 # A5: 7,9 => CTR => A5: 1,5 * PRF C3: 1,9 + I3: 5,6,9 + A6: 1,5,7 + A5: 1,5 # F4: 7,9 => SOL * STA C3: 1,9 + I3: 5,6,9 + A6: 1,5,7 + A5: 1,5 + F4: 7,9 * CNT 5 HDP CHAINS / 13 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2006, 20060315, absurd
Solution
position: 671435892358926417429781635847169523592348761136257984264593178915872346783614259 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 # E1: 5,8 => UNS * INC # E1: 3 => UNS * DIS # C3: 5,8 => CTR => C3: 1,9 * INC # C3: 1,9 => UNS * INC # H1: 1,4 => UNS * INC # I2: 1,4 => UNS * DIS # I3: 1,4 => CTR => I3: 5,6,9 * INC # I3: 5,6,9 => UNS * DIS # A6: 4,9 => CTR => A6: 1,5,7 * INC # A6: 1,5,7 => UNS * DIS # I4: 4,9 => CTR => I4: 3,7 * INC # I4: 3,7 => UNS * DIS # A5: 7,9 => CTR => A5: 1,5 * INC # A5: 1,5 => UNS * DIS # A6: 7,9 => CTR => A6: 1,4,5 * INC # A6: 1,4,5 => UNS * PRF # F4: 7,9 => SOL * DIS # F4: 3 => CTR => F4: 7,9 * DIS # I4: 7,9 => CTR => I4: 3,4 * INC # I4: 3,4 => UNS * DIS # C9: 7,9 => CTR => C9: 3,8 * INC # C9: 3,8 => UNS * PRF # A5: 5,9 => SOL * INC # A5: 1,7 => UNS * INC # A6: 5,9 => UNS * DIS # D1: 3,5 => CTR => D1: 4 * INC # D1: 4 => UNS * INC # D7: 3,5 => UNS * DIS # F6: 5,9 => CTR => F6: 7 * INC # F6: 7 => UNS * INC # A6: 5,9 => UNS * PRF # A6: 1,4,7 => SOL * INC # E7: 5,9 => UNS * INC # E7: 3 => UNS * DIS # B9: 6,9 => CTR => B9: 8 * INC # B9: 8 => UNS * INC # G8: 3,9 => UNS * DIS # I8: 3,9 => CTR => I8: 4,6 * INC # I8: 4,6 => UNS * DIS # A9: 3,9 => CTR => A9: 7 * INC # A9: 7 => UNS * INC # C9: 3,9 => UNS * INC # I4: 3,9 => UNS * DIS # I5: 3,9 => CTR => I5: 1,6,7 * INC # I5: 1,6,7 => UNS * CNT 45 HDP CHAINS / 45 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # E1: 5,8 => UNS * INC # E1: 3 => UNS * DIS # C3: 5,8 => CTR => C3: 1,9 * INC C3: 1,9 # E1: 5,8 => UNS * INC C3: 1,9 # E1: 3 => UNS * INC C3: 1,9 # H1: 1,4 => UNS * INC C3: 1,9 # I2: 1,4 => UNS * DIS C3: 1,9 # I3: 1,4 => CTR => I3: 5,6,9 * INC C3: 1,9 + I3: 5,6,9 # H1: 1,4 => UNS * INC C3: 1,9 + I3: 5,6,9 # I2: 1,4 => UNS * DIS C3: 1,9 + I3: 5,6,9 # A6: 4,9 => CTR => A6: 1,5,7 * DIS C3: 1,9 + I3: 5,6,9 + A6: 1,5,7 # A5: 7,9 => CTR => A5: 1,5 * PRF C3: 1,9 + I3: 5,6,9 + A6: 1,5,7 + A5: 1,5 # F4: 7,9 => SOL * STA C3: 1,9 + I3: 5,6,9 + A6: 1,5,7 + A5: 1,5 + F4: 7,9 * CNT 13 HDP CHAINS / 13 HYP OPENED