Analysis of zz-www.sudokuoftheday.co.uk-20190218-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Feb&YEAR=2019
level: medium
position: .975..1.......9..8.85.........73....628.....1..4.2.....6..45.2...23....7......46. initial
Autosolve
position: .9758.1.6.36..9..8.85.........73....628954..1374.21...76..45.2..423...17......46. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A3: 2,4 => CTR => A3: 1 * DIS # F3: 7 => CTR => F3: 2,3 * PRF # E3: 1,7 => SOL * DIS # E3: 6 => CTR => E3: 1,7 * DIS # E9: 1,7 => CTR => E9: 9 * PRF # E9: 9 => SOL * PRF # H3: 3,4 => SOL * DIS # A3: 2,4 => CTR => A3: 1 * DIS # D3: 2,4 => CTR => D3: 1,6 * DIS # A9: 5,9 => CTR => A9: 8 * DIS # H3: 3,7 => CTR => H3: 4,9 * DIS # G6: 5,9 => CTR => G6: 6 * PRF # G6: 6 => SOL * PRF # H6: 5,9 => SOL * DIS # H6: 8 => CTR => H6: 5,9 * DIS # D9: 1,8 => CTR => D9: 2 * DIS # F3: 2,7 => CTR => F3: 3 * DIS # G8: 8,9 => CTR => G8: 5 * DIS # I9: 5 => CTR => I9: 3,9 * DIS # C7: 1 => CTR => C7: 3,9 * CNT 20 HDP CHAINS / 40 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A3: 2,4 => CTR => A3: 1 * DIS A3: 1 # F3: 7 => CTR => F3: 2,3 * PRF A3: 1 + F3: 2,3 # H3: 3,4 => SOL * STA A3: 1 + F3: 2,3 + H3: 3,4 * CNT 3 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .975..1.......9..8.85.........73....628.....1..4.2.....6..45.2...23....7......46. | initial |
| .9758.1.6.36..9..8.85.........73....628954..1374.21...76..45.2..423...17......46. | autosolve |
| 497582136236419758185673942519736284628954371374821695763145829942368517851297463 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (23) A1: 2,4 F1: 2,3 E2: 1,7 H1: 3,4 I3: 2,4 A4: 5,9 B4: 1,5 C4: 1,9 F4: 6,8 D6: 6,8 G4: 2,6 H4: 4,8 I4: 2,4 G5: 3,7 H5: 3,7 I6: 5,9 B9: 1,5 D7: 1,8 E8: 6,9 F8: 6,8 F9: 2,7 G7: 8,9 I7: 3,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A2,A3: 1.. / A2 = 1 => 0 pairs (X) / A3 = 1 => 25 pairs (_) B4,C4: 1.. / B4 = 1 => 23 pairs (_) / C4 = 1 => 25 pairs (_) C7,D7: 1.. / C7 = 1 => 0 pairs (X) / D7 = 1 => 26 pairs (_) B4,B9: 1.. / B4 = 1 => 23 pairs (_) / B9 = 1 => 25 pairs (_) G4,I4: 2.. / G4 = 2 => 0 pairs (*) / I4 = 2 => 0 pairs (X) D9,F9: 2.. / D9 = 2 => 26 pairs (_) / F9 = 2 => 0 pairs (X) A1,F1: 2.. / A1 = 2 => 0 pairs (X) / F1 = 2 => 24 pairs (_) I3,I4: 2.. / I3 = 2 => 0 pairs (*) / I4 = 2 => 0 pairs (X) F1,F3: 3.. / F1 = 3 => 0 pairs (X) / F3 = 3 => 24 pairs (_) G5,H5: 3.. / G5 = 3 => 22 pairs (_) / H5 = 3 => 0 pairs (X) C7,C9: 3.. / C7 = 3 => 27 pairs (_) / C9 = 3 => 24 pairs (_) I7,I9: 3.. / I7 = 3 => 24 pairs (_) / I9 = 3 => 27 pairs (_) F1,H1: 3.. / F1 = 3 => 0 pairs (X) / H1 = 3 => 24 pairs (_) C7,I7: 3.. / C7 = 3 => 27 pairs (_) / I7 = 3 => 24 pairs (_) C9,I9: 3.. / C9 = 3 => 24 pairs (_) / I9 = 3 => 27 pairs (_) G3,G5: 3.. / G3 = 3 => 0 pairs (X) / G5 = 3 => 22 pairs (_) D2,D3: 4.. / D2 = 4 => 25 pairs (_) / D3 = 4 => 0 pairs (X) H4,I4: 4.. / H4 = 4 => 0 pairs (X) / I4 = 4 => 0 pairs (_) A1,H1: 4.. / A1 = 4 => 24 pairs (_) / H1 = 4 => 0 pairs (X) I3,I4: 4.. / I3 = 4 => 0 pairs (X) / I4 = 4 => 0 pairs (_) G2,H2: 5.. / G2 = 5 => 0 pairs (X) / H2 = 5 => 25 pairs (_) A4,B4: 5.. / A4 = 5 => 23 pairs (_) / B4 = 5 => 25 pairs (_) G8,I9: 5.. / G8 = 5 => 29 pairs (_) / I9 = 5 => 0 pairs (X) A8,G8: 5.. / A8 = 5 => 0 pairs (X) / G8 = 5 => 29 pairs (_) B4,B9: 5.. / B4 = 5 => 25 pairs (_) / B9 = 5 => 23 pairs (_) H2,H6: 5.. / H2 = 5 => 25 pairs (_) / H6 = 5 => 0 pairs (X) I6,I9: 5.. / I6 = 5 => 29 pairs (_) / I9 = 5 => 0 pairs (X) D3,E3: 6.. / D3 = 6 => 0 pairs (*) / E3 = 6 => 0 pairs (X) F4,D6: 6.. / F4 = 6 => 0 pairs (*) / D6 = 6 => 0 pairs (X) G4,G6: 6.. / G4 = 6 => 0 pairs (X) / G6 = 6 => 0 pairs (_) E8,F8: 6.. / E8 = 6 => 0 pairs (*) / F8 = 6 => 0 pairs (X) F4,G4: 6.. / F4 = 6 => 0 pairs (*) / G4 = 6 => 0 pairs (X) D6,G6: 6.. / D6 = 6 => 0 pairs (X) / G6 = 6 => 0 pairs (_) D3,D6: 6.. / D3 = 6 => 0 pairs (*) / D6 = 6 => 0 pairs (X) E3,E8: 6.. / E3 = 6 => 0 pairs (X) / E8 = 6 => 0 pairs (_) F4,F8: 6.. / F4 = 6 => 0 pairs (*) / F8 = 6 => 0 pairs (X) G5,H5: 7.. / G5 = 7 => 0 pairs (X) / H5 = 7 => 22 pairs (_) E9,F9: 7.. / E9 = 7 => 0 pairs (X) / F9 = 7 => 26 pairs (_) F3,F9: 7.. / F3 = 7 => 0 pairs (X) / F9 = 7 => 26 pairs (_) F4,D6: 8.. / F4 = 8 => 0 pairs (X) / D6 = 8 => 0 pairs (_) H4,H6: 8.. / H4 = 8 => 0 pairs (*) / H6 = 8 => 0 pairs (X) A8,A9: 8.. / A8 = 8 => 0 pairs (X) / A9 = 8 => 25 pairs (_) G7,G8: 8.. / G7 = 8 => 26 pairs (_) / G8 = 8 => 0 pairs (X) F4,H4: 8.. / F4 = 8 => 0 pairs (X) / H4 = 8 => 0 pairs (_) D6,H6: 8.. / D6 = 8 => 0 pairs (*) / H6 = 8 => 0 pairs (X) D7,G7: 8.. / D7 = 8 => 0 pairs (X) / G7 = 8 => 26 pairs (_) A9,D9: 8.. / A9 = 8 => 25 pairs (_) / D9 = 8 => 0 pairs (X) F4,F8: 8.. / F4 = 8 => 0 pairs (X) / F8 = 8 => 0 pairs (_) G3,H3: 9.. / G3 = 9 => 0 pairs (*) / H3 = 9 => 0 pairs (X) A4,C4: 9.. / A4 = 9 => 25 pairs (_) / C4 = 9 => 23 pairs (_) E8,E9: 9.. / E8 = 9 => 0 pairs (X) / E9 = 9 => 0 pairs (_) H3,H6: 9.. / H3 = 9 => 24 pairs (_) / H6 = 9 => 0 pairs (*) * DURATION: 0:01:09.046121 START: 03:49:23.724585 END: 03:50:32.770706 2019-05-01 * CP COUNT: (52) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A4,B4,B9,C4,D6,D7,E2,E8,F1,F4,F8,F9,G4,G5,G7,H1,H4,H5,I3,I4,I6,I7) * .9758.1.6.36..9..8.85.........73....628954..1374.21...76..45.2..423...17......46. * PAIR A1: 2,4 BLK 1 A2: 2,4,1 # reduction candidate for 2,4 A2: 2,4 # 25 pairs A3: 2,4,1 # reduction candidate for 2,4 A3: 2,4 => CTR * .9758.1.6136479258.85.....4...73.642628954..1374621.8.76.845923.423.68178.32.746. A3: 1 # 25 pairs * PAIR F1: 2,3 BLK 2 F3: 2,3,7 # reduction candidate for 2,3 F3: 7 => CTR * .97583146.36..9..8.85..7..2...73.284628954..13748216..76.14582..423.8.178..2..46. F3: 2,3 # 26 pairs * PAIR E2: 1,7 BLK 2 E3: 1,7,6 # reduction candidate for 1,7 E3: 1,7 => SOLVED * 497582136236419758185673942519736284628954371374821695763145829942368517851297463 E3: 6 => CTR * 497582136.364.9.58.85163794...738642628954371374621.8.761845923.4239681785....46. * PAIR E2: 1,7 COL E E9: 1,7,9 # reduction candidate for 1,7 E9: 1,7 => CTR * 497582136.364.9.58.85163.94...738642628954371374621.8.761845923.4239681785....46. E9: 9 => SOLVED * 497582136236419758185673942519736284628954371374821695763145829942368517851297463 * PAIR H1: 3,4 BLK 3 H3: 3,4,7,9 # reduction candidate for 3,4 H3: 3,4 => SOLVED * 497582136236419758185673942519736284628954371374821695763145829942368517851297463 H3: 7,9 # 24 pairs * PAIR I3: 2,4 ROW 3 A3: 2,4,1 # reduction candidate for 2,4 A3: 2,4 => CTR * .9758.1.6136479258.85.....4...73.642628954..1374621.8.76.845923.423.68178.32.746. A3: 1 # 25 pairs D3: 2,4,1,6 # reduction candidate for 2,4 D3: 2,4 => CTR * 4975821362364.9.58185.6..9....738642628954.71374621.8.76..45.2..42396.17......46. D3: 1,6 # 28 pairs * PAIR A4: 5,9 COL A A8: 5,9,8 # reduction candidate for 5,9 A8: 5,9 # 25 pairs A9: 5,9,8 # reduction candidate for 5,9 A9: 5,9 => CTR * 297583146.36..9.58.85.67..2...738...628954..1374.21...76..45.2.8423.6517...8.246. A9: 8 # 25 pairs * PAIR C4: 1,9 COL C C7: 1,9,3 # reduction candidate for 1,9 C7: 1,9 # 24 pairs C9: 1,9,3 # reduction candidate for 1,9 C9: 1,9 # 27 pairs * PAIR G5: 3,7 COL G G3: 3,7,2,9 # reduction candidate for 3,7 G3: 2,9 # 28 pairs G3: 3,7 # 26 pairs * PAIR H5: 3,7 COL H H3: 3,7,4,9 # reduction candidate for 3,7 H3: 3,7 => CTR * .9758.1.6.36..9758.85...932...73.28462895437137482169576.14582..423.85178512.746. H3: 4,9 # 24 pairs * PAIR I6: 5,9 BLK 6 G6: 5,9,6 # reduction candidate for 5,9 G6: 5,9 => CTR * 497582136.364.9.58.85163794...738642628954371374621.8.761845923.4239681785....46. G6: 6 => SOLVED * 497582136236419758185673942519736284628954371374821695763145829942368517851297463 H6: 5,9,8 # reduction candidate for 5,9 H6: 5,9 => SOLVED * 497582136236419758185673942519736284628954371374821695763145829942368517851297463 H6: 8 => CTR * 497582136.364.9.58.85163794...738642628954371374621.8.761845923.4239681785...746. * PAIR I6: 5,9 COL I I9: 5,9,3 # reduction candidate for 5,9 I9: 3 # 27 pairs I9: 5,9 # 24 pairs * PAIR D7: 1,8 BLK 8 D9: 1,8,2 # reduction candidate for 1,8 D9: 1,8 => CTR * 297583146.36..9..8.85..7..2...73.284628954..13748216..76.145.2..423...17.....246. D9: 2 # 26 pairs * PAIR F9: 2,7 COL F F3: 2,7,3 # reduction candidate for 2,7 F3: 2,7 => CTR * .97583146.36..9..8.85.....2...73.284628954..13748216..76.14582..423.8.178..2.746. F3: 3 # 24 pairs * PAIR G7: 8,9 BLK 9 G8: 8,9,5 # reduction candidate for 8,9 G8: 8,9 => CTR * .9758.1462364.9..8.856...9.951736284628954..1374821659769145823542368917813297465 G8: 5 # 29 pairs * PAIR I7: 3,9 BLK 9 I9: 3,9,5 # reduction candidate for 3,9 I9: 5 => CTR * .9758.1462364.9..8.856...9.951736284628954..1374821659769145823542368917813297465 I9: 3,9 # 29 pairs * PAIR I7: 3,9 ROW 7 C7: 3,9,1 # reduction candidate for 3,9 C7: 1 => CTR * .9758.1.6.36..9..8.85.........73....628954..1374.21...761845923.423.681785....46. C7: 3,9 # 26 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190218-absurd-base-pr-000.dot * REASONING * DIS # A3: 2,4 => CTR => A3: 1 * DIS # F3: 7 => CTR => F3: 2,3 * PRF # E3: 1,7 => SOL * DIS # E3: 6 => CTR => E3: 1,7 * DIS # E9: 1,7 => CTR => E9: 9 * PRF # E9: 9 => SOL * PRF # H3: 3,4 => SOL * DIS # A3: 2,4 => CTR => A3: 1 * DIS # D3: 2,4 => CTR => D3: 1,6 * DIS # A9: 5,9 => CTR => A9: 8 * DIS # H3: 3,7 => CTR => H3: 4,9 * DIS # G6: 5,9 => CTR => G6: 6 * PRF # G6: 6 => SOL * PRF # H6: 5,9 => SOL * DIS # H6: 8 => CTR => H6: 5,9 * DIS # D9: 1,8 => CTR => D9: 2 * DIS # F3: 2,7 => CTR => F3: 3 * DIS # G8: 8,9 => CTR => G8: 5 * DIS # I9: 5 => CTR => I9: 3,9 * DIS # C7: 1 => CTR => C7: 3,9 * CNT 20 HDP CHAINS / 40 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A4,B4,B9,C4,D6,D7,E2,E8,F1,F4,F8,F9,G4,G5,G7,H1,H4,H5,I3,I4,I6,I7) * .9758.1.6.36..9..8.85.........73....628954..1374.21...76..45.2..423...17......46. * PAIR A1: 2,4 BLK 1 A2: 2,4,1 # reduction candidate for 2,4 A2: 2,4 # 25 pairs A3: 2,4,1 # reduction candidate for 2,4 A3: 2,4 => CTR * .9758.1.6136479258.85.....4...73.642628954..1374621.8.76.845923.423.68178.32.746. * RESTART * PAIR F1: 2,3 BLK 2 F3: 2,3,7 # reduction candidate for 2,3 F3: 7 => CTR * .97583146436..9..8185467..2...73.284628954..1374.21...76..45.2..423...17......46. * PAIR H1: 3,4 BLK 3 H3: 3,4,7,9 # reduction candidate for 3,4 H3: 3,4 => SOLVED * 497582136236419758185673942519736284628954371374821695763145829942368517851297463 * DURATION: 0:00:04.626925 START: 03:51:02.931633 END: 03:51:07.558558 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190218-absurd-base-pr-001.dot * REASONING * DIS # A3: 2,4 => CTR => A3: 1 * DIS A3: 1 # F3: 7 => CTR => F3: 2,3 * PRF A3: 1 + F3: 2,3 # H3: 3,4 => SOL * STA A3: 1 + F3: 2,3 + H3: 3,4 * CNT 3 HDP CHAINS / 5 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Feb&YEAR=2019, 20190218, absurd
Solution
position: 497582136236419758185673942519736284628954371374821695763145829942368517851297463 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 # A2: 2,4 => UNS * DIS # A3: 2,4 => CTR => A3: 1 * INC # A3: 1 => UNS * INC # F3: 2,3 => UNS * DIS # F3: 7 => CTR => F3: 2,3 * PRF # E3: 1,7 => SOL * DIS # E3: 6 => CTR => E3: 1,7 * DIS # E9: 1,7 => CTR => E9: 9 * PRF # E9: 9 => SOL * PRF # H3: 3,4 => SOL * INC # H3: 7,9 => UNS * DIS # A3: 2,4 => CTR => A3: 1 * INC # A3: 1 => UNS * DIS # D3: 2,4 => CTR => D3: 1,6 * INC # D3: 1,6 => UNS * INC # A8: 5,9 => UNS * DIS # A9: 5,9 => CTR => A9: 8 * INC # A9: 8 => UNS * INC # C7: 1,9 => UNS * INC # C9: 1,9 => UNS * INC # G3: 3,7 => UNS * INC # G3: 2,9 => UNS * DIS # H3: 3,7 => CTR => H3: 4,9 * INC # H3: 4,9 => UNS * DIS # G6: 5,9 => CTR => G6: 6 * PRF # G6: 6 => SOL * PRF # H6: 5,9 => SOL * DIS # H6: 8 => CTR => H6: 5,9 * INC # I9: 5,9 => UNS * INC # I9: 3 => UNS * DIS # D9: 1,8 => CTR => D9: 2 * INC # D9: 2 => UNS * DIS # F3: 2,7 => CTR => F3: 3 * INC # F3: 3 => UNS * DIS # G8: 8,9 => CTR => G8: 5 * INC # G8: 5 => UNS * INC # I9: 3,9 => UNS * DIS # I9: 5 => CTR => I9: 3,9 * INC # C7: 3,9 => UNS * DIS # C7: 1 => CTR => C7: 3,9 * CNT 40 HDP CHAINS / 40 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A2: 2,4 => UNS * DIS # A3: 2,4 => CTR => A3: 1 * INC A3: 1 # F3: 2,3 => UNS * DIS A3: 1 # F3: 7 => CTR => F3: 2,3 * PRF A3: 1 + F3: 2,3 # H3: 3,4 => SOL * STA A3: 1 + F3: 2,3 + H3: 3,4 * CNT 5 HDP CHAINS / 5 HYP OPENED