Analysis of zz-www.sudokuoftheday.co.uk-20190409-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019
level: medium
position: .25.....1.1.94...28.....4.6.6..1...5...68.2....3......5......1..9...6....31....5. initial
Autosolve
position: 425.6...131694.5.2879521436.6..1...51..68.2....3...16.5.2.3.61.79.156.2.631....5. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F7: 7,8 => CTR => F7: 4,9 * DIS # F9: 7,8 => CTR => F9: 2,4,9 * PRF # B6: 4,5 => SOL * DIS # F5: 4,5 => CTR => F5: 3,7,9 * PRF # C4: 8 => SOL * DIS # F6: 2,9 => CTR => F6: 4,5,7 * DIS # F6: 7,9 => CTR => F6: 2,4,5 * PRF # I6: 8 => SOL * DIS # F7: 4,8 => CTR => F7: 7,9 * DIS # I7: 4,8 => CTR => I7: 7,9 * DIS # B6: 5 => CTR => B6: 4,8 * PRF # I8: 3 => SOL * DIS # F9: 7,9 => CTR => F9: 2,4,8 * DIS # I9: 7,9 => CTR => I9: 4,8 * PRF # I8: 3,8 => SOL * CNT 15 HDP CHAINS / 49 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # F7: 7,8 => CTR => F7: 4,9 * DIS F7: 4,9 # F9: 7,8 => CTR => F9: 2,4,9 * DIS F7: 4,9 + F9: 2,4,9 # F1: 3 => CTR => F1: 7,8 * DIS F7: 4,9 + F9: 2,4,9 + F1: 7,8 # F4: 2,9 => CTR => F4: 3,4 * PRF F7: 4,9 + F9: 2,4,9 + F1: 7,8 + F4: 3,4 # B6: 4,5 => SOL * STA F7: 4,9 + F9: 2,4,9 + F1: 7,8 + F4: 3,4 + B6: 4,5 * CNT 5 HDP CHAINS / 12 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .25.....1.1.94...28.....4.6.6..1...5...68.2....3......5......1..9...6....31....5. | initial |
| 425.6...131694.5.2879521436.6..1...51..68.2....3...16.5.2.3.61.79.156.2.631....5. | autosolve |
| 425368791316947582879521436968214375157683249243795168582439617794156823631872954 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (11) F2: 7,8 H2: 7,8 A4: 2,9 B5: 4,5 C5: 4,7 A6: 2,9 E6: 7,9 B7: 4,8 C8: 4,8 E9: 7,9 G8: 3,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A4,A6: 2.. / A4 = 2 => 0 pairs (X) / A6 = 2 => 10 pairs (_) D9,F9: 2.. / D9 = 2 => 12 pairs (_) / F9 = 2 => 11 pairs (_) D1,F1: 3.. / D1 = 3 => 13 pairs (_) / F1 = 3 => 12 pairs (_) G4,I5: 3.. / G4 = 3 => 0 pairs (*) / I5 = 3 => 0 pairs (X) G8,I8: 3.. / G8 = 3 => 11 pairs (_) / I8 = 3 => 0 pairs (*) F5,I5: 3.. / F5 = 3 => 0 pairs (*) / I5 = 3 => 0 pairs (X) D1,D4: 3.. / D1 = 3 => 13 pairs (_) / D4 = 3 => 12 pairs (_) G4,G8: 3.. / G4 = 3 => 0 pairs (*) / G8 = 3 => 0 pairs (X) I5,I8: 3.. / I5 = 3 => 11 pairs (_) / I8 = 3 => 0 pairs (*) H4,H5: 4.. / H4 = 4 => 14 pairs (_) / H5 = 4 => 13 pairs (_) B7,C8: 4.. / B7 = 4 => 13 pairs (_) / C8 = 4 => 0 pairs (*) C8,I8: 4.. / C8 = 4 => 0 pairs (*) / I8 = 4 => 0 pairs (X) B5,B6: 5.. / B5 = 5 => 11 pairs (_) / B6 = 5 => 0 pairs (X) F5,F6: 5.. / F5 = 5 => 0 pairs (X) / F6 = 5 => 11 pairs (_) B5,F5: 5.. / B5 = 5 => 11 pairs (_) / F5 = 5 => 0 pairs (X) B6,F6: 5.. / B6 = 5 => 0 pairs (X) / F6 = 5 => 11 pairs (_) C4,C5: 7.. / C4 = 7 => 12 pairs (_) / C5 = 7 => 13 pairs (_) F2,H2: 7.. / F2 = 7 => 13 pairs (_) / H2 = 7 => 14 pairs (_) E6,E9: 7.. / E6 = 7 => 0 pairs (X) / E9 = 7 => 0 pairs (_) C4,B6: 8.. / C4 = 8 => 0 pairs (*) / B6 = 8 => 0 pairs (X) B7,C8: 8.. / B7 = 8 => 0 pairs (*) / C8 = 8 => 0 pairs (X) F2,H2: 8.. / F2 = 8 => 14 pairs (_) / H2 = 8 => 13 pairs (_) B6,I6: 8.. / B6 = 8 => 13 pairs (_) / I6 = 8 => 0 pairs (*) B6,B7: 8.. / B6 = 8 => 13 pairs (_) / B7 = 8 => 0 pairs (*) C4,C8: 8.. / C4 = 8 => 0 pairs (*) / C8 = 8 => 0 pairs (X) G1,H1: 9.. / G1 = 9 => 17 pairs (_) / H1 = 9 => 15 pairs (_) A4,A6: 9.. / A4 = 9 => 10 pairs (_) / A6 = 9 => 0 pairs (X) F7,I7: 9.. / F7 = 9 => 0 pairs (*) / I7 = 9 => 0 pairs (X) E6,E9: 9.. / E6 = 9 => 0 pairs (*) / E9 = 9 => 0 pairs (X) * DURATION: 0:00:31.442921 START: 05:09:39.449318 END: 05:10:10.892239 2019-05-01 * CP COUNT: (29) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,B5,B7,C5,C8,E6,E9,F2,G8,H2) * 425.6...131694.5.2879521436.6..1...51..68.2....3...16.5.2.3.61.79.156.2.631....5. * PAIR F2: 7,8 BLK 2 D1: 7,8,3 # reduction candidate for 7,8 D1: 7,8 # 12 pairs F1: 7,8,3 # reduction candidate for 7,8 F1: 7,8 # 13 pairs * PAIR F2: 7,8 COL F F7: 7,8,4,9 # reduction candidate for 7,8 F7: 7,8 => CTR * 425.6...131694.5.2879521436.6..1...51..68.2....3.7.168582437619794156823631.9.754 F7: 4,9 # 12 pairs F9: 7,8,2,4,9 # reduction candidate for 7,8 F9: 7,8 => CTR * 425863791316947582879521436.6831...51.768.2....3...168582.3.6177941568236312.8954 F9: 2,4,9 # 11 pairs * PAIR H2: 7,8 BLK 3 G1: 7,8,9 # reduction candidate for 7,8 G1: 7,8 # 15 pairs H1: 7,8,9 # reduction candidate for 7,8 H1: 7,8 # 17 pairs * PAIR H2: 7,8 COL H H4: 7,8,4,9 # reduction candidate for 7,8 H4: 7,8 # 15 pairs H4: 4,9 # 13 pairs * PAIR A4: 2,9 ROW 4 F4: 2,9,3,4,7 # reduction candidate for 2,9 F4: 2,9 # 12 pairs F4: 3,4,7 # 11 pairs * PAIR B5: 4,5 BLK 4 B6: 4,5,8 # reduction candidate for 4,5 B6: 4,5 => SOLVED * 425368791316947582879521436968214375157683249243795168582439617794156823631872954 B6: 8 # 13 pairs * PAIR B5: 4,5 ROW 5 F5: 4,5,3,7,9 # reduction candidate for 4,5 F5: 4,5 => CTR * 425.6.9.131694.5.2879521436.6..1..451.768.293..3...16.5.2.3.61.794156328631...75. F5: 3,7,9 # 11 pairs * PAIR C5: 4,7 BLK 4 C4: 4,7,8 # reduction candidate for 4,7 C4: 8 => SOLVED * 425368791316947582879521436968214375157683249243795168582439617794156823631872954 C4: 4,7 # 13 pairs * PAIR C5: 4,7 ROW 5 F5: 4,7,3,5,9 # reduction candidate for 4,7 F5: 4,7 # 18 pairs H5: 4,7,9 # reduction candidate for 4,7 H5: 4,7 # 14 pairs * PAIR A6: 2,9 ROW 6 F6: 2,9,4,5,7 # reduction candidate for 2,9 F6: 2,9 => CTR * 425.6...131694.5.2879521436.6..1...51..6852.3.534..16858273.61.794156.2.631....5. F6: 4,5,7 # 11 pairs * PAIR E6: 7,9 BLK 5 F4: 7,9,2,3,4 # reduction candidate for 7,9 F4: 7,9 # 14 pairs F5: 7,9,3,4,5 # reduction candidate for 7,9 F5: 7,9 # 13 pairs F6: 7,9,2,4,5 # reduction candidate for 7,9 F6: 7,9 => CTR * 425.6...131694.5.2879521436.6..1...51..6852.3.534..16858273.61.794156.2.631....5. F6: 2,4,5 # 11 pairs * PAIR E6: 7,9 ROW 6 I6: 7,9,8 # reduction candidate for 7,9 I6: 8 => SOLVED * 425368791316947582879521436968214375157683249243795168582439617794156823631872954 I6: 7,9 # 13 pairs * PAIR B7: 4,8 ROW 7 D7: 4,8,7 # reduction candidate for 4,8 D7: 4,8 # 14 pairs F7: 4,8,7,9 # reduction candidate for 4,8 F7: 4,8 => CTR * 425.6...131694.5.2879521436.6..1...51..68.2....3.7.168582734619794156823631.9.754 F7: 7,9 # 14 pairs I7: 4,8,7,9 # reduction candidate for 4,8 I7: 4,8 => CTR * 425.6...131694.5.2879521436.6..1...51..68.2....3...16.5.2.3961.79.156.2.631.7..5. I7: 7,9 # 12 pairs * PAIR B7: 4,8 COL B B6: 4,8,5 # reduction candidate for 4,8 B6: 5 => CTR * 425.6...131694.5.2879521436.68.1...51.768.2...53...168582.3.61.794156823631....5. B6: 4,8 # 11 pairs * PAIR C8: 4,8 ROW 8 I8: 4,8,3 # reduction candidate for 4,8 I8: 3 => SOLVED * 425368791316947582879521436968214375157683249243795168582439617794156823631872954 I8: 4,8 # 11 pairs * PAIR C8: 4,8 COL C C4: 4,8,7 # reduction candidate for 4,8 C4: 4,8 # 13 pairs C4: 7 # 12 pairs * PAIR E9: 7,9 BLK 8 F7: 7,9,4,8 # reduction candidate for 7,9 F7: 7,9 # 14 pairs F9: 7,9,2,4,8 # reduction candidate for 7,9 F9: 7,9 => CTR * 425.6...131694.5.2879521436.6..1...51..68.2....3...16.5.2.3.61.794156.2.6312..854 F9: 2,4,8 # 11 pairs * PAIR E9: 7,9 ROW 9 G9: 7,9,8 # reduction candidate for 7,9 G9: 7,9 # 14 pairs I9: 7,9,4,8 # reduction candidate for 7,9 I9: 7,9 => CTR * 425.6...131694.5.2879521436.6..1...51..68.2.3..3...16858273961.79.15632.631...85. I9: 4,8 # 14 pairs * PAIR G8: 3,8 BLK 9 I8: 3,8,4 # reduction candidate for 3,8 I8: 3,8 => SOLVED * 425368791316947582879521436968214375157683249243795168582439617794156823631872954 I8: 4 # 13 pairs * PAIR G8: 3,8 COL G G4: 3,8,7,9 # reduction candidate for 3,8 G4: 3,8 # 16 pairs G4: 7,9 # 12 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190409-absurd-base-pr-000.dot * REASONING * DIS # F7: 7,8 => CTR => F7: 4,9 * DIS # F9: 7,8 => CTR => F9: 2,4,9 * PRF # B6: 4,5 => SOL * DIS # F5: 4,5 => CTR => F5: 3,7,9 * PRF # C4: 8 => SOL * DIS # F6: 2,9 => CTR => F6: 4,5,7 * DIS # F6: 7,9 => CTR => F6: 2,4,5 * PRF # I6: 8 => SOL * DIS # F7: 4,8 => CTR => F7: 7,9 * DIS # I7: 4,8 => CTR => I7: 7,9 * DIS # B6: 5 => CTR => B6: 4,8 * PRF # I8: 3 => SOL * DIS # F9: 7,9 => CTR => F9: 2,4,8 * DIS # I9: 7,9 => CTR => I9: 4,8 * PRF # I8: 3,8 => SOL * CNT 15 HDP CHAINS / 49 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,B5,B7,C5,C8,E6,E9,F2,G8,H2) * 425.6...131694.5.2879521436.6..1...51..68.2....3...16.5.2.3.61.79.156.2.631....5. * PAIR F2: 7,8 BLK 2 D1: 7,8,3 # reduction candidate for 7,8 D1: 7,8 # 12 pairs F1: 7,8,3 # reduction candidate for 7,8 F1: 7,8 # 13 pairs * PAIR F2: 7,8 COL F F7: 7,8,4,9 # reduction candidate for 7,8 F7: 7,8 => CTR * 425.6...131694.5.2879521436.6..1...51..68.2....3.7.168582437619794156823631.9.754 F9: 7,8,2,4,9 # reduction candidate for 7,8 F9: 7,8 => CTR * 425863791316947582879521436.6831...51.768.2....3...168582.3.6177941568236312.8954 * RESTART * PAIR RESTART * PAIR F2: 7,8 BLK 2 F1: 7,8,3 # reduction candidate for 7,8 F1: 3 => CTR * 425763..1316948572879521436.6.31.7.51.768.2.3..3.9716858243961779415632.631.7..5. * PAIR H2: 7,8 BLK 3 G1: 7,8,9 # reduction candidate for 7,8 G1: 7,8 # 17 pairs H1: 7,8,9 # reduction candidate for 7,8 H1: 7,8 # 19 pairs * PAIR H2: 7,8 COL H H4: 7,8,4,9 # reduction candidate for 7,8 H4: 7,8 # 17 pairs H4: 4,9 # 15 pairs * PAIR A4: 2,9 ROW 4 F4: 2,9,3,4 # reduction candidate for 2,9 F4: 2,9 => CTR * 42536...131694.5.2879521436.68.193.515768324994327516858273.61.79.1568236318.2.54 * PAIR RESTART * PAIR B5: 4,5 BLK 4 B6: 4,5,8 # reduction candidate for 4,5 B6: 4,5 => SOLVED * 425368791316947582879521436968214375157683249243795168582439617794156823631872954 * DURATION: 0:00:09.415388 START: 05:10:41.104202 END: 05:10:50.519590 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190409-absurd-base-pr-001.dot * REASONING * DIS # F7: 7,8 => CTR => F7: 4,9 * DIS F7: 4,9 # F9: 7,8 => CTR => F9: 2,4,9 * DIS F7: 4,9 + F9: 2,4,9 # F1: 3 => CTR => F1: 7,8 * DIS F7: 4,9 + F9: 2,4,9 + F1: 7,8 # F4: 2,9 => CTR => F4: 3,4 * PRF F7: 4,9 + F9: 2,4,9 + F1: 7,8 + F4: 3,4 # B6: 4,5 => SOL * STA F7: 4,9 + F9: 2,4,9 + F1: 7,8 + F4: 3,4 + B6: 4,5 * CNT 5 HDP CHAINS / 12 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019, 20190409, absurd
Solution
position: 425368791316947582879521436968214375157683249243795168582439617794156823631872954 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 # D1: 7,8 => UNS * INC # F1: 7,8 => UNS * DIS # F7: 7,8 => CTR => F7: 4,9 * INC # F7: 4,9 => UNS * DIS # F9: 7,8 => CTR => F9: 2,4,9 * INC # F9: 2,4,9 => UNS * INC # G1: 7,8 => UNS * INC # H1: 7,8 => UNS * INC # H4: 7,8 => UNS * INC # H4: 4,9 => UNS * INC # F4: 2,9 => UNS * INC # F4: 3,4,7 => UNS * PRF # B6: 4,5 => SOL * INC # B6: 8 => UNS * DIS # F5: 4,5 => CTR => F5: 3,7,9 * INC # F5: 3,7,9 => UNS * INC # C4: 4,7 => UNS * PRF # C4: 8 => SOL * INC # F5: 4,7 => UNS * INC # H5: 4,7 => UNS * DIS # F6: 2,9 => CTR => F6: 4,5,7 * INC # F6: 4,5,7 => UNS * INC # F4: 7,9 => UNS * INC # F5: 7,9 => UNS * DIS # F6: 7,9 => CTR => F6: 2,4,5 * INC # F6: 2,4,5 => UNS * INC # I6: 7,9 => UNS * PRF # I6: 8 => SOL * INC # D7: 4,8 => UNS * DIS # F7: 4,8 => CTR => F7: 7,9 * INC # F7: 7,9 => UNS * DIS # I7: 4,8 => CTR => I7: 7,9 * INC # I7: 7,9 => UNS * INC # B6: 4,8 => UNS * DIS # B6: 5 => CTR => B6: 4,8 * INC # I8: 4,8 => UNS * PRF # I8: 3 => SOL * INC # C4: 4,8 => UNS * INC # C4: 7 => UNS * INC # F7: 7,9 => UNS * DIS # F9: 7,9 => CTR => F9: 2,4,8 * INC # F9: 2,4,8 => UNS * INC # G9: 7,9 => UNS * DIS # I9: 7,9 => CTR => I9: 4,8 * INC # I9: 4,8 => UNS * PRF # I8: 3,8 => SOL * INC # I8: 4 => UNS * INC # G4: 3,8 => UNS * INC # G4: 7,9 => UNS * CNT 49 HDP CHAINS / 49 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # D1: 7,8 => UNS * INC # F1: 7,8 => UNS * DIS # F7: 7,8 => CTR => F7: 4,9 * DIS F7: 4,9 # F9: 7,8 => CTR => F9: 2,4,9 * INC F7: 4,9 + F9: 2,4,9 # F1: 7,8 => UNS * DIS F7: 4,9 + F9: 2,4,9 # F1: 3 => CTR => F1: 7,8 * INC F7: 4,9 + F9: 2,4,9 + F1: 7,8 # G1: 7,8 => UNS * INC F7: 4,9 + F9: 2,4,9 + F1: 7,8 # H1: 7,8 => UNS * INC F7: 4,9 + F9: 2,4,9 + F1: 7,8 # H4: 7,8 => UNS * INC F7: 4,9 + F9: 2,4,9 + F1: 7,8 # H4: 4,9 => UNS * DIS F7: 4,9 + F9: 2,4,9 + F1: 7,8 # F4: 2,9 => CTR => F4: 3,4 * PRF F7: 4,9 + F9: 2,4,9 + F1: 7,8 + F4: 3,4 # B6: 4,5 => SOL * STA F7: 4,9 + F9: 2,4,9 + F1: 7,8 + F4: 3,4 + B6: 4,5 * CNT 12 HDP CHAINS / 12 HYP OPENED