Analysis of zz-www.sudokuoftheday.co.uk-20060704-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: ....7...62.5.6...1.6.52.8...3.85..4...2....78..6..7..5.8.........3......5213..... initial
Autosolve
position: ..8.7...62.5.68.31.6.52.89..3.85..4..52....788.6..7..5.8......3..3......5213..... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A1: 1,3 => CTR => A1: 4,9 * DIS # B2: 9 => CTR => B2: 4,7 * DIS # C7: 4,7 => CTR => C7: 9 * DIS # F1: 4,9 => CTR => F1: 1,3 * DIS # B2: 4,9 => CTR => B2: 7 * DIS # D5: 4,9 => CTR => D5: 1,6 * DIS # D6: 4,9 => CTR => D6: 1,2 * DIS # D7: 4,9 => CTR => D7: 1,2,6,7 * DIS # D8: 4,9 => CTR => D8: 1,2,6,7 * DIS # F1: 4,9 => CTR => F1: 1,3 * DIS # H7: 2,5 => CTR => H7: 1,6 * DIS # H8: 2,5 => CTR => H8: 1,6,8 * DIS # B2: 9 => CTR => B2: 4,7 * DIS # G9: 9 => CTR => G9: 4,7 * DIS # I9: 9 => CTR => I9: 4,7 * DIS # A4: 7,9 => CTR => A4: 1 * PRF # A4: 1 => SOL * DIS # C7: 4 => CTR => C7: 7,9 * DIS # G4: 2,9 => CTR => G4: 1,6 * DIS # G6: 2,9 => CTR => G6: 1,3 * PRF # F4: 2,9 => SOL * DIS # F4: 1,6 => CTR => F4: 2,9 * DIS # I8: 4 => CTR => I8: 2,9 * DIS # G4: 1,2 => CTR => G4: 6,9 * DIS # G6: 1,2 => CTR => G6: 3,9 * DIS # D6: 4,9 => CTR => D6: 1,2 * CNT 26 HDP CHAINS / 55 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A1: 1,3 => CTR => A1: 4,9 * DIS A1: 4,9 # B2: 9 => CTR => B2: 4,7 * DIS A1: 4,9 + B2: 4,7 # C7: 4,7 => CTR => C7: 9 * PRF A1: 4,9 + B2: 4,7 + C7: 9 => SOL * STA A1: 4,9 + B2: 4,7 + C7: 9 * CNT 4 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....7...62.5.6...1.6.52.8...3.85..4...2....78..6..7..5.8.........3......5213..... | initial |
| ..8.7...62.5.68.31.6.52.89..3.85..4..52....788.6..7..5.8......3..3......5213..... | autosolve |
| 918473256275968431364521897137852649452639178896147325789214563643785912521396784 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (12) A3: 1,3 C3: 4,7 D2: 4,9 F3: 1,3 G1: 2,5 H1: 2,5 G2: 4,7 I3: 4,7 C4: 7,9 I4: 2,9 H6: 1,2 H9: 6,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A3,F3: 1.. / A3 = 1 => 0 pairs (X) / F3 = 1 => 16 pairs (_) B1,B6: 1.. / B1 = 1 => 16 pairs (_) / B6 = 1 => 0 pairs (X) G1,H1: 2.. / G1 = 2 => 10 pairs (_) / H1 = 2 => 0 pairs (X) F4,D6: 2.. / F4 = 2 => 0 pairs (*) / D6 = 2 => 0 pairs (X) I4,I8: 2.. / I4 = 2 => 0 pairs (X) / I8 = 2 => 0 pairs (_) A1,A3: 3.. / A1 = 3 => 0 pairs (X) / A3 = 3 => 16 pairs (_) F1,F3: 3.. / F1 = 3 => 16 pairs (_) / F3 = 3 => 0 pairs (X) E5,E6: 3.. / E5 = 3 => 12 pairs (_) / E6 = 3 => 0 pairs (X) G5,G6: 3.. / G5 = 3 => 0 pairs (X) / G6 = 3 => 12 pairs (_) A1,F1: 3.. / A1 = 3 => 0 pairs (X) / F1 = 3 => 16 pairs (_) A3,F3: 3.. / A3 = 3 => 16 pairs (_) / F3 = 3 => 0 pairs (X) E5,G5: 3.. / E5 = 3 => 12 pairs (_) / G5 = 3 => 0 pairs (X) E6,G6: 3.. / E6 = 3 => 0 pairs (X) / G6 = 3 => 12 pairs (_) G2,I3: 4.. / G2 = 4 => 13 pairs (_) / I3 = 4 => 0 pairs (X) A5,B6: 4.. / A5 = 4 => 13 pairs (_) / B6 = 4 => 19 pairs (_) C3,I3: 4.. / C3 = 4 => 13 pairs (_) / I3 = 4 => 0 pairs (X) C3,C7: 4.. / C3 = 4 => 13 pairs (_) / C7 = 4 => 0 pairs (X) G1,H1: 5.. / G1 = 5 => 0 pairs (X) / H1 = 5 => 10 pairs (_) F7,F8: 5.. / F7 = 5 => 12 pairs (_) / F8 = 5 => 12 pairs (_) G4,G5: 6.. / G4 = 6 => 12 pairs (_) / G5 = 6 => 0 pairs (X) A7,A8: 6.. / A7 = 6 => 13 pairs (_) / A8 = 6 => 12 pairs (_) F4,G4: 6.. / F4 = 6 => 0 pairs (X) / G4 = 6 => 12 pairs (_) F9,H9: 6.. / F9 = 6 => 12 pairs (_) / H9 = 6 => 12 pairs (_) B2,C3: 7.. / B2 = 7 => 13 pairs (_) / C3 = 7 => 0 pairs (X) G2,I3: 7.. / G2 = 7 => 0 pairs (X) / I3 = 7 => 13 pairs (_) A4,C4: 7.. / A4 = 7 => 0 pairs (X) / C4 = 7 => 19 pairs (_) D7,D8: 7.. / D7 = 7 => 13 pairs (_) / D8 = 7 => 13 pairs (_) G9,I9: 7.. / G9 = 7 => 13 pairs (_) / I9 = 7 => 0 pairs (X) B2,G2: 7.. / B2 = 7 => 13 pairs (_) / G2 = 7 => 0 pairs (X) C3,I3: 7.. / C3 = 7 => 0 pairs (X) / I3 = 7 => 13 pairs (_) B2,B8: 7.. / B2 = 7 => 13 pairs (_) / B8 = 7 => 0 pairs (X) G2,G9: 7.. / G2 = 7 => 0 pairs (X) / G9 = 7 => 13 pairs (_) I3,I9: 7.. / I3 = 7 => 13 pairs (_) / I9 = 7 => 0 pairs (X) E8,E9: 8.. / E8 = 8 => 12 pairs (_) / E9 = 8 => 12 pairs (_) H8,H9: 8.. / H8 = 8 => 12 pairs (_) / H9 = 8 => 12 pairs (_) E8,H8: 8.. / E8 = 8 => 12 pairs (_) / H8 = 8 => 12 pairs (_) E9,H9: 8.. / E9 = 8 => 12 pairs (_) / H9 = 8 => 12 pairs (_) B2,D2: 9.. / B2 = 9 => 0 pairs (X) / D2 = 9 => 14 pairs (_) C4,C7: 9.. / C4 = 9 => 0 pairs (X) / C7 = 9 => 19 pairs (_) * DURATION: 0:00:45.528638 START: 00:19:11.306153 END: 00:19:56.834791 2019-05-01 * CP COUNT: (39) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,C3,C4,D2,F3,G1,G2,H1,H6,H9,I3,I4) * ..8.7...62.5.68.31.6.52.89..3.85..4..52....788.6..7..5.8......3..3......5213..... * PAIR A3: 1,3 BLK 1 A1: 1,3,4,9 # reduction candidate for 1,3 A1: 1,3 => CTR * ..8.7.2562.5.68.31.6.52.89..3.852.4..52....78816..7.25.8......3..3.....25213..... A1: 4,9 # 16 pairs * PAIR C3: 4,7 BLK 1 B2: 4,7,9 # reduction candidate for 4,7 B2: 9 => CTR * .18973..6295468731367521894739856.42.52....788.62.7.15.847....3.73.....95213..4.7 B2: 4,7 # 14 pairs * PAIR C3: 4,7 COL C C7: 4,7,9 # reduction candidate for 4,7 C7: 4,7 => CTR * .18.7...62.5.68.3136.52189..3985..42.52....788.62.7.15.8......3..3......5213..... C7: 9 # 19 pairs * PAIR D2: 4,9 BLK 2 D1: 4,9,1 # reduction candidate for 4,9 D1: 4,9 # 16 pairs F1: 4,9,1,3 # reduction candidate for 4,9 F1: 4,9 => CTR * 3.817.2562.5.68.3116.52389..3.852.4..52....78816..7.25.8......3..3.....25213..... F1: 1,3 # 16 pairs * PAIR D2: 4,9 ROW 2 B2: 4,9,7 # reduction candidate for 4,9 B2: 4,9 => CTR * .18.7...6295468731367521894739856.42.52....788.62.7.15.847....3.73.....95213..4.7 B2: 7 # 13 pairs * PAIR D2: 4,9 COL D D5: 4,9,1,6 # reduction candidate for 4,9 D5: 4,9 => CTR * ..817...62.5.68.3116.52389..3.85..4..52....788162.7..5.8......3..3....8.52138..6. D5: 1,6 # 13 pairs D6: 4,9,1,2 # reduction candidate for 4,9 D6: 4,9 => CTR * .18.7...6275968.31.6452.897137852649.52....788.6..7..5.892....3..37....25213..7.4 D6: 1,2 # 16 pairs D7: 4,9,1,2,6,7 # reduction candidate for 4,9 D7: 4,9 => CTR * .18.7...6275968431.6452.897.3.85..4..526...788.62.7.15.8.4....3..37.....5213..7.4 D7: 1,2,6,7 # 12 pairs D8: 4,9,1,2,6,7 # reduction candidate for 4,9 D8: 4,9 => CTR * .18.7...62.5.68.3136.52189.137859642.52614378846237915.8974.1.3..3......5213..... D8: 1,2,6,7 # 12 pairs * PAIR F3: 1,3 BLK 2 F1: 1,3,4,9 # reduction candidate for 1,3 F1: 4,9 => CTR * 3.817.2562.5.68.3116.52389..3.852.4..52....78816..7.25.8......3..3.....25213..... F1: 1,3 # 16 pairs * PAIR G1: 2,5 COL G G7: 2,5,1,4,9 # reduction candidate for 2,5 G7: 2,5 # 13 pairs G8: 2,5,1,4,9 # reduction candidate for 2,5 G8: 2,5 # 13 pairs * PAIR H1: 2,5 COL H H7: 2,5,1,6 # reduction candidate for 2,5 H7: 2,5 => CTR * 918473..627596843136452189713785..4.452....78896247315.89.14..3.43......5213..7.4 H7: 1,6 # 13 pairs H8: 2,5,1,6,8 # reduction candidate for 2,5 H8: 2,5 => CTR * .18.73..627596843136452189713785.64.452619378896437.15789.4..6364378.1..521396.8. H8: 1,6,8 # 12 pairs * PAIR G2: 4,7 ROW 2 B2: 4,7,9 # reduction candidate for 4,7 B2: 9 => CTR * .18973..6295468731367521894739856.42.52....788.62.7.15.847....3.73.....95213..4.7 B2: 4,7 # 14 pairs * PAIR G2: 4,7 COL G G9: 4,7,9 # reduction candidate for 4,7 G9: 9 => CTR * ..8.7...62.5.68731.6752.89473985..42.52....788.62.7.15.847....3.73...4.95213..... G9: 4,7 # 13 pairs * PAIR I3: 4,7 COL I I9: 4,7,9 # reduction candidate for 4,7 I9: 9 => CTR * 918473..6275968431364521897.3.85..42.52....788462.7.1548......36937....45213..7.9 I9: 4,7 # 14 pairs * PAIR C4: 7,9 BLK 4 A4: 7,9,1 # reduction candidate for 7,9 A4: 7,9 => CTR * .18.7...62.5.68.3136.52189..3.856.42.52....788.62.7.15.8......3..3......5213..... A4: 1 => SOLVED * 918473256275968431364521897137852649452639178896147325789214563643785912521396784 * PAIR C4: 7,9 COL C C7: 7,9,4 # reduction candidate for 7,9 C7: 4 => CTR * .18.7...62.5.68.31367521894.3985..42.52....788.62.7.15.84.....3..3......5213..... C7: 7,9 # 13 pairs * PAIR I4: 2,9 BLK 6 G4: 2,9,1,6 # reduction candidate for 2,9 G4: 2,9 => CTR * .18.73..6275968431364521897137856.4..5213.678896247315.89.1...3.43.9.182521384769 G4: 1,6 # 13 pairs G6: 2,9,1,3 # reduction candidate for 2,9 G6: 2,9 => CTR * .18.73..627596843136452189713785.64..52...378896437.15.89.....3..3......5213..... G6: 1,3 # 13 pairs * PAIR I4: 2,9 ROW 4 F4: 2,9,1,6 # reduction candidate for 2,9 F4: 2,9 => SOLVED * 918473256275968431364521897137852649452639178896147325789214563643785912521396784 F4: 1,6 => CTR * .18.73..6275968431364521897137856.4..52.3.678896247315.89.1...3.43...18.52138.764 * PAIR I4: 2,9 COL I I8: 2,9,4 # reduction candidate for 2,9 I8: 4 => CTR * .18.7...62.5.6843136452189713785..42.52....788462.7.15489.....3..3.....45213....9 I8: 2,9 # 14 pairs * PAIR H6: 1,2 BLK 6 G4: 1,2,6,9 # reduction candidate for 1,2 G4: 1,2 => CTR * .18.73526275968431364521897137856249.5213.678896247315.89.1...3..3....8252138..6. G4: 6,9 # 13 pairs G6: 1,2,3,9 # reduction candidate for 1,2 G6: 1,2 => CTR * ..8.7...6275968431.6452.897137852649.526..378896437..57892....36437..9.25213..7.4 G6: 3,9 # 13 pairs * PAIR H6: 1,2 ROW 6 D6: 1,2,4,9 # reduction candidate for 1,2 D6: 4,9 => CTR * .18.7...6275968.31.6452.897137852649.52....788.6..7..5.892....3..37....25213..7.4 D6: 1,2 # 16 pairs * PAIR H6: 1,2 COL H H7: 1,2,5,6 # reduction candidate for 1,2 H7: 1,2 # 12 pairs H8: 1,2,5,6,8 # reduction candidate for 1,2 H8: 1,2 # 11 pairs * PAIR H9: 6,8 BLK 9 H8: 6,8,1,2,5 # reduction candidate for 6,8 H8: 6,8 # 13 pairs H8: 1,2,5 # 12 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060704-absurd-base-pr-000.dot * REASONING * DIS # A1: 1,3 => CTR => A1: 4,9 * DIS # B2: 9 => CTR => B2: 4,7 * DIS # C7: 4,7 => CTR => C7: 9 * DIS # F1: 4,9 => CTR => F1: 1,3 * DIS # B2: 4,9 => CTR => B2: 7 * DIS # D5: 4,9 => CTR => D5: 1,6 * DIS # D6: 4,9 => CTR => D6: 1,2 * DIS # D7: 4,9 => CTR => D7: 1,2,6,7 * DIS # D8: 4,9 => CTR => D8: 1,2,6,7 * DIS # F1: 4,9 => CTR => F1: 1,3 * DIS # H7: 2,5 => CTR => H7: 1,6 * DIS # H8: 2,5 => CTR => H8: 1,6,8 * DIS # B2: 9 => CTR => B2: 4,7 * DIS # G9: 9 => CTR => G9: 4,7 * DIS # I9: 9 => CTR => I9: 4,7 * DIS # A4: 7,9 => CTR => A4: 1 * PRF # A4: 1 => SOL * DIS # C7: 4 => CTR => C7: 7,9 * DIS # G4: 2,9 => CTR => G4: 1,6 * DIS # G6: 2,9 => CTR => G6: 1,3 * PRF # F4: 2,9 => SOL * DIS # F4: 1,6 => CTR => F4: 2,9 * DIS # I8: 4 => CTR => I8: 2,9 * DIS # G4: 1,2 => CTR => G4: 6,9 * DIS # G6: 1,2 => CTR => G6: 3,9 * DIS # D6: 4,9 => CTR => D6: 1,2 * CNT 26 HDP CHAINS / 55 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,C3,C4,D2,F3,G1,G2,H1,H6,H9,I3,I4) * ..8.7...62.5.68.31.6.52.89..3.85..4..52....788.6..7..5.8......3..3......5213..... * PAIR A3: 1,3 BLK 1 A1: 1,3,4,9 # reduction candidate for 1,3 A1: 1,3 => CTR * ..8.7.2562.5.68.31.6.52.89..3.852.4..52....78816..7.25.8......3..3.....25213..... * PAIR C3: 4,7 BLK 1 B2: 4,7,9 # reduction candidate for 4,7 B2: 9 => CTR * .18.73..629546873136752189473985.142.52....788.6..7..5.8......3..3......5213..... * PAIR C3: 4,7 COL C C7: 4,7,9 # reduction candidate for 4,7 C7: 4,7 => CTR * 918473..62.5968.3136.52189..3985..42.52....788462.7.15.8......3.93.....45213....9 C7: 9 => SOLVED * 918473256275968431364521897137852649452639178896147325789214563643785912521396784 * DURATION: 0:00:05.541284 START: 00:20:31.818431 END: 00:20:37.359715 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060704-absurd-base-pr-001.dot * REASONING * DIS # A1: 1,3 => CTR => A1: 4,9 * DIS A1: 4,9 # B2: 9 => CTR => B2: 4,7 * DIS A1: 4,9 + B2: 4,7 # C7: 4,7 => CTR => C7: 9 * PRF A1: 4,9 + B2: 4,7 + C7: 9 => SOL * STA A1: 4,9 + B2: 4,7 + C7: 9 * CNT 4 HDP CHAINS / 4 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006, 20060704, absurd
Solution
position: 918473256275968431364521897137852649452639178896147325789214563643785912521396784 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: 1,3 => CTR => A1: 4,9 * INC # A1: 4,9 => UNS * INC # B2: 4,7 => UNS * DIS # B2: 9 => CTR => B2: 4,7 * DIS # C7: 4,7 => CTR => C7: 9 * INC # C7: 9 => UNS * INC # D1: 4,9 => UNS * DIS # F1: 4,9 => CTR => F1: 1,3 * INC # F1: 1,3 => UNS * DIS # B2: 4,9 => CTR => B2: 7 * INC # B2: 7 => UNS * DIS # D5: 4,9 => CTR => D5: 1,6 * INC # D5: 1,6 => UNS * DIS # D6: 4,9 => CTR => D6: 1,2 * INC # D6: 1,2 => UNS * DIS # D7: 4,9 => CTR => D7: 1,2,6,7 * INC # D7: 1,2,6,7 => UNS * DIS # D8: 4,9 => CTR => D8: 1,2,6,7 * INC # D8: 1,2,6,7 => UNS * INC # F1: 1,3 => UNS * DIS # F1: 4,9 => CTR => F1: 1,3 * INC # G7: 2,5 => UNS * INC # G8: 2,5 => UNS * DIS # H7: 2,5 => CTR => H7: 1,6 * INC # H7: 1,6 => UNS * DIS # H8: 2,5 => CTR => H8: 1,6,8 * INC # H8: 1,6,8 => UNS * INC # B2: 4,7 => UNS * DIS # B2: 9 => CTR => B2: 4,7 * INC # G9: 4,7 => UNS * DIS # G9: 9 => CTR => G9: 4,7 * INC # I9: 4,7 => UNS * DIS # I9: 9 => CTR => I9: 4,7 * DIS # A4: 7,9 => CTR => A4: 1 * PRF # A4: 1 => SOL * INC # C7: 7,9 => UNS * DIS # C7: 4 => CTR => C7: 7,9 * DIS # G4: 2,9 => CTR => G4: 1,6 * INC # G4: 1,6 => UNS * DIS # G6: 2,9 => CTR => G6: 1,3 * INC # G6: 1,3 => UNS * PRF # F4: 2,9 => SOL * DIS # F4: 1,6 => CTR => F4: 2,9 * INC # I8: 2,9 => UNS * DIS # I8: 4 => CTR => I8: 2,9 * DIS # G4: 1,2 => CTR => G4: 6,9 * INC # G4: 6,9 => UNS * DIS # G6: 1,2 => CTR => G6: 3,9 * INC # G6: 3,9 => UNS * INC # D6: 1,2 => UNS * DIS # D6: 4,9 => CTR => D6: 1,2 * INC # H7: 1,2 => UNS * INC # H8: 1,2 => UNS * INC # H8: 6,8 => UNS * INC # H8: 1,2,5 => UNS * CNT 55 HDP CHAINS / 55 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A1: 1,3 => CTR => A1: 4,9 * INC A1: 4,9 # B2: 4,7 => UNS * DIS A1: 4,9 # B2: 9 => CTR => B2: 4,7 * DIS A1: 4,9 + B2: 4,7 # C7: 4,7 => CTR => C7: 9 * PRF A1: 4,9 + B2: 4,7 + C7: 9 => SOL * STA A1: 4,9 + B2: 4,7 + C7: 9 * CNT 5 HDP CHAINS / 4 HYP OPENED