Analysis of zz-www.sudokuoftheday.co.uk-20190306-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019
level: medium
position: 72.4...6...1......5...12..7...7.5.8.....396.....6...3..4.........7.6.9.....8.45.3 initial
Autosolve
position: 72.4...6...1.76...5...12..7...7.5.8..7..396.....6..73..4...7..6..7.6.9.....8.4573 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # A2: 3,9 => SOL * DIS # B3: 3,9 => CTR => B3: 6,8 * DIS # C3: 3,9 => CTR => C3: 4,6,8 * DIS # B3: 3,9 => CTR => B3: 6,8 * DIS # C3: 3,9 => CTR => C3: 4,6,8 * DIS # H2: 4,9 => CTR => H2: 2,5 * PRF # C3: 4,9 => SOL * DIS # E6: 2,4 => CTR => E6: 8 * DIS # A4: 2,4 => CTR => A4: 1,3,6,9 * PRF # C4: 2,4 => SOL * DIS # I4: 2,4 => CTR => I4: 1,9 * DIS # H5: 1,2 => CTR => H5: 4,5 * DIS # D7: 2,9 => CTR => D7: 1,3,5 * PRF # G7: 1,2 => SOL * DIS # H5: 1,2 => CTR => H5: 4,5 * CNT 15 HDP CHAINS / 53 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # A2: 3,9 => SOL * STA A2: 3,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 72.4...6...1......5...12..7...7.5.8.....396.....6...3..4.........7.6.9.....8.45.3 | initial |
| 72.4...6...1.76...5...12..7...7.5.8..7..396.....6..73..4...7..6..7.6.9.....8.4573 | autosolve |
| 729458361381976425564312897632745189178239654495681732843597216257163948916824573 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (12) C1: 3,9 F1: 3,8 D3: 3,9 G1: 1,3 I1: 1,5 H3: 4,9 E4: 2,4 D5: 1,2 F6: 1,8 F8: 1,3 E9: 2,9 H7: 1,2 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G1,I1: 1.. / G1 = 1 => 18 pairs (_) / I1 = 1 => 16 pairs (_) D5,F6: 1.. / D5 = 1 => 0 pairs (X) / F6 = 1 => 15 pairs (_) A9,B9: 1.. / A9 = 1 => 13 pairs (_) / B9 = 1 => 13 pairs (_) F6,F8: 1.. / F6 = 1 => 15 pairs (_) / F8 = 1 => 0 pairs (X) F1,F8: 3.. / F1 = 3 => 0 pairs (X) / F8 = 3 => 15 pairs (_) A2,C3: 4.. / A2 = 4 => 12 pairs (_) / C3 = 4 => 0 pairs (*) E4,E6: 4.. / E4 = 4 => 15 pairs (_) / E6 = 4 => 0 pairs (X) H8,I8: 4.. / H8 = 4 => 16 pairs (_) / I8 = 4 => 20 pairs (_) E1,D2: 5.. / E1 = 5 => 16 pairs (_) / D2 = 5 => 18 pairs (_) C7,B8: 5.. / C7 = 5 => 0 pairs (X) / B8 = 5 => 13 pairs (_) E1,I1: 5.. / E1 = 5 => 16 pairs (_) / I1 = 5 => 18 pairs (_) B8,D8: 5.. / B8 = 5 => 13 pairs (_) / D8 = 5 => 0 pairs (X) B6,B8: 5.. / B6 = 5 => 0 pairs (X) / B8 = 5 => 13 pairs (_) E1,E7: 5.. / E1 = 5 => 16 pairs (_) / E7 = 5 => 18 pairs (_) H2,H5: 5.. / H2 = 5 => 19 pairs (_) / H5 = 5 => 13 pairs (_) B3,C3: 6.. / B3 = 6 => 13 pairs (_) / C3 = 6 => 16 pairs (_) A4,A9: 6.. / A4 = 6 => 12 pairs (_) / A9 = 6 => 14 pairs (_) E1,F1: 8.. / E1 = 8 => 0 pairs (X) / F1 = 8 => 15 pairs (_) A5,C5: 8.. / A5 = 8 => 16 pairs (_) / C5 = 8 => 12 pairs (_) E6,F6: 8.. / E6 = 8 => 15 pairs (_) / F6 = 8 => 0 pairs (X) G7,I8: 8.. / G7 = 8 => 17 pairs (_) / I8 = 8 => 0 pairs (*) E1,E6: 8.. / E1 = 8 => 0 pairs (X) / E6 = 8 => 15 pairs (_) F1,F6: 8.. / F1 = 8 => 15 pairs (_) / F6 = 8 => 0 pairs (X) I2,I8: 8.. / I2 = 8 => 17 pairs (_) / I8 = 8 => 0 pairs (*) H2,H3: 9.. / H2 = 9 => 0 pairs (X) / H3 = 9 => 15 pairs (_) I4,I6: 9.. / I4 = 9 => 12 pairs (_) / I6 = 9 => 14 pairs (_) C1,E1: 9.. / C1 = 9 => 14 pairs (_) / E1 = 9 => 0 pairs (X) * DURATION: 0:00:40.412511 START: 04:17:05.986602 END: 04:17:46.399113 2019-05-01 * CP COUNT: (27) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C1,D3,D5,E4,E9,F1,F6,F8,G1,H3,H7,I1) * 72.4...6...1.76...5...12..7...7.5.8..7..396.....6..73..4...7..6..7.6.9.....8.4573 * PAIR C1: 3,9 BLK 1 A2: 3,9,4,8 # reduction candidate for 3,9 A2: 3,9 => SOLVED * 729458361381976425564312897632745189178239654495681732843597216257163948916824573 A2: 4,8 # 13 pairs B2: 3,9,8 # reduction candidate for 3,9 B2: 3,9 # 15 pairs B3: 3,9,6,8 # reduction candidate for 3,9 B3: 3,9 => CTR * 72.4...6...1.76...5.6.12847...7.548..7..396.....64873..4...7..6..7.619.....8.4573 B3: 6,8 # 13 pairs C3: 3,9,4,6,8 # reduction candidate for 3,9 C3: 3,9 => CTR * 72.4...6.4.1.76...56..12847...7.548..74.396.....64873..48..7..6.57.6.9.....8.4573 C3: 4,6,8 # 12 pairs * PAIR C1: 3,9 COL C C4: 3,9,2,4,6 # reduction candidate for 3,9 C4: 3,9 # 14 pairs C7: 3,9,2,5,8 # reduction candidate for 3,9 C7: 3,9 # 16 pairs * PAIR D3: 3,9 BLK 2 D2: 3,9,5 # reduction candidate for 3,9 D2: 5 # 18 pairs D2: 3,9 # 16 pairs * PAIR D3: 3,9 ROW 3 B3: 3,9,6,8 # reduction candidate for 3,9 B3: 3,9 => CTR * 72.4...6...1.76...5.6.12847...7.548..7..396.....64873..4...7..6..7.619.....8.4573 B3: 6,8 # 13 pairs C3: 3,9,4,6,8 # reduction candidate for 3,9 C3: 3,9 => CTR * 72.4...6.4.1.76...56..12847...7.548..74.396.....64873..48..7..6.57.6.9.....8.4573 C3: 4,6,8 # 12 pairs * PAIR D3: 3,9 COL D D7: 3,9,1,2,5 # reduction candidate for 3,9 D7: 3,9 # 20 pairs D7: 1,2,5 # 16 pairs * PAIR I1: 1,5 COL I I5: 1,5,2,4 # reduction candidate for 1,5 I5: 1,5 # 13 pairs I6: 1,5,2,4,9 # reduction candidate for 1,5 I6: 1,5 # 14 pairs * PAIR H3: 4,9 BLK 3 H2: 4,9,2,5 # reduction candidate for 4,9 H2: 4,9 => CTR * 72.483165..15762.85..912347...72548..74139652...64873..4.257816.57361924...894573 H2: 2,5 # 15 pairs * PAIR H3: 4,9 ROW 3 C3: 4,9,3,6,8 # reduction candidate for 4,9 C3: 4,9 => SOLVED * 729458361381976425564312897632745189178239654495681732843597216257163948916824573 C3: 3,6,8 # 12 pairs * PAIR E4: 2,4 BLK 5 E6: 2,4,8 # reduction candidate for 2,4 E6: 2,4 => CTR * 7294831654.1576298586912347...72548..74139652..564873.948.57..6.57.61924...894573 E6: 8 # 15 pairs * PAIR E4: 2,4 ROW 4 A4: 2,4,1,3,6,9 # reduction candidate for 2,4 A4: 2,4 => CTR * 7294583613819762..564.12..7...7.5189.7..396...9.68173.943527816.571639..612894573 A4: 1,3,6,9 # 12 pairs C4: 2,4,3,6,9 # reduction candidate for 2,4 C4: 2,4 => SOLVED * 729458361381976425564312897632745189178239654495681732843597216257163948916824573 C4: 3,6,9 # 12 pairs G4: 2,4,1 # reduction candidate for 2,4 G4: 2,4 # 14 pairs I4: 2,4,1,9 # reduction candidate for 2,4 I4: 2,4 => CTR * 729458361831976..55...12..7.9.7451821782396...5.681739.45..7..6.87563914.1.8.4573 I4: 1,9 # 13 pairs * PAIR D5: 1,2 ROW 5 A5: 1,2,4,8 # reduction candidate for 1,2 A5: 1,2 # 20 pairs H5: 1,2,4,5 # reduction candidate for 1,2 H5: 1,2 => CTR * 729458361..1976.5.56.312.97613745289.7.23961..9.68173..4.5.7126257163948..6824573 H5: 4,5 # 14 pairs I5: 1,2,4,5 # reduction candidate for 1,2 I5: 1,2 # 16 pairs * PAIR D5: 1,2 COL D D7: 1,2,3,5,9 # reduction candidate for 1,2 D7: 1,2 # 26 pairs D8: 1,2,3,5 # reduction candidate for 1,2 D8: 1,2 # 15 pairs * PAIR F8: 1,3 BLK 8 D7: 1,3,2,5,9 # reduction candidate for 1,3 D7: 1,3 # 16 pairs D8: 1,3,2,5 # reduction candidate for 1,3 D8: 1,3 # 16 pairs * PAIR E9: 2,9 BLK 8 D7: 2,9,1,3,5 # reduction candidate for 2,9 D7: 2,9 => CTR * 72.4981659.1576...564312897...74528..7..3965...56..73..4.957.16.57.6.9.....824573 D7: 1,3,5 # 14 pairs E7: 2,9,5 # reduction candidate for 2,9 E7: 2,9 # 16 pairs * PAIR E9: 2,9 ROW 9 A9: 2,9,1,6 # reduction candidate for 2,9 A9: 2,9 # 16 pairs C9: 2,9,6 # reduction candidate for 2,9 C9: 2,9 # 15 pairs * PAIR H7: 1,2 BLK 9 G7: 1,2,8 # reduction candidate for 1,2 G7: 1,2 => SOLVED * 729458361381976425564312897632745189178239654495681732843597216257163948916824573 G7: 8 # 17 pairs H8: 1,2,4 # reduction candidate for 1,2 H8: 1,2 # 20 pairs I8: 1,2,4,8 # reduction candidate for 1,2 I8: 1,2 # 21 pairs * PAIR H7: 1,2 ROW 7 D7: 1,2,3,5,9 # reduction candidate for 1,2 D7: 1,2 # 26 pairs D7: 3,5,9 # 15 pairs * PAIR H7: 1,2 COL H H5: 1,2,4,5 # reduction candidate for 1,2 H5: 1,2 => CTR * 729458361..1976.5.56.312.97613745289.7.23961..9.68173..4.5.7126257163948..6824573 H5: 4,5 # 14 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190306-absurd-base-pr-000.dot * REASONING * PRF # A2: 3,9 => SOL * DIS # B3: 3,9 => CTR => B3: 6,8 * DIS # C3: 3,9 => CTR => C3: 4,6,8 * DIS # B3: 3,9 => CTR => B3: 6,8 * DIS # C3: 3,9 => CTR => C3: 4,6,8 * DIS # H2: 4,9 => CTR => H2: 2,5 * PRF # C3: 4,9 => SOL * DIS # E6: 2,4 => CTR => E6: 8 * DIS # A4: 2,4 => CTR => A4: 1,3,6,9 * PRF # C4: 2,4 => SOL * DIS # I4: 2,4 => CTR => I4: 1,9 * DIS # H5: 1,2 => CTR => H5: 4,5 * DIS # D7: 2,9 => CTR => D7: 1,3,5 * PRF # G7: 1,2 => SOL * DIS # H5: 1,2 => CTR => H5: 4,5 * CNT 15 HDP CHAINS / 53 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C1,D3,D5,E4,E9,F1,F6,F8,G1,H3,H7,I1) * 72.4...6...1.76...5...12..7...7.5.8..7..396.....6..73..4...7..6..7.6.9.....8.4573 * PAIR C1: 3,9 BLK 1 A2: 3,9,4,8 # reduction candidate for 3,9 A2: 3,9 => SOLVED * 729458361381976425564312897632745189178239654495681732843597216257163948916824573 * DURATION: 0:00:02.267219 START: 04:18:27.285574 END: 04:18:29.552793 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190306-absurd-base-pr-001.dot * REASONING * PRF # A2: 3,9 => SOL * STA A2: 3,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019, 20190306, absurd
Solution
position: 729458361381976425564312897632745189178239654495681732843597216257163948916824573 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:
* PRF # A2: 3,9 => SOL * INC # A2: 4,8 => UNS * INC # B2: 3,9 => UNS * DIS # B3: 3,9 => CTR => B3: 6,8 * INC # B3: 6,8 => UNS * DIS # C3: 3,9 => CTR => C3: 4,6,8 * INC # C3: 4,6,8 => UNS * INC # C4: 3,9 => UNS * INC # C7: 3,9 => UNS * INC # D2: 3,9 => UNS * INC # D2: 5 => UNS * DIS # B3: 3,9 => CTR => B3: 6,8 * INC # B3: 6,8 => UNS * DIS # C3: 3,9 => CTR => C3: 4,6,8 * INC # C3: 4,6,8 => UNS * INC # D7: 3,9 => UNS * INC # D7: 1,2,5 => UNS * INC # I5: 1,5 => UNS * INC # I6: 1,5 => UNS * DIS # H2: 4,9 => CTR => H2: 2,5 * INC # H2: 2,5 => UNS * PRF # C3: 4,9 => SOL * INC # C3: 3,6,8 => UNS * DIS # E6: 2,4 => CTR => E6: 8 * INC # E6: 8 => UNS * DIS # A4: 2,4 => CTR => A4: 1,3,6,9 * INC # A4: 1,3,6,9 => UNS * PRF # C4: 2,4 => SOL * INC # C4: 3,6,9 => UNS * INC # G4: 2,4 => UNS * DIS # I4: 2,4 => CTR => I4: 1,9 * INC # I4: 1,9 => UNS * INC # A5: 1,2 => UNS * DIS # H5: 1,2 => CTR => H5: 4,5 * INC # H5: 4,5 => UNS * INC # I5: 1,2 => UNS * INC # D7: 1,2 => UNS * INC # D8: 1,2 => UNS * INC # D7: 1,3 => UNS * INC # D8: 1,3 => UNS * DIS # D7: 2,9 => CTR => D7: 1,3,5 * INC # D7: 1,3,5 => UNS * INC # E7: 2,9 => UNS * INC # A9: 2,9 => UNS * INC # C9: 2,9 => UNS * PRF # G7: 1,2 => SOL * INC # G7: 8 => UNS * INC # H8: 1,2 => UNS * INC # I8: 1,2 => UNS * INC # D7: 1,2 => UNS * INC # D7: 3,5,9 => UNS * DIS # H5: 1,2 => CTR => H5: 4,5 * INC # H5: 4,5 => UNS * CNT 53 HDP CHAINS / 53 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # A2: 3,9 => SOL * STA A2: 3,9 * CNT 1 HDP CHAINS / 1 HYP OPENED