Analysis of zz-www.sudokuoftheday.co.uk-20060517-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006
level: medium
position: ....8..4......61.2..5....8...6......49...7.3..2..14....4..759...7.4.961....8..... initial
Autosolve
position: ....8..4..84..61.2..5.4..8...6..8...49...7.3..2..14.6..4..7592..7.4.961....8..... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # I4: 1,5 => CTR => I4: 4,7,9 * DIS # A8: 2,3 => CTR => A8: 5,8 * DIS # E4: 2,3 => CTR => E4: 5,9 * DIS # I8: 5 => CTR => I8: 3,8 * PRF # A7: 3,8 => SOL * DIS # G9: 5,7 => CTR => G9: 3,4 * PRF # I9: 5,7 => SOL * CNT 7 HDP CHAINS / 29 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # I4: 1,5 => CTR => I4: 4,7,9 * PRF I4: 4,7,9 # E9: 2,3 => SOL * STA I4: 4,7,9 + E9: 2,3 * CNT 2 HDP CHAINS / 11 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....8..4......61.2..5....8...6......49...7.3..2..14....4..759...7.4.961....8..... | initial |
| ....8..4..84..61.2..5.4..8...6..8...49...7.3..2..14.6..4..7592..7.4.961....8..... | autosolve |
| 967182345384756192215943786156398274498267531723514869841675923572439618639821457 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (6) G3: 3,7 C5: 1,8 I5: 1,5 E8: 2,3 I7: 3,8 H9: 5,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) I4,I5: 1.. / I4 = 1 => 0 pairs (X) / I5 = 1 => 10 pairs (_) D7,F9: 1.. / D7 = 1 => 9 pairs (_) / F9 = 1 => 17 pairs (_) C5,I5: 1.. / C5 = 1 => 0 pairs (X) / I5 = 1 => 10 pairs (_) G4,G5: 2.. / G4 = 2 => 0 pairs (*) / G5 = 2 => 0 pairs (X) G4,I4: 4.. / G4 = 4 => 12 pairs (_) / I4 = 4 => 10 pairs (_) G9,I9: 4.. / G9 = 4 => 10 pairs (_) / I9 = 4 => 12 pairs (_) G4,G9: 4.. / G4 = 4 => 12 pairs (_) / G9 = 4 => 10 pairs (_) I4,I9: 4.. / I4 = 4 => 10 pairs (_) / I9 = 4 => 12 pairs (_) A8,I8: 5.. / A8 = 5 => 8 pairs (_) / I8 = 5 => 0 pairs (X) B4,B9: 5.. / B4 = 5 => 7 pairs (_) / B9 = 5 => 0 pairs (X) I1,I3: 6.. / I1 = 6 => 7 pairs (_) / I3 = 6 => 7 pairs (_) D5,E5: 6.. / D5 = 6 => 8 pairs (_) / E5 = 6 => 18 pairs (_) D7,E9: 6.. / D7 = 6 => 18 pairs (_) / E9 = 6 => 8 pairs (_) A7,D7: 6.. / A7 = 6 => 8 pairs (_) / D7 = 6 => 18 pairs (_) D5,D7: 6.. / D5 = 6 => 8 pairs (_) / D7 = 6 => 18 pairs (_) E5,E9: 6.. / E5 = 6 => 18 pairs (_) / E9 = 6 => 8 pairs (_) C1,C6: 7.. / C1 = 7 => 20 pairs (_) / C6 = 7 => 8 pairs (_) G5,G6: 8.. / G5 = 8 => 0 pairs (X) / G6 = 8 => 10 pairs (_) I7,I8: 8.. / I7 = 8 => 7 pairs (_) / I8 = 8 => 10 pairs (_) C5,G5: 8.. / C5 = 8 => 10 pairs (_) / G5 = 8 => 0 pairs (X) A9,C9: 9.. / A9 = 9 => 10 pairs (_) / C9 = 9 => 6 pairs (_) D6,I6: 9.. / D6 = 9 => 14 pairs (_) / I6 = 9 => 12 pairs (_) C1,C9: 9.. / C1 = 9 => 10 pairs (_) / C9 = 9 => 6 pairs (_) E2,E4: 9.. / E2 = 9 => 14 pairs (_) / E4 = 9 => 12 pairs (_) H2,H4: 9.. / H2 = 9 => 12 pairs (_) / H4 = 9 => 14 pairs (_) * DURATION: 0:00:21.790840 START: 23:13:02.174155 END: 23:13:23.964995 2019-04-30 * CP COUNT: (25) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C5,E8,G3,H9,I5,I7) * ....8..4..84..61.2..5.4..8...6..8...49...7.3..2..14.6..4..7592..7.4.961....8..... * PAIR G3: 3,7 BLK 3 G1: 3,7,5 # reduction candidate for 3,7 G1: 3,7 # 11 pairs I1: 3,7,5,6,9 # reduction candidate for 3,7 I1: 3,7 # 16 pairs I3: 3,7,6,9 # reduction candidate for 3,7 I3: 3,7 # 18 pairs * PAIR G3: 3,7 ROW 3 A3: 3,7,1,2,6,9 # reduction candidate for 3,7 A3: 3,7 # 11 pairs D3: 3,7,1,2,9 # reduction candidate for 3,7 D3: 3,7 # 10 pairs * PAIR G3: 3,7 COL G G9: 3,7,4,5 # reduction candidate for 3,7 G9: 3,7 # 14 pairs G9: 4,5 # 7 pairs * PAIR C5: 1,8 COL C C7: 1,8,3 # reduction candidate for 1,8 C7: 1,8 # 11 pairs C7: 3 # 10 pairs * PAIR I5: 1,5 BLK 6 I4: 1,5,4,7,9 # reduction candidate for 1,5 I4: 1,5 => CTR * ....8..4..84..61.2..5.4..8...6..84.5498..723152..1486..4..7592..7.4.961..5.8...74 I4: 4,7,9 # 10 pairs * PAIR E8: 2,3 BLK 8 E9: 2,3,6 # reduction candidate for 2,3 E9: 2,3 # 18 pairs F9: 2,3,1 # reduction candidate for 2,3 F9: 2,3 # 9 pairs * PAIR E8: 2,3 ROW 8 A8: 2,3,5,8 # reduction candidate for 2,3 A8: 2,3 => CTR * ....8..4..84..61.2..5.4..8...6..8...49...7.31.2..14.6..4..75928.784.9615...8...7. A8: 5,8 # 7 pairs C8: 2,3,8 # reduction candidate for 2,3 C8: 2,3 # 9 pairs * PAIR E8: 2,3 COL E E4: 2,3,5,9 # reduction candidate for 2,3 E4: 2,3 => CTR * ....8..4..84.96152..5.4..8...6..85944986572315239148676413759288724.9615...86..7. E4: 5,9 # 8 pairs * PAIR I7: 3,8 BLK 9 I8: 3,8,5 # reduction candidate for 3,8 I8: 5 => CTR * ....8..4.3847.6192..5.4..8.136.98.5.498..7231527314869643175928872439615.5.8...7. I8: 3,8 # 8 pairs * PAIR I7: 3,8 ROW 7 A7: 3,8,1,6 # reduction candidate for 3,8 A7: 3,8 => SOLVED * 967182345384756192215943786156398274498267531723514869841675923572439618639821457 A7: 1,6 # 7 pairs C7: 3,8,1 # reduction candidate for 3,8 C7: 3,8 # 9 pairs * PAIR H9: 5,7 BLK 9 G9: 5,7,3,4 # reduction candidate for 5,7 G9: 5,7 => CTR * ....8..4..84.961.2..5.4..8.156..84974985.7231.2.91486584167592357.4.9618...8.1..4 G9: 3,4 # 7 pairs I9: 5,7,3,4 # reduction candidate for 5,7 I9: 5,7 => SOLVED * 967182345384756192215943786156398274498267531723514869841675923572439618639821457 I9: 3,4 # 7 pairs * PAIR H9: 5,7 COL H H2: 5,7,9 # reduction candidate for 5,7 H2: 5,7 # 14 pairs H4: 5,7,9 # reduction candidate for 5,7 H4: 5,7 # 12 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060517-absurd-base-pr-000.dot * REASONING * DIS # I4: 1,5 => CTR => I4: 4,7,9 * DIS # A8: 2,3 => CTR => A8: 5,8 * DIS # E4: 2,3 => CTR => E4: 5,9 * DIS # I8: 5 => CTR => I8: 3,8 * PRF # A7: 3,8 => SOL * DIS # G9: 5,7 => CTR => G9: 3,4 * PRF # I9: 5,7 => SOL * CNT 7 HDP CHAINS / 29 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C5,E8,G3,H9,I5,I7) * ....8..4..84..61.2..5.4..8...6..8...49...7.3..2..14.6..4..7592..7.4.961....8..... * PAIR G3: 3,7 BLK 3 G1: 3,7,5 # reduction candidate for 3,7 G1: 3,7 # 11 pairs I1: 3,7,5,6,9 # reduction candidate for 3,7 I1: 3,7 # 16 pairs I3: 3,7,6,9 # reduction candidate for 3,7 I3: 3,7 # 18 pairs * PAIR G3: 3,7 ROW 3 A3: 3,7,1,2,6,9 # reduction candidate for 3,7 A3: 3,7 # 11 pairs D3: 3,7,1,2,9 # reduction candidate for 3,7 D3: 3,7 # 10 pairs * PAIR G3: 3,7 COL G G9: 3,7,4,5 # reduction candidate for 3,7 G9: 3,7 # 14 pairs G9: 4,5 # 7 pairs * PAIR C5: 1,8 COL C C7: 1,8,3 # reduction candidate for 1,8 C7: 1,8 # 11 pairs C7: 3 # 10 pairs * PAIR I5: 1,5 BLK 6 I4: 1,5,4,7,9 # reduction candidate for 1,5 I4: 1,5 => CTR * ....8..4..84..61.2..5.4..8...6..84.5498..723152..1486..4..7592..7.4.961..5.8...74 * PAIR E8: 2,3 BLK 8 E9: 2,3,6 # reduction candidate for 2,3 E9: 2,3 => SOLVED * 967182345384756192215943786156398274498267531723514869841675923572439618639821457 * DURATION: 0:00:07.022467 START: 23:13:38.781692 END: 23:13:45.804159 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060517-absurd-base-pr-001.dot * REASONING * DIS # I4: 1,5 => CTR => I4: 4,7,9 * PRF I4: 4,7,9 # E9: 2,3 => SOL * STA I4: 4,7,9 + E9: 2,3 * CNT 2 HDP CHAINS / 11 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006, 20060517, absurd
Solution
position: 967182345384756192215943786156398274498267531723514869841675923572439618639821457 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 # G1: 3,7 => UNS * INC # I1: 3,7 => UNS * INC # I3: 3,7 => UNS * INC # A3: 3,7 => UNS * INC # D3: 3,7 => UNS * INC # G9: 3,7 => UNS * INC # G9: 4,5 => UNS * INC # C7: 1,8 => UNS * INC # C7: 3 => UNS * DIS # I4: 1,5 => CTR => I4: 4,7,9 * INC # I4: 4,7,9 => UNS * INC # E9: 2,3 => UNS * INC # F9: 2,3 => UNS * DIS # A8: 2,3 => CTR => A8: 5,8 * INC # A8: 5,8 => UNS * INC # C8: 2,3 => UNS * DIS # E4: 2,3 => CTR => E4: 5,9 * INC # E4: 5,9 => UNS * INC # I8: 3,8 => UNS * DIS # I8: 5 => CTR => I8: 3,8 * PRF # A7: 3,8 => SOL * INC # A7: 1,6 => UNS * INC # C7: 3,8 => UNS * DIS # G9: 5,7 => CTR => G9: 3,4 * INC # G9: 3,4 => UNS * PRF # I9: 5,7 => SOL * INC # I9: 3,4 => UNS * INC # H2: 5,7 => UNS * INC # H4: 5,7 => UNS * CNT 29 HDP CHAINS / 29 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # G1: 3,7 => UNS * INC # I1: 3,7 => UNS * INC # I3: 3,7 => UNS * INC # A3: 3,7 => UNS * INC # D3: 3,7 => UNS * INC # G9: 3,7 => UNS * INC # G9: 4,5 => UNS * INC # C7: 1,8 => UNS * INC # C7: 3 => UNS * DIS # I4: 1,5 => CTR => I4: 4,7,9 * PRF I4: 4,7,9 # E9: 2,3 => SOL * STA I4: 4,7,9 + E9: 2,3 * CNT 11 HDP CHAINS / 11 HYP OPENED