Analysis of zz-www.sudokuoftheday.co.uk-20060717-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006
level: medium
position: .372.....86.........2..39.....71...5....2......19.4.....8..7.2..2.6.945.41..3.8.. initial
Autosolve
position: .372.....86.4......428.39.....71...5...32......19.4.....8147.2.72368945141.5328.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A1: 5,9 => CTR => A1: 1 * PRF # A1: 1 => SOL * DIS # E2: 5,9 => CTR => E2: 7 * PRF # E2: 7 => SOL * DIS # C5: 4,6 => CTR => C5: 5,9 * PRF # A1: 1,5 => SOL * DIS # A1: 9 => CTR => A1: 1,5 * PRF # F1: 1,5 => SOL * DIS # F1: 6 => CTR => F1: 1,5 * PRF # G2: 1,5 => SOL * DIS # H3: 6,7 => CTR => H3: 1 * PRF # H3: 1 => SOL * PRF # E3: 6,7 => SOL * DIS # E3: 5 => CTR => E3: 6,7 * DIS # I5: 6,7 => CTR => I5: 4,8,9 * DIS # G4: 6 => CTR => G4: 2,3 * DIS # B5: 8,9 => CTR => B5: 5,7 * PRF # H4: 8,9 => SOL * PRF # F5: 6,8 => SOL * DIS # F5: 5 => CTR => F5: 6,8 * PRF # H4: 6,8 => SOL * DIS # F5: 5,6 => CTR => F5: 8 * PRF # F5: 8 => SOL * DIS # E1: 5,6 => CTR => E1: 9 * PRF # E1: 9 => SOL * PRF # E3: 5,6 => SOL * DIS # E3: 7 => CTR => E3: 5,6 * DIS # A7: 6 => CTR => A7: 5,9 * DIS # B5: 5,9 => CTR => B5: 7,8 * PRF # A7: 6,9 => SOL * DIS # A7: 5 => CTR => A7: 6,9 * DIS # C4: 6,9 => CTR => C4: 4 * DIS # C5: 6,9 => CTR => C5: 4,5 * DIS # I7: 9 => CTR => I7: 3,6 * CNT 34 HDP CHAINS / 58 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A1: 5,9 => CTR => A1: 1 * PRF A1: 1 => SOL * STA A1: 1 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .372.....86.........2..39.....71...5....2......19.4.....8..7.2..2.6.945.41..3.8.. | initial |
| .372.....86.4......428.39.....71...5...32......19.4.....8147.2.72368945141.5328.. | autosolve |
| 137295648869471532542863917394716285675328194281954763958147326723689451416532879 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) C2: 5,9 A3: 1,5 F2: 1,5 H1: 4,8 I1: 4,8 I3: 6,7 A4: 2,3 B4: 8,9 A6: 2,3 F4: 6,8 E6: 5,6 B7: 5,9 C9: 6,9 G7: 3,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,A3: 1.. / A1 = 1 => 0 pairs (*) / A3 = 1 => 0 pairs (X) F1,F2: 1.. / F1 = 1 => 0 pairs (X) / F2 = 1 => 15 pairs (_) G5,H5: 1.. / G5 = 1 => 15 pairs (_) / H5 = 1 => 0 pairs (X) A3,H3: 1.. / A3 = 1 => 0 pairs (X) / H3 = 1 => 0 pairs (_) G2,I2: 2.. / G2 = 2 => 22 pairs (_) / I2 = 2 => 14 pairs (_) A4,A6: 2.. / A4 = 2 => 17 pairs (_) / A6 = 2 => 12 pairs (_) A4,G4: 2.. / A4 = 2 => 17 pairs (_) / G4 = 2 => 12 pairs (_) I2,I6: 2.. / I2 = 2 => 14 pairs (_) / I6 = 2 => 22 pairs (_) A4,A6: 3.. / A4 = 3 => 12 pairs (_) / A6 = 3 => 17 pairs (_) G7,I7: 3.. / G7 = 3 => 20 pairs (_) / I7 = 3 => 22 pairs (_) H1,I1: 4.. / H1 = 4 => 15 pairs (_) / I1 = 4 => 12 pairs (_) C4,C5: 4.. / C4 = 4 => 16 pairs (_) / C5 = 4 => 0 pairs (X) C4,H4: 4.. / C4 = 4 => 16 pairs (_) / H4 = 4 => 0 pairs (X) I1,I5: 4.. / I1 = 4 => 12 pairs (_) / I5 = 4 => 15 pairs (_) G1,G2: 5.. / G1 = 5 => 18 pairs (_) / G2 = 5 => 0 pairs (*) F5,E6: 5.. / F5 = 5 => 0 pairs (X) / E6 = 5 => 0 pairs (_) A7,B7: 5.. / A7 = 5 => 0 pairs (X) / B7 = 5 => 0 pairs (_) A3,E3: 5.. / A3 = 5 => 0 pairs (*) / E3 = 5 => 0 pairs (X) B6,E6: 5.. / B6 = 5 => 0 pairs (X) / E6 = 5 => 0 pairs (_) C2,C5: 5.. / C2 = 5 => 0 pairs (X) / C5 = 5 => 0 pairs (_) A7,C9: 6.. / A7 = 6 => 0 pairs (X) / C9 = 6 => 20 pairs (_) A5,A7: 6.. / A5 = 6 => 20 pairs (_) / A7 = 6 => 0 pairs (X) E2,E3: 7.. / E2 = 7 => 0 pairs (*) / E3 = 7 => 0 pairs (X) B5,B6: 7.. / B5 = 7 => 16 pairs (_) / B6 = 7 => 0 pairs (X) H9,I9: 7.. / H9 = 7 => 17 pairs (_) / I9 = 7 => 19 pairs (_) H1,I1: 8.. / H1 = 8 => 12 pairs (_) / I1 = 8 => 15 pairs (_) F4,F5: 8.. / F4 = 8 => 0 pairs (X) / F5 = 8 => 0 pairs (_) A1,C2: 9.. / A1 = 9 => 0 pairs (X) / C2 = 9 => 0 pairs (_) E1,E2: 9.. / E1 = 9 => 0 pairs (*) / E2 = 9 => 0 pairs (X) A1,E1: 9.. / A1 = 9 => 0 pairs (X) / E1 = 9 => 0 pairs (_) C2,E2: 9.. / C2 = 9 => 0 pairs (*) / E2 = 9 => 0 pairs (X) * DURATION: 0:00:35.571432 START: 00:45:07.332055 END: 00:45:42.903487 2019-05-01 * CP COUNT: (31) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,A6,B4,B7,C2,C9,E6,F2,F4,G7,H1,I1,I3) * .372.....86.4......428.39.....71...5...32......19.4.....8147.2.72368945141.5328.. * PAIR C2: 5,9 BLK 1 A1: 5,9,1 # reduction candidate for 5,9 A1: 5,9 => CTR * .372.....86.4.....1428539.....71...5...325....51964...598147.2.7236894514165328.. A1: 1 => SOLVED * 137295648869471532542863917394716285675328194281954763958147326723689451416532879 * PAIR C2: 5,9 ROW 2 E2: 5,9,7 # reduction candidate for 5,9 E2: 5,9 => CTR * .372.....86.4.....542873916...71...5..532.1....1954....58147.2.72368945141.5328.. E2: 7 => SOLVED * 137295648869471532542863917394716285675328194281954763958147326723689451416532879 * PAIR C2: 5,9 COL C C5: 5,9,4,6 # reduction candidate for 5,9 C5: 4,6 => CTR * .372.....865491....428.39.....71...5...32......19.4.....8147.2.72368945141.5328.. C5: 5,9 # 20 pairs * PAIR A3: 1,5 BLK 1 A1: 1,5,9 # reduction candidate for 1,5 A1: 1,5 => SOLVED * 137295648869471532542863917394716285675328194281954763958147326723689451416532879 A1: 9 => CTR * 9372.....865491....428.39.....71...5...32......19.4.....8147.2.72368945141.5328.. * PAIR F2: 1,5 BLK 2 F1: 1,5,6 # reduction candidate for 1,5 F1: 1,5 => SOLVED * 137295648869471532542863917394716285675328194281954763958147326723689451416532879 F1: 6 => CTR * .372.6...86.4.1....428.39.....718..5...325....51964...598147.2.72368945141.5328.. * PAIR F2: 1,5 ROW 2 G2: 1,5,2,3,7 # reduction candidate for 1,5 G2: 1,5 => SOLVED * 137295648869471532542863917394716285675328194281954763958147326723689451416532879 G2: 2,3,7 # 18 pairs * PAIR H1: 4,8 COL H H4: 4,8,3,6,9 # reduction candidate for 4,8 H4: 4,8 # 17 pairs H5: 4,8,1,6,7,9 # reduction candidate for 4,8 H5: 4,8 # 17 pairs * PAIR I1: 4,8 COL I I5: 4,8,6,7,9 # reduction candidate for 4,8 I5: 6,7,9 # 21 pairs I5: 4,8 # 16 pairs * PAIR I3: 6,7 BLK 3 H3: 6,7,1 # reduction candidate for 6,7 H3: 6,7 => CTR * .372.....86.4.....1428539.....71...5...325....51964...598147.2.7236894514165328.. H3: 1 => SOLVED * 137295648869471532542863917394716285675328194281954763958147326723689451416532879 * PAIR I3: 6,7 ROW 3 E3: 6,7,5 # reduction candidate for 6,7 E3: 6,7 => SOLVED * 137295648869471532542863917394716285675328194281954763958147326723689451416532879 E3: 5 => CTR * .372.....86.47.....428539.....71...5...325....51964...598147.2.7236894514165328.. * PAIR I3: 6,7 COL I I5: 6,7,4,8,9 # reduction candidate for 6,7 I5: 6,7 => CTR * .372...8486.4..7325428739.....71...56..32...7.71954.68..8147623723689451416532879 I5: 4,8,9 # 14 pairs I6: 6,7,2,3,8 # reduction candidate for 6,7 I6: 6,7 # 23 pairs I9: 6,7,9 # reduction candidate for 6,7 I9: 6,7 # 17 pairs * PAIR A4: 2,3 ROW 4 G4: 2,3,6 # reduction candidate for 2,3 G4: 6 => CTR * .372.6...86.4.1.73.428739.62.4718635...325...351964.82..814732.72368945141.5328.. G4: 2,3 # 15 pairs * PAIR B4: 8,9 BLK 4 B5: 8,9,5,7 # reduction candidate for 8,9 B5: 8,9 => CTR * 13729....869471532542863917..471...56.5328174.71954...958147.2.72368945141653289. B5: 5,7 # 15 pairs * PAIR B4: 8,9 ROW 4 H4: 8,9,3,4,6 # reduction candidate for 8,9 H4: 8,9 => SOLVED * 137295648869471532542863917394716285675328194281954763958147326723689451416532879 H4: 3,4,6 # 15 pairs * PAIR A6: 2,3 ROW 6 G6: 2,3,6,7 # reduction candidate for 2,3 G6: 2,3 # 22 pairs I6: 2,3,6,7,8 # reduction candidate for 2,3 I6: 2,3 # 18 pairs * PAIR F4: 6,8 BLK 5 F5: 6,8,5 # reduction candidate for 6,8 F5: 6,8 => SOLVED * 137295648869471532542863917394716285675328194281954763958147326723689451416532879 F5: 5 => CTR * .372.....86.4......428.39.....718..5...325....51964...598147.2.72368945141.5328.. * PAIR F4: 6,8 ROW 4 H4: 6,8,3,4,9 # reduction candidate for 6,8 H4: 6,8 => SOLVED * 137295648869471532542863917394716285675328194281954763958147326723689451416532879 H4: 3,4,9 # 14 pairs * PAIR E6: 5,6 BLK 5 F5: 5,6,8 # reduction candidate for 5,6 F5: 5,6 => CTR * .372.....86.4.....5428.391..9.718..56..32......1954....58147.2.72368945141.5328.. F5: 8 => SOLVED * 137295648869471532542863917394716285675328194281954763958147326723689451416532879 * PAIR E6: 5,6 COL E E1: 5,6,9 # reduction candidate for 5,6 E1: 5,6 => CTR * 9372.....865491....428.39.....71...5...32......19.4.....8147.2.72368945141.5328.. E1: 9 => SOLVED * 137295648869471532542863917394716285675328194281954763958147326723689451416532879 E3: 5,6,7 # reduction candidate for 5,6 E3: 5,6 => SOLVED * 137295648869471532542863917394716285675328194281954763958147326723689451416532879 E3: 7 => CTR * .372.....86.4.....542873916...71...5..532.1....1954....58147.2.72368945141.5328.. * PAIR B7: 5,9 BLK 7 A7: 5,9,6 # reduction candidate for 5,9 A7: 6 => CTR * 9372.....865491....428.39.....71...5...32......19.4...6581473297236894514195328.. A7: 5,9 # 20 pairs * PAIR B7: 5,9 COL B B5: 5,9,7,8 # reduction candidate for 5,9 B5: 5,9 => CTR * 1372956..86.4.....5428.391..8.716..5..53281...71954....58147.2.7236894514165328.. B5: 7,8 # 15 pairs * PAIR C9: 6,9 BLK 7 A7: 6,9,5 # reduction candidate for 6,9 A7: 6,9 => SOLVED * 137295648869471532542863917394716285675328194281954763958147326723689451416532879 A7: 5 => CTR * 9372.....865491....428.39.....71...56..32......19.4...598147.2.7236894514165328.. * PAIR C9: 6,9 ROW 9 H9: 6,9,7 # reduction candidate for 6,9 H9: 6,9 # 19 pairs I9: 6,9,7 # reduction candidate for 6,9 I9: 6,9 # 17 pairs * PAIR C9: 6,9 COL C C4: 6,9,4 # reduction candidate for 6,9 C4: 6,9 => CTR * .372...84865491....428.39.....71..45..432......19.4.....8147.2.72368945141.5328.. C4: 4 # 16 pairs C5: 6,9,4,5 # reduction candidate for 6,9 C5: 6,9 => CTR * .372.....865491....428.39.....71...5...32......19.4.....8147.2.72368945141.5328.. C5: 4,5 # 15 pairs * PAIR G7: 3,6 BLK 9 I7: 3,6,9 # reduction candidate for 3,6 I7: 9 => CTR * 9372.....865491....428.39.....71...5...32......19.4.....81473297236894514195328.. I7: 3,6 # 20 pairs * PAIR G7: 3,6 COL G G4: 3,6,2 # reduction candidate for 3,6 G4: 3,6 # 17 pairs G6: 3,6,2,7 # reduction candidate for 3,6 G6: 3,6 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060717-absurd-base-pr-000.dot * REASONING * DIS # A1: 5,9 => CTR => A1: 1 * PRF # A1: 1 => SOL * DIS # E2: 5,9 => CTR => E2: 7 * PRF # E2: 7 => SOL * DIS # C5: 4,6 => CTR => C5: 5,9 * PRF # A1: 1,5 => SOL * DIS # A1: 9 => CTR => A1: 1,5 * PRF # F1: 1,5 => SOL * DIS # F1: 6 => CTR => F1: 1,5 * PRF # G2: 1,5 => SOL * DIS # H3: 6,7 => CTR => H3: 1 * PRF # H3: 1 => SOL * PRF # E3: 6,7 => SOL * DIS # E3: 5 => CTR => E3: 6,7 * DIS # I5: 6,7 => CTR => I5: 4,8,9 * DIS # G4: 6 => CTR => G4: 2,3 * DIS # B5: 8,9 => CTR => B5: 5,7 * PRF # H4: 8,9 => SOL * PRF # F5: 6,8 => SOL * DIS # F5: 5 => CTR => F5: 6,8 * PRF # H4: 6,8 => SOL * DIS # F5: 5,6 => CTR => F5: 8 * PRF # F5: 8 => SOL * DIS # E1: 5,6 => CTR => E1: 9 * PRF # E1: 9 => SOL * PRF # E3: 5,6 => SOL * DIS # E3: 7 => CTR => E3: 5,6 * DIS # A7: 6 => CTR => A7: 5,9 * DIS # B5: 5,9 => CTR => B5: 7,8 * PRF # A7: 6,9 => SOL * DIS # A7: 5 => CTR => A7: 6,9 * DIS # C4: 6,9 => CTR => C4: 4 * DIS # C5: 6,9 => CTR => C5: 4,5 * DIS # I7: 9 => CTR => I7: 3,6 * CNT 34 HDP CHAINS / 58 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,A6,B4,B7,C2,C9,E6,F2,F4,G7,H1,I1,I3) * .372.....86.4......428.39.....71...5...32......19.4.....8147.2.72368945141.5328.. * PAIR C2: 5,9 BLK 1 A1: 5,9,1 # reduction candidate for 5,9 A1: 5,9 => CTR * .372.....86.4.....1428539.....71...5...325....51964...598147.2.7236894514165328.. A1: 1 => SOLVED * 137295648869471532542863917394716285675328194281954763958147326723689451416532879 * DURATION: 0:00:02.154174 START: 00:46:21.674714 END: 00:46:23.828888 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060717-absurd-base-pr-001.dot * REASONING * DIS # A1: 5,9 => CTR => A1: 1 * PRF A1: 1 => SOL * STA A1: 1 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006, 20060717, absurd
Solution
position: 137295648869471532542863917394716285675328194281954763958147326723689451416532879 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 # A1: 5,9 => CTR => A1: 1 * PRF # A1: 1 => SOL * DIS # E2: 5,9 => CTR => E2: 7 * PRF # E2: 7 => SOL * INC # C5: 5,9 => UNS * DIS # C5: 4,6 => CTR => C5: 5,9 * PRF # A1: 1,5 => SOL * DIS # A1: 9 => CTR => A1: 1,5 * PRF # F1: 1,5 => SOL * DIS # F1: 6 => CTR => F1: 1,5 * PRF # G2: 1,5 => SOL * INC # G2: 2,3,7 => UNS * INC # H4: 4,8 => UNS * INC # H5: 4,8 => UNS * INC # I5: 4,8 => UNS * INC # I5: 6,7,9 => UNS * DIS # H3: 6,7 => CTR => H3: 1 * PRF # H3: 1 => SOL * PRF # E3: 6,7 => SOL * DIS # E3: 5 => CTR => E3: 6,7 * DIS # I5: 6,7 => CTR => I5: 4,8,9 * INC # I5: 4,8,9 => UNS * INC # I6: 6,7 => UNS * INC # I9: 6,7 => UNS * INC # G4: 2,3 => UNS * DIS # G4: 6 => CTR => G4: 2,3 * DIS # B5: 8,9 => CTR => B5: 5,7 * INC # B5: 5,7 => UNS * PRF # H4: 8,9 => SOL * INC # H4: 3,4,6 => UNS * INC # G6: 2,3 => UNS * INC # I6: 2,3 => UNS * PRF # F5: 6,8 => SOL * DIS # F5: 5 => CTR => F5: 6,8 * PRF # H4: 6,8 => SOL * INC # H4: 3,4,9 => UNS * DIS # F5: 5,6 => CTR => F5: 8 * PRF # F5: 8 => SOL * DIS # E1: 5,6 => CTR => E1: 9 * PRF # E1: 9 => SOL * PRF # E3: 5,6 => SOL * DIS # E3: 7 => CTR => E3: 5,6 * INC # A7: 5,9 => UNS * DIS # A7: 6 => CTR => A7: 5,9 * DIS # B5: 5,9 => CTR => B5: 7,8 * INC # B5: 7,8 => UNS * PRF # A7: 6,9 => SOL * DIS # A7: 5 => CTR => A7: 6,9 * INC # H9: 6,9 => UNS * INC # I9: 6,9 => UNS * DIS # C4: 6,9 => CTR => C4: 4 * INC # C4: 4 => UNS * DIS # C5: 6,9 => CTR => C5: 4,5 * INC # C5: 4,5 => UNS * INC # I7: 3,6 => UNS * DIS # I7: 9 => CTR => I7: 3,6 * INC # G4: 3,6 => UNS * INC # G6: 3,6 => UNS * CNT 58 HDP CHAINS / 58 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A1: 5,9 => CTR => A1: 1 * PRF A1: 1 => SOL * STA A1: 1 * CNT 2 HDP CHAINS / 1 HYP OPENED