Analysis of zz-sudoku-de-657771-base.sdk
Contents
Original Sudoku
level: medium
position: ..2...5......9.8.16..31..2....9....7..72.69..5....8....5..64..87.4.2......3...4.. initial
Autosolve
position: ..2..75...75.928.16..31572....9.1..7..72.69..5....8....5..64..87.4.23.....3..94.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A1: 3,4 => CTR => A1: 1,9 * DIS # B1: 3,4 => CTR => B1: 1,9 * DIS # H2: 6 => CTR => H2: 3,4 * DIS # B3: 8,9 => CTR => B3: 4 * DIS # D1: 6 => CTR => D1: 4,8 * DIS # D1: 4,6 => CTR => D1: 8 * PRF # D1: 8 => SOL * DIS # H2: 3 => CTR => H2: 4,6 * DIS # I1: 4,9 => CTR => I1: 3,6 * DIS # B3: 8 => CTR => B3: 4,9 * DIS # H4: 3,4,5 => CTR => H4: 6,8 * PRF # E6: 4,7 => SOL * DIS # E6: 3 => CTR => E6: 4,7 * PRF # A7: 1,9 => SOL * DIS # B8: 1,9 => CTR => B8: 6,8 * DIS # H7: 1,9 => CTR => H7: 3,7 * DIS # C6: 6 => CTR => C6: 1,9 * PRF # D9: 1,7 => SOL * DIS # H7: 1,7 => CTR => H7: 3,9 * PRF # H7: 3,9 => SOL * DIS # D9: 7,8 => CTR => D9: 1,5 * DIS # H9: 1,6 => CTR => H9: 5,7 * DIS # B8: 1,6 => CTR => B8: 8,9 * CNT 23 HDP CHAINS / 46 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A1: 3,4 => CTR => A1: 1,9 * DIS A1: 1,9 # B1: 3,4 => CTR => B1: 1,9 * DIS A1: 1,9 + B1: 1,9 # D1: 6 => CTR => D1: 4,8 * PRF A1: 1,9 + B1: 1,9 + D1: 4,8 # E6: 4,7 => SOL * STA A1: 1,9 + B1: 1,9 + D1: 4,8 + E6: 4,7 * CNT 4 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..2...5......9.8.16..31..2....9....7..72.69..5....8....5..64..87.4.2......3...4.. | initial |
| ..2..75...75.928.16..31572....9.1..7..72.69..5....8....5..64..87.4.23.....3..94.. | autosolve |
| 192847563375692841648315729426951387817236954539478612951764238784523196263189475 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (11) A2: 3,4 C3: 8,9 E1: 4,8 D2: 4,6 I3: 4,9 C4: 6,8 D6: 4,7 C7: 1,9 D7: 1,7 E9: 7,8 G8: 1,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,B1: 1.. / A1 = 1 => 0 pairs (*) / B1 = 1 => 0 pairs (X) C6,C7: 1.. / C6 = 1 => 0 pairs (X) / C7 = 1 => 0 pairs (_) G7,I9: 2.. / G7 = 2 => 0 pairs (*) / I9 = 2 => 0 pairs (X) A7,G7: 2.. / A7 = 2 => 16 pairs (_) / G7 = 2 => 0 pairs (*) I6,I9: 2.. / I6 = 2 => 0 pairs (*) / I9 = 2 => 0 pairs (X) G7,H7: 3.. / G7 = 3 => 0 pairs (X) / H7 = 3 => 0 pairs (_) A2,H2: 3.. / A2 = 3 => 11 pairs (_) / H2 = 3 => 0 pairs (X) B3,I3: 4.. / B3 = 4 => 13 pairs (_) / I3 = 4 => 0 pairs (X) E4,E5: 5.. / E4 = 5 => 12 pairs (_) / E5 = 5 => 0 pairs (X) D8,D9: 5.. / D8 = 5 => 19 pairs (_) / D9 = 5 => 13 pairs (_) E4,H4: 5.. / E4 = 5 => 12 pairs (_) / H4 = 5 => 0 pairs (X) D1,D2: 6.. / D1 = 6 => 0 pairs (X) / D2 = 6 => 12 pairs (_) C4,C6: 6.. / C4 = 6 => 12 pairs (_) / C6 = 6 => 0 pairs (X) B8,B9: 6.. / B8 = 6 => 0 pairs (X) / B9 = 6 => 12 pairs (_) D2,H2: 6.. / D2 = 6 => 12 pairs (_) / H2 = 6 => 0 pairs (X) D6,E6: 7.. / D6 = 7 => 0 pairs (X) / E6 = 7 => 0 pairs (_) H7,H9: 7.. / H7 = 7 => 0 pairs (X) / H9 = 7 => 0 pairs (_) D7,H7: 7.. / D7 = 7 => 0 pairs (*) / H7 = 7 => 0 pairs (X) E6,E9: 7.. / E6 = 7 => 0 pairs (*) / E9 = 7 => 0 pairs (X) B3,C3: 8.. / B3 = 8 => 0 pairs (X) / C3 = 8 => 12 pairs (_) D1,E1: 8.. / D1 = 8 => 0 pairs (*) / E1 = 8 => 0 pairs (X) H4,H5: 8.. / H4 = 8 => 13 pairs (_) / H5 = 8 => 0 pairs (X) B8,D8: 8.. / B8 = 8 => 15 pairs (_) / D8 = 8 => 0 pairs (X) C3,C4: 8.. / C3 = 8 => 12 pairs (_) / C4 = 8 => 0 pairs (X) E1,E9: 8.. / E1 = 8 => 0 pairs (X) / E9 = 8 => 0 pairs (_) B6,C6: 9.. / B6 = 9 => 14 pairs (_) / C6 = 9 => 0 pairs (*) A1,A7: 9.. / A1 = 9 => 13 pairs (_) / A7 = 9 => 0 pairs (*) * DURATION: 0:00:43.750007 START: 07:40:11.805657 END: 07:40:55.555664 2017-05-01 * CP COUNT: (27) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,C3,C4,C7,D2,D6,D7,E1,E9,G8,I3) * ..2..75...75.928.16..31572....9.1..7..72.69..5....8....5..64..87.4.23.....3..94.. * PAIR A2: 3,4 BLK 1 A1: 3,4,1,9 # reduction candidate for 3,4 A1: 3,4 => CTR * .128475.3.75.928.16..31572....9.1..7..72.69..5....8...9517642387.4.23.....3.8947. A1: 1,9 # 12 pairs B1: 3,4,1,9 # reduction candidate for 3,4 B1: 3,4 => CTR * 1.28475.3.75.928.16..31572....9.1..7..72.69..5....8...9517642387.4.23.....3.8947. B1: 1,9 # 12 pairs * PAIR A2: 3,4 ROW 2 H2: 3,4,6 # reduction candidate for 3,4 H2: 6 => CTR * 9126875..375492861648315729..69512.7..72.69155.17.8....591643787.4.231....3.79452 H2: 3,4 # 12 pairs * PAIR A2: 3,4 COL A A4: 3,4,2,8 # reduction candidate for 3,4 A4: 3,4 # 14 pairs A5: 3,4,1,8 # reduction candidate for 3,4 A5: 3,4 # 16 pairs * PAIR C3: 8,9 BLK 1 B3: 8,9,4 # reduction candidate for 8,9 B3: 8,9 => CTR * ..28475.3.75.928.16..315724...9.1..7..72.69..5....8...9517642387.4.23.....3.8947. B3: 4 # 13 pairs * PAIR E1: 4,8 BLK 2 D1: 4,8,6 # reduction candidate for 4,8 D1: 6 => CTR * 9126875..375492861648315729..69512.7..72.69155.17.8....591643787.4.231....3.79452 D1: 4,8 # 12 pairs * PAIR D2: 4,6 BLK 2 D1: 4,6,8 # reduction candidate for 4,6 D1: 4,6 => CTR * 912.875..375.928.1648315729..69.12.7..72.691.5.17.8....591643787.4.231....3.794.2 D1: 8 => SOLVED * 192847563375692841648315729426951387817236954539478612951764238784523196263189475 * PAIR D2: 4,6 ROW 2 H2: 4,6,3 # reduction candidate for 4,6 H2: 3 => CTR * 9.2..75..4756928316..315724...9.1..7..72.69..5....8...25..643.87.4.23.....3..94.2 H2: 4,6 # 11 pairs * PAIR I3: 4,9 BLK 3 H1: 4,9,3,6 # reduction candidate for 4,9 H1: 4,9 # 14 pairs I1: 4,9,3,6 # reduction candidate for 4,9 I1: 4,9 => CTR * 912..7534375492861648315729..69.12.7..72.69..5297.8...251.643.87.4.23....63..94.2 I1: 3,6 # 12 pairs * PAIR I3: 4,9 ROW 3 B3: 4,9,8 # reduction candidate for 4,9 B3: 8 => CTR * ..2..75...75.928.1689315724..89.1..7..72.698.596..8...951764238764823.....3..94.. B3: 4,9 # 12 pairs * PAIR C4: 6,8 ROW 4 H4: 6,8,3,4,5 # reduction candidate for 6,8 H4: 3,4,5 => CTR * ..28475...756928.16.831572.8.69.1.57..72569845.9478..2951764238784523...263189475 H4: 6,8 # 14 pairs * PAIR D6: 4,7 BLK 5 E6: 4,7,3 # reduction candidate for 4,7 E6: 4,7 => SOLVED * 192847563375692841648315729426951387817236954539478612951764238784523196263189475 E6: 3 => CTR * 912.875..375.928.1648315729..69.12.7..72.691.5.1738....591643787.4.231....3.794.2 * PAIR C7: 1,9 BLK 7 A7: 1,9,2 # reduction candidate for 1,9 A7: 1,9 => SOLVED * 192847563375692841648315729426951387817236954539478612951764238784523196263189475 A7: 2 # 16 pairs B8: 1,9,6,8 # reduction candidate for 1,9 B8: 1,9 => CTR * ..2.875...75.928.16..31572....9.1..7..72.69..5..7.81..251.64..87.4823....63579412 B8: 6,8 # 12 pairs * PAIR C7: 1,9 ROW 7 H7: 1,9,3,7 # reduction candidate for 1,9 H7: 1,9 => CTR * 9128475..3756928416483157294.69.12878.72.69..5..478...25.7643.8784.23...163589472 H7: 3,7 # 12 pairs * PAIR C7: 1,9 COL C C6: 1,9,6 # reduction candidate for 1,9 C6: 6 => CTR * ..28475...756928.16.9315724..89.1..7..72.698.596478...9517642387.4.23.....3.8947. C6: 1,9 # 12 pairs * PAIR D7: 1,7 BLK 8 D9: 1,7,5,8 # reduction candidate for 1,7 D9: 1,7 => SOLVED * 192847563375692841648315729426951387817236954539478612951764238784523196263189475 D9: 5,8 # 12 pairs * PAIR D7: 1,7 ROW 7 H7: 1,7,3,9 # reduction candidate for 1,7 H7: 1,7 => CTR * 912..75..375.928.1648315729..69.12.7..72.69..5....8...259.643.87.4.23.....3..94.2 H7: 3,9 => SOLVED * 192847563375692841648315729426951387817236954539478612951764238784523196263189475 * PAIR E9: 7,8 BLK 8 D9: 7,8,1,5 # reduction candidate for 7,8 D9: 7,8 => CTR * 912..75..375.928.1648315729..69512.7.372.69..5.1..8....591643787845231..163..9452 D9: 1,5 # 12 pairs * PAIR G8: 1,6 BLK 9 H8: 1,6,5,9 # reduction candidate for 1,6 H8: 1,6 # 18 pairs H9: 1,6,5,7 # reduction candidate for 1,6 H9: 1,6 => CTR * 912.875.6375692841648315729..69.12.7..72.691.5.1..8...2591643787.4.231....3579462 H9: 5,7 # 12 pairs * PAIR G8: 1,6 ROW 8 B8: 1,6,8,9 # reduction candidate for 1,6 B8: 1,6 => CTR * 912.875.6375692841648315729..69.12.7..72.691.5.17.8....591643787.48231....3579462 B8: 8,9 # 13 pairs * PAIR G8: 1,6 COL G G6: 1,6,2,3 # reduction candidate for 1,6 G6: 1,6 # 14 pairs G6: 2,3 # 12 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-sudoku-de-657771-base-pr-000.dot * REASONING * DIS # A1: 3,4 => CTR => A1: 1,9 * DIS # B1: 3,4 => CTR => B1: 1,9 * DIS # H2: 6 => CTR => H2: 3,4 * DIS # B3: 8,9 => CTR => B3: 4 * DIS # D1: 6 => CTR => D1: 4,8 * DIS # D1: 4,6 => CTR => D1: 8 * PRF # D1: 8 => SOL * DIS # H2: 3 => CTR => H2: 4,6 * DIS # I1: 4,9 => CTR => I1: 3,6 * DIS # B3: 8 => CTR => B3: 4,9 * DIS # H4: 3,4,5 => CTR => H4: 6,8 * PRF # E6: 4,7 => SOL * DIS # E6: 3 => CTR => E6: 4,7 * PRF # A7: 1,9 => SOL * DIS # B8: 1,9 => CTR => B8: 6,8 * DIS # H7: 1,9 => CTR => H7: 3,7 * DIS # C6: 6 => CTR => C6: 1,9 * PRF # D9: 1,7 => SOL * DIS # H7: 1,7 => CTR => H7: 3,9 * PRF # H7: 3,9 => SOL * DIS # D9: 7,8 => CTR => D9: 1,5 * DIS # H9: 1,6 => CTR => H9: 5,7 * DIS # B8: 1,6 => CTR => B8: 8,9 * CNT 23 HDP CHAINS / 46 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,C3,C4,C7,D2,D6,D7,E1,E9,G8,I3) * ..2..75...75.928.16..31572....9.1..7..72.69..5....8....5..64..87.4.23.....3..94.. * PAIR A2: 3,4 BLK 1 A1: 3,4,1,9 # reduction candidate for 3,4 A1: 3,4 => CTR * .128475.3.75.928.16..31572....9.1..7..72.69..5....8...9517642387.4.23.....3.8947. B1: 3,4,1,9 # reduction candidate for 3,4 B1: 3,4 => CTR * 1.28475.3.75.928.16..31572....9.1..7..72.69..5....8...9517642387.4.23.....3.8947. * PAIR E1: 4,8 BLK 2 D1: 4,8,6 # reduction candidate for 4,8 D1: 6 => CTR * 9126875..375492861648315729..69512.7..72.69155.17.8....591643787.4.2319...3.79452 * PAIR D6: 4,7 BLK 5 E6: 4,7,3 # reduction candidate for 4,7 E6: 4,7 => SOLVED * 192847563375692841648315729426951387817236954539478612951764238784523196263189475 * DURATION: 0:00:06.183469 START: 07:41:33.104888 END: 07:41:39.288357 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-sudoku-de-657771-base-pr-001.dot * REASONING * DIS # A1: 3,4 => CTR => A1: 1,9 * DIS A1: 1,9 # B1: 3,4 => CTR => B1: 1,9 * DIS A1: 1,9 + B1: 1,9 # D1: 6 => CTR => D1: 4,8 * PRF A1: 1,9 + B1: 1,9 + D1: 4,8 # E6: 4,7 => SOL * STA A1: 1,9 + B1: 1,9 + D1: 4,8 + E6: 4,7 * CNT 4 HDP CHAINS / 5 HYP OPENED
Header Info
http://www.sudokus.de/657771.html sehr schwierig -------------------------------------------------- level: medium * PAIR REDUCTION .. * ROUND 1: ..2..75...75.928.16..31572....9.1..7..72.69..5....8....5..64..87.4.23.....3..94.. A2: 3,4 A1: 1,3,4,9 # reduction candidate for 3,4 A1: 3,4 => CTR * .128475.3.75.928.16..31572....9.1..7..72.69..5....8...9517642387.4.23.....3.8947. B1: 1,3,4,9 # reduction candidate for 3,4 B1: 3,4 => CTR * 1.28475.3.75.928.16..31572....9.1..7..72.69..5....8...9517642387.4.23.....3.8947. E1: 4,8 D1: 4,6,8 # reduction candidate for 4,8 D1: 6 => CTR * 9126875..375492861648315729..69512.7..72.69155.17.8....591643787.4.2319...3.79452 D6: 4,7 E6: 3,4,7 # reduction candidate for 4,7 E6: 4,7 => SOLVED * 192847563375692841648315729426951387817236954539478612951764238784523196263189475 * SOLVED! -------------------------------------------------- * AUTO .. F1 = 7 # set value F3: 5 # naked single C2 = 5 # set value F2: 2 # naked single F2 = 2 # set value F3 = 5 # set value G3 = 7 # set value F8 = 3 # set value F4: 1 # naked single B2: 7.. # hidden single F9: 9.. # hidden single B2 = 7 # set value F4 = 1 # set value F9: 9 # naked single F9 = 9 # set value Q2: 8.. = D1,E1: 8.. => A1,B1 != 8 Q7: 6.. = B8,B9: 6.. => B4,B6 != 6 Q5: 5.. = E4,E5: 5.. => E9 != 5 * UNSOLVED! |:step:| 00 -------------------------------------------------- * DISABLE VALUE:: E6 != 3 |:step:| 01 --------------------------------------------------
Solution
position: 192847563375692841648315729426951387817236954539478612951764238784523196263189475 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: 3,4 => CTR => A1: 1,9 * INC # A1: 1,9 => UNS * DIS # B1: 3,4 => CTR => B1: 1,9 * INC # B1: 1,9 => UNS * INC # H2: 3,4 => UNS * DIS # H2: 6 => CTR => H2: 3,4 * INC # A4: 3,4 => UNS * INC # A5: 3,4 => UNS * DIS # B3: 8,9 => CTR => B3: 4 * INC # B3: 4 => UNS * INC # D1: 4,8 => UNS * DIS # D1: 6 => CTR => D1: 4,8 * DIS # D1: 4,6 => CTR => D1: 8 * PRF # D1: 8 => SOL * INC # H2: 4,6 => UNS * DIS # H2: 3 => CTR => H2: 4,6 * INC # H1: 4,9 => UNS * DIS # I1: 4,9 => CTR => I1: 3,6 * INC # I1: 3,6 => UNS * INC # B3: 4,9 => UNS * DIS # B3: 8 => CTR => B3: 4,9 * INC # H4: 6,8 => UNS * DIS # H4: 3,4,5 => CTR => H4: 6,8 * PRF # E6: 4,7 => SOL * DIS # E6: 3 => CTR => E6: 4,7 * PRF # A7: 1,9 => SOL * INC # A7: 2 => UNS * DIS # B8: 1,9 => CTR => B8: 6,8 * INC # B8: 6,8 => UNS * DIS # H7: 1,9 => CTR => H7: 3,7 * INC # H7: 3,7 => UNS * INC # C6: 1,9 => UNS * DIS # C6: 6 => CTR => C6: 1,9 * PRF # D9: 1,7 => SOL * INC # D9: 5,8 => UNS * DIS # H7: 1,7 => CTR => H7: 3,9 * PRF # H7: 3,9 => SOL * DIS # D9: 7,8 => CTR => D9: 1,5 * INC # D9: 1,5 => UNS * INC # H8: 1,6 => UNS * DIS # H9: 1,6 => CTR => H9: 5,7 * INC # H9: 5,7 => UNS * DIS # B8: 1,6 => CTR => B8: 8,9 * INC # B8: 8,9 => UNS * INC # G6: 1,6 => UNS * INC # G6: 2,3 => UNS * CNT 46 HDP CHAINS / 46 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A1: 3,4 => CTR => A1: 1,9 * DIS A1: 1,9 # B1: 3,4 => CTR => B1: 1,9 * INC A1: 1,9 + B1: 1,9 # D1: 4,8 => UNS * DIS A1: 1,9 + B1: 1,9 # D1: 6 => CTR => D1: 4,8 * PRF A1: 1,9 + B1: 1,9 + D1: 4,8 # E6: 4,7 => SOL * STA A1: 1,9 + B1: 1,9 + D1: 4,8 + E6: 4,7 * CNT 5 HDP CHAINS / 5 HYP OPENED