Analysis of zz-www.sudokuoftheday.co.uk-20060617-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006
level: medium
position: ....5..84.65..4......1..3..........7.3.6.725..2....9..3....8..2..8.1.....1.2...7. initial
Autosolve
position: 1.3.52684.65..4721..21.6395....2...7.316.7258.2....9..3....8..22.8.1.....1.2..87. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B7: 7,9 => CTR => B7: 4,5 * PRF # B7: 4,5 => SOL * PRF # B8: 7,9 => SOL * DIS # B8: 4,5 => CTR => B8: 7,9 * DIS # A4: 8,9 => CTR => A4: 4,5,6 * PRF # D7: 7,9 => SOL * DIS # D7: 4,5 => CTR => D7: 7,9 * DIS # D8: 7,9 => CTR => D8: 3,4,5 * PRF # D8: 3,4,5 => SOL * DIS # B3: 7,8 => CTR => B3: 4 * DIS # A4: 4,9 => CTR => A4: 5,6,8 * DIS # B4: 4,9 => CTR => B4: 5,8 * PRF # A9: 4,9 => SOL * DIS # E7: 4,9 => CTR => E7: 6,7 * DIS # E9: 4,9 => CTR => E9: 3,6 * DIS # B8: 4,5 => CTR => B8: 7,9 * PRF # B8: 7,9 => SOL * PRF # D8: 4,5 => SOL * DIS # E9: 3,9 => CTR => E9: 4,6 * DIS # F9: 3,9 => CTR => F9: 5 * CNT 20 HDP CHAINS / 56 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B7: 7,9 => CTR => B7: 4,5 * PRF B7: 4,5 => SOL * STA B7: 4,5 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....5..84.65..4......1..3..........7.3.6.725..2....9..3....8..2..8.1.....1.2...7. | initial |
| 1.3.52684.65..4721..21.6395....2...7.316.7258.2....9..3....8..22.8.1.....1.2..87. | autosolve |
| 193752684865394721742186395684529137931647258527831946356978412278413569419265873 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (12) B1: 7,9 A2: 8,9 D1: 7,9 E3: 7,8 A5: 4,9 E5: 4,9 G4: 1,4 I6: 3,6 H7: 1,4 G8: 4,5 H8: 3,6 I9: 3,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F4,F6: 1.. / F4 = 1 => 18 pairs (_) / F6 = 1 => 12 pairs (_) G7,H7: 1.. / G7 = 1 => 13 pairs (_) / H7 = 1 => 11 pairs (_) F6,H6: 1.. / F6 = 1 => 12 pairs (_) / H6 = 1 => 18 pairs (_) G4,G7: 1.. / G4 = 1 => 11 pairs (_) / G7 = 1 => 13 pairs (_) D2,E2: 3.. / D2 = 3 => 14 pairs (_) / E2 = 3 => 14 pairs (_) A3,B3: 4.. / A3 = 4 => 0 pairs (X) / B3 = 4 => 19 pairs (_) A5,E5: 4.. / A5 = 4 => 0 pairs (X) / E5 = 4 => 0 pairs (_) G7,G8: 5.. / G7 = 5 => 9 pairs (_) / G8 = 5 => 15 pairs (_) A9,F9: 5.. / A9 = 5 => 0 pairs (X) / F9 = 5 => 19 pairs (_) E7,E9: 6.. / E7 = 6 => 0 pairs (X) / E9 = 6 => 0 pairs (_) H8,I8: 6.. / H8 = 6 => 12 pairs (_) / I8 = 6 => 14 pairs (_) C7,E7: 6.. / C7 = 6 => 0 pairs (*) / E7 = 6 => 0 pairs (X) I6,I8: 6.. / I6 = 6 => 12 pairs (_) / I8 = 6 => 14 pairs (_) D1,E3: 7.. / D1 = 7 => 0 pairs (*) / E3 = 7 => 0 pairs (X) A6,C6: 7.. / A6 = 7 => 0 pairs (X) / C6 = 7 => 0 pairs (_) B1,D1: 7.. / B1 = 7 => 0 pairs (X) / D1 = 7 => 0 pairs (_) B8,D8: 7.. / B8 = 7 => 0 pairs (*) / D8 = 7 => 0 pairs (X) A3,A6: 7.. / A3 = 7 => 0 pairs (*) / A6 = 7 => 0 pairs (X) C6,C7: 7.. / C6 = 7 => 0 pairs (*) / C7 = 7 => 0 pairs (X) E3,E7: 7.. / E3 = 7 => 0 pairs (X) / E7 = 7 => 0 pairs (_) B3,B4: 8.. / B3 = 8 => 0 pairs (X) / B4 = 8 => 19 pairs (_) B1,A2: 9.. / B1 = 9 => 0 pairs (*) / A2 = 9 => 0 pairs (X) I8,I9: 9.. / I8 = 9 => 12 pairs (_) / I9 = 9 => 15 pairs (_) B1,D1: 9.. / B1 = 9 => 0 pairs (*) / D1 = 9 => 0 pairs (X) A5,E5: 9.. / A5 = 9 => 0 pairs (*) / E5 = 9 => 0 pairs (X) * DURATION: 0:00:26.664680 START: 23:54:42.087337 END: 23:55:08.752017 2019-04-30 * CP COUNT: (25) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A5,B1,D1,E3,E5,G4,G8,H7,H8,I6,I9) * 1.3.52684.65..4721..21.6395....2...7.316.7258.2....9..3....8..22.8.1.....1.2..87. * PAIR B1: 7,9 COL B B7: 7,9,4,5 # reduction candidate for 7,9 B7: 7,9 => CTR * 17395268496538472184217639558942...7431697258726...9.3397.68..22.871..36614235879 B7: 4,5 => SOLVED * 193752684865394721742186395684529137931647258527831946356978412278413569419265873 B8: 7,9,4,5 # reduction candidate for 7,9 B8: 7,9 => SOLVED * 193752684865394721742186395684529137931647258527831946356978412278413569419265873 B8: 4,5 => CTR * 17395268496538472184217639558942...7431697258726...9.33.7.68..22.871..36614235879 * PAIR A2: 8,9 ROW 2 D2: 8,9,3 # reduction candidate for 8,9 D2: 8,9 # 14 pairs E2: 8,9,3 # reduction candidate for 8,9 E2: 8,9 # 14 pairs * PAIR A2: 8,9 COL A A4: 8,9,4,5,6 # reduction candidate for 8,9 A4: 8,9 => CTR * 1.3.52684.65..4721742186395.8..2...74316972585278..9..3...78..2278.1....61.2.587. A4: 4,5,6 # 12 pairs * PAIR D1: 7,9 COL D D7: 7,9,4,5 # reduction candidate for 7,9 D7: 7,9 => SOLVED * 193752684865394721742186395684529137931647258527831946356978412278413569419265873 D7: 4,5 => CTR * 17395268496538472184217639558942...7431697258726...9.3397.68..22.871..36614235879 D8: 7,9,3,4,5 # reduction candidate for 7,9 D8: 7,9 => CTR * 17395268496538472184217639558942...7431697258726...9.3397.68..22.871..36614235879 D8: 3,4,5 => SOLVED * 193752684865394721742186395684529137931647258527831946356978412278413569419265873 * PAIR E3: 7,8 ROW 3 A3: 7,8,4 # reduction candidate for 7,8 A3: 7,8 # 19 pairs B3: 7,8,4 # reduction candidate for 7,8 B3: 7,8 => CTR * 1.3.52684.65..47214.21.6395....2...793164725872....9..3.7.68..22.871.....1.2..87. B3: 4 # 19 pairs * PAIR A5: 4,9 BLK 4 A4: 4,9,5,6,8 # reduction candidate for 4,9 A4: 4,9 => CTR * 193752684865..4721742186395....2...7.316.7258.2....9..3....8..22.8.1.....1.2..87. A4: 5,6,8 # 12 pairs B4: 4,9,5,8 # reduction candidate for 4,9 B4: 4,9 => CTR * 1.3.52684.65..4721.82176395....2...7.316.725872....9..3.7.68..22.871.....1.2..87. B4: 5,8 # 13 pairs C4: 4,9,6 # reduction candidate for 4,9 C4: 4,9 # 15 pairs * PAIR A5: 4,9 COL A A9: 4,9,5,6 # reduction candidate for 4,9 A9: 4,9 => SOLVED * 193752684865394721742186395684529137931647258527831946356978412278413569419265873 A9: 5,6 # 13 pairs * PAIR E5: 4,9 BLK 5 D4: 4,9,3,5,8 # reduction candidate for 4,9 D4: 4,9 # 15 pairs D4: 3,5,8 # 12 pairs * PAIR E5: 4,9 COL E E7: 4,9,6,7 # reduction candidate for 4,9 E7: 4,9 => CTR * 1.3.52684.65..4721..2176395....2...7.316.725872....9..3....8..22.8.1.....1.2..87. E7: 6,7 # 13 pairs E9: 4,9,3,6 # reduction candidate for 4,9 E9: 4,9 => CTR * 173952684965..4721..2176395....2...7431697258726...9.3397.68..22.871..366142..87. E9: 3,6 # 20 pairs * PAIR G4: 1,4 BLK 6 H4: 1,4,3,6 # reduction candidate for 1,4 H4: 1,4 # 17 pairs H6: 1,4,3,6 # reduction candidate for 1,4 H6: 1,4 # 14 pairs * PAIR G4: 1,4 COL G G7: 1,4,5 # reduction candidate for 1,4 G7: 1,4 # 15 pairs G7: 5 # 9 pairs * PAIR I6: 3,6 BLK 6 H4: 3,6,1,4 # reduction candidate for 3,6 H4: 3,6 # 14 pairs H6: 3,6,1,4 # reduction candidate for 3,6 H6: 3,6 # 17 pairs * PAIR I6: 3,6 COL I I8: 3,6,9 # reduction candidate for 3,6 I8: 3,6 # 15 pairs I8: 9 # 12 pairs * PAIR H7: 1,4 BLK 9 G7: 1,4,5 # reduction candidate for 1,4 G7: 1,4 # 15 pairs G7: 5 # 9 pairs * PAIR H7: 1,4 COL H H4: 1,4,3,6 # reduction candidate for 1,4 H4: 1,4 # 17 pairs H6: 1,4,3,6 # reduction candidate for 1,4 H6: 1,4 # 14 pairs * PAIR G8: 4,5 BLK 9 G7: 4,5,1 # reduction candidate for 4,5 G7: 1 # 13 pairs G7: 4,5 # 11 pairs * PAIR G8: 4,5 ROW 8 B8: 4,5,7,9 # reduction candidate for 4,5 B8: 4,5 => CTR * 17395268496538472184217639558942...7431697258726...9.33.7.68..22.871..36614235879 B8: 7,9 => SOLVED * 193752684865394721742186395684529137931647258527831946356978412278413569419265873 D8: 4,5,3,7,9 # reduction candidate for 4,5 D8: 4,5 => SOLVED * 193752684865394721742186395684529137931647258527831946356978412278413569419265873 D8: 3,7,9 # 12 pairs * PAIR H8: 3,6 BLK 9 I8: 3,6,9 # reduction candidate for 3,6 I8: 3,6 # 15 pairs I8: 9 # 12 pairs * PAIR H8: 3,6 COL H H4: 3,6,1,4 # reduction candidate for 3,6 H4: 3,6 # 14 pairs H6: 3,6,1,4 # reduction candidate for 3,6 H6: 3,6 # 17 pairs * PAIR I9: 3,9 BLK 9 I8: 3,9,6 # reduction candidate for 3,9 I8: 6 # 14 pairs I8: 3,9 # 12 pairs * PAIR I9: 3,9 ROW 9 E9: 3,9,4,6 # reduction candidate for 3,9 E9: 3,9 => CTR * 173952684965..4721..2176395....2...7431697258726.4.9.33974685122.871.....1.2..87. E9: 4,6 # 13 pairs F9: 3,9,5 # reduction candidate for 3,9 F9: 3,9 => CTR * 1.3.52684.65..4721.82176395.5..2...7.316.725872....9..3.7.68..22.871....51624.87. F9: 5 # 19 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060617-absurd-base-pr-000.dot * REASONING * DIS # B7: 7,9 => CTR => B7: 4,5 * PRF # B7: 4,5 => SOL * PRF # B8: 7,9 => SOL * DIS # B8: 4,5 => CTR => B8: 7,9 * DIS # A4: 8,9 => CTR => A4: 4,5,6 * PRF # D7: 7,9 => SOL * DIS # D7: 4,5 => CTR => D7: 7,9 * DIS # D8: 7,9 => CTR => D8: 3,4,5 * PRF # D8: 3,4,5 => SOL * DIS # B3: 7,8 => CTR => B3: 4 * DIS # A4: 4,9 => CTR => A4: 5,6,8 * DIS # B4: 4,9 => CTR => B4: 5,8 * PRF # A9: 4,9 => SOL * DIS # E7: 4,9 => CTR => E7: 6,7 * DIS # E9: 4,9 => CTR => E9: 3,6 * DIS # B8: 4,5 => CTR => B8: 7,9 * PRF # B8: 7,9 => SOL * PRF # D8: 4,5 => SOL * DIS # E9: 3,9 => CTR => E9: 4,6 * DIS # F9: 3,9 => CTR => F9: 5 * CNT 20 HDP CHAINS / 56 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A5,B1,D1,E3,E5,G4,G8,H7,H8,I6,I9) * 1.3.52684.65..4721..21.6395....2...7.316.7258.2....9..3....8..22.8.1.....1.2..87. * PAIR B1: 7,9 COL B B7: 7,9,4,5 # reduction candidate for 7,9 B7: 7,9 => CTR * 17395268496538472184217639558942...7431697258726...9.3397.68..22.871..36614235879 B7: 4,5 => SOLVED * 193752684865394721742186395684529137931647258527831946356978412278413569419265873 * DURATION: 0:00:01.411368 START: 23:55:42.148249 END: 23:55:43.559617 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060617-absurd-base-pr-001.dot * REASONING * DIS # B7: 7,9 => CTR => B7: 4,5 * PRF B7: 4,5 => SOL * STA B7: 4,5 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006, 20060617, absurd
Solution
position: 193752684865394721742186395684529137931647258527831946356978412278413569419265873 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 # B7: 7,9 => CTR => B7: 4,5 * PRF # B7: 4,5 => SOL * PRF # B8: 7,9 => SOL * DIS # B8: 4,5 => CTR => B8: 7,9 * INC # D2: 8,9 => UNS * INC # E2: 8,9 => UNS * DIS # A4: 8,9 => CTR => A4: 4,5,6 * INC # A4: 4,5,6 => UNS * PRF # D7: 7,9 => SOL * DIS # D7: 4,5 => CTR => D7: 7,9 * DIS # D8: 7,9 => CTR => D8: 3,4,5 * PRF # D8: 3,4,5 => SOL * INC # A3: 7,8 => UNS * DIS # B3: 7,8 => CTR => B3: 4 * INC # B3: 4 => UNS * DIS # A4: 4,9 => CTR => A4: 5,6,8 * INC # A4: 5,6,8 => UNS * DIS # B4: 4,9 => CTR => B4: 5,8 * INC # B4: 5,8 => UNS * INC # C4: 4,9 => UNS * PRF # A9: 4,9 => SOL * INC # A9: 5,6 => UNS * INC # D4: 4,9 => UNS * INC # D4: 3,5,8 => UNS * DIS # E7: 4,9 => CTR => E7: 6,7 * INC # E7: 6,7 => UNS * DIS # E9: 4,9 => CTR => E9: 3,6 * INC # E9: 3,6 => UNS * INC # H4: 1,4 => UNS * INC # H6: 1,4 => UNS * INC # G7: 1,4 => UNS * INC # G7: 5 => UNS * INC # H4: 3,6 => UNS * INC # H6: 3,6 => UNS * INC # I8: 3,6 => UNS * INC # I8: 9 => UNS * INC # G7: 1,4 => UNS * INC # G7: 5 => UNS * INC # H4: 1,4 => UNS * INC # H6: 1,4 => UNS * INC # G7: 4,5 => UNS * INC # G7: 1 => UNS * DIS # B8: 4,5 => CTR => B8: 7,9 * PRF # B8: 7,9 => SOL * PRF # D8: 4,5 => SOL * INC # D8: 3,7,9 => UNS * INC # I8: 3,6 => UNS * INC # I8: 9 => UNS * INC # H4: 3,6 => UNS * INC # H6: 3,6 => UNS * INC # I8: 3,9 => UNS * INC # I8: 6 => UNS * DIS # E9: 3,9 => CTR => E9: 4,6 * INC # E9: 4,6 => UNS * DIS # F9: 3,9 => CTR => F9: 5 * INC # F9: 5 => UNS * CNT 56 HDP CHAINS / 56 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B7: 7,9 => CTR => B7: 4,5 * PRF B7: 4,5 => SOL * STA B7: 4,5 * CNT 2 HDP CHAINS / 1 HYP OPENED