Analysis of zz-sudoku-de-678907-base.sdk
Contents
Original Sudoku
level: medium
position: .1.5.6.7...3...8...4.3.2.5..91...63.6.......1.52...48..7.9.3.1...8...9...2.6.8.4. initial
Autosolve
position: 219586374563..18298473921567918..63.684.3..913521694874769.3.18138...96.925618743 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # D8: 4,7 => SOL * DIS # D8: 2 => CTR => D8: 4,7 * PRF # E8: 2,5 => SOL * PRF # E4: 4,5 => SOL * DIS # E4: 2 => CTR => E4: 4,5 * PRF # F8: 4,5 => SOL * DIS # F8: 7 => CTR => F8: 4,5 * DIS # D8: 4 => CTR => D8: 2,7 * PRF # F8: 4 => SOL * PRF # E4: 4 => SOL * PRF # E8: 2,5 => SOL * PRF # E4: 4 => SOL * PRF # E8: 2,5 => SOL * CNT 13 HDP CHAINS / 20 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # D8: 4,7 => SOL * STA D8: 4,7 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .1.5.6.7...3...8...4.3.2.5..91...63.6.......1.52...48..7.9.3.1...8...9...2.6.8.4. | initial |
| 219586374563..18298473921567918..63.684.3..913521694874769.3.18138...96.925618743 | autosolve |
| 219586374563471829847392156791845632684237591352169487476953218138724965925618743 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (10) D2: 4,7 E2: 4,7 F4: 4,5 D5: 2,7 F5: 5,7 I4: 2,5 G5: 2,5 E7: 2,5 G7: 2,5 I8: 2,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E4,D5: 2.. / E4 = 2 => 0 pairs (X) / D5 = 2 => 0 pairs (_) I4,G5: 2.. / I4 = 2 => 0 pairs (*) / G5 = 2 => 0 pairs (X) G7,I8: 2.. / G7 = 2 => 0 pairs (*) / I8 = 2 => 0 pairs (X) E4,I4: 2.. / E4 = 2 => 0 pairs (X) / I4 = 2 => 0 pairs (_) D5,G5: 2.. / D5 = 2 => 0 pairs (*) / G5 = 2 => 0 pairs (X) E7,G7: 2.. / E7 = 2 => 0 pairs (X) / G7 = 2 => 0 pairs (_) D5,D8: 2.. / D5 = 2 => 0 pairs (*) / D8 = 2 => 0 pairs (X) G5,G7: 2.. / G5 = 2 => 0 pairs (X) / G7 = 2 => 0 pairs (_) I4,I8: 2.. / I4 = 2 => 0 pairs (*) / I8 = 2 => 0 pairs (X) D2,E2: 4.. / D2 = 4 => 9 pairs (_) / E2 = 4 => 0 pairs (X) E4,F4: 4.. / E4 = 4 => 0 pairs (*) / F4 = 4 => 0 pairs (X) D2,D8: 4.. / D2 = 4 => 9 pairs (_) / D8 = 4 => 0 pairs (X) F4,F8: 4.. / F4 = 4 => 12 pairs (_) / F8 = 4 => 0 pairs (*) I4,G5: 5.. / I4 = 5 => 0 pairs (X) / G5 = 5 => 0 pairs (_) G7,I8: 5.. / G7 = 5 => 0 pairs (X) / I8 = 5 => 0 pairs (_) F5,G5: 5.. / F5 = 5 => 0 pairs (X) / G5 = 5 => 0 pairs (_) E7,G7: 5.. / E7 = 5 => 0 pairs (*) / G7 = 5 => 0 pairs (X) G5,G7: 5.. / G5 = 5 => 0 pairs (*) / G7 = 5 => 0 pairs (X) I4,I8: 5.. / I4 = 5 => 0 pairs (X) / I8 = 5 => 0 pairs (_) D2,E2: 7.. / D2 = 7 => 0 pairs (X) / E2 = 7 => 9 pairs (_) D5,F5: 7.. / D5 = 7 => 0 pairs (X) / F5 = 7 => 0 pairs (_) E2,E8: 7.. / E2 = 7 => 9 pairs (_) / E8 = 7 => 0 pairs (X) F5,F8: 7.. / F5 = 7 => 0 pairs (*) / F8 = 7 => 0 pairs (X) * DURATION: 0:00:40.560394 START: 07:46:26.093343 END: 07:47:06.653737 2017-05-01 * CP COUNT: (23) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D2,D5,E2,E7,F4,F5,G5,G7,I4,I8) * 219586374563..18298473921567918..63.684.3..913521694874769.3.18138...96.925618743 * PAIR D2: 4,7 COL D D8: 4,7,2 # reduction candidate for 4,7 D8: 4,7 => SOLVED * 219586374563471829847392156791845632684237591352169487476953218138724965925618743 D8: 2 => CTR * 2195863745634718298473921567918..63.684735291352169487476923.18138...96.925618743 * PAIR E2: 4,7 COL E E8: 4,7,2,5 # reduction candidate for 4,7 E8: 2,5 => SOLVED * 219586374563471829847392156791845632684237591352169487476953218138724965925618743 E8: 4,7 # 12 pairs * PAIR F4: 4,5 BLK 5 E4: 4,5,2 # reduction candidate for 4,5 E4: 4,5 => SOLVED * 219586374563471829847392156791845632684237591352169487476953218138724965925618743 E4: 2 => CTR * 219586374563..18298473921567918246356847352913521694874769.3.18138...96.925618743 * PAIR F4: 4,5 COL F F8: 4,5,7 # reduction candidate for 4,5 F8: 4,5 => SOLVED * 219586374563471829847392156791845632684237591352169487476953218138724965925618743 F8: 7 => CTR * 219586374563..18298473921567918.463.684.35291352169487476923.18138...96.925618743 * PAIR D5: 2,7 COL D D8: 2,7,4 # reduction candidate for 2,7 D8: 4 => CTR * 219586374563..18298473921567918..63.6842375913521694874769532181384..96.925618743 D8: 2,7 # 9 pairs * PAIR F5: 5,7 COL F F8: 5,7,4 # reduction candidate for 5,7 F8: 4 => SOLVED * 219586374563471829847392156791845632684237591352169487476953218138724965925618743 F8: 5,7 # 12 pairs * PAIR I4: 2,5 ROW 4 E4: 2,5,4 # reduction candidate for 2,5 E4: 4 => SOLVED * 219586374563471829847392156791845632684237591352169487476953218138724965925618743 E4: 2,5 # 12 pairs * PAIR E7: 2,5 BLK 8 E8: 2,5,4,7 # reduction candidate for 2,5 E8: 2,5 => SOLVED * 219586374563471829847392156791845632684237591352169487476953218138724965925618743 E8: 4,7 # 12 pairs * PAIR E7: 2,5 COL E E4: 2,5,4 # reduction candidate for 2,5 E4: 4 => SOLVED * 219586374563471829847392156791845632684237591352169487476953218138724965925618743 E4: 2,5 # 12 pairs * PAIR I8: 2,5 ROW 8 E8: 2,5,4,7 # reduction candidate for 2,5 E8: 2,5 => SOLVED * 219586374563471829847392156791845632684237591352169487476953218138724965925618743 E8: 4,7 # 12 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-sudoku-de-678907-base-pr-000.dot * REASONING * PRF # D8: 4,7 => SOL * DIS # D8: 2 => CTR => D8: 4,7 * PRF # E8: 2,5 => SOL * PRF # E4: 4,5 => SOL * DIS # E4: 2 => CTR => E4: 4,5 * PRF # F8: 4,5 => SOL * DIS # F8: 7 => CTR => F8: 4,5 * DIS # D8: 4 => CTR => D8: 2,7 * PRF # F8: 4 => SOL * PRF # E4: 4 => SOL * PRF # E8: 2,5 => SOL * PRF # E4: 4 => SOL * PRF # E8: 2,5 => SOL * CNT 13 HDP CHAINS / 20 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D2,D5,E2,E7,F4,F5,G5,G7,I4,I8) * 219586374563..18298473921567918..63.684.3..913521694874769.3.18138...96.925618743 * PAIR D2: 4,7 COL D D8: 4,7,2 # reduction candidate for 4,7 D8: 4,7 => SOLVED * 219586374563471829847392156791845632684237591352169487476953218138724965925618743 * DURATION: 0:00:01.790650 START: 07:47:38.202124 END: 07:47:39.992774 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-sudoku-de-678907-base-pr-001.dot * REASONING * PRF # D8: 4,7 => SOL * STA D8: 4,7 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokus.de/678907.html sehr schwierig -------------------------------------------------- level: medium * PAIR REDUCTION .. * ROUND 1: 219586374563..18298473921567918..63.684.3..913521694874769.3.18138...96.925618743 D2: 4,7 D8: 2,4,7 # reduction candidate for 4,7 D8: 4,7 => SOLVED * 219586374563471829847392156791845632684237591352169487476953218138724965925618743 * SOLVED! -------------------------------------------------- -------------------------------------------------- * AUTO .. C1 = 9 # set value C9: 5 # naked single A2 = 5 # set value A7: 4 # naked single B2 = 6 # set value C3: 7 # naked single B8: 3 # naked single C3 = 7 # set value A3: 8 # naked single C5: 4 # naked single G3 = 1 # set value B5 = 8 # set value C5 = 4 # set value A4: 7 # naked single E6 = 6 # set value A7 = 4 # set value I7 = 8 # set value B8 = 3 # set value A8: 1 # naked single C9 = 5 # set value C7: 6 # naked single A1: 2.. # hidden single I3: 6.. # hidden single A6: 3.. # hidden single E5: 3.. # hidden single A9: 9.. # hidden single D4: 8.. # hidden single H8: 6.. # hidden single A1 = 2 # set value G1: 3 # naked single G1 = 3 # set value I1: 4 # naked single G9: 7 # naked single I1 = 4 # set value E1: 8 # naked single A3 = 8 # set value E3: 9 # naked single E3 = 9 # set value I3: 6 # naked single I3 = 6 # set value A4 = 7 # set value A6: 3 # naked single D4 = 8 # set value E5 = 3 # set value A6 = 3 # set value C7 = 6 # set value A8 = 1 # set value A9: 9 # naked single H8 = 6 # set value A9 = 9 # set value G9 = 7 # set value I9: 3 # naked single E9: 1 # naked single I9 = 3 # set value I6: 7.. # hidden single E1 = 8 # set value I6 = 7 # set value D6: 1 # naked single E9 = 1 # set value H5: 9.. # hidden single F6: 9.. # hidden single I2: 9.. # hidden single I2 = 9 # set value H2: 2 # naked single H5 = 9 # set value D6 = 1 # set value F6: 9 # naked single F6 = 9 # set value F2: 1.. # hidden single F2 = 1 # set value H2 = 2 # set value * UNSOLVED! |:step:| 00 -------------------------------------------------- highlight 2,5 * FORCE VALUE:: E4 = 4 E4 = 4 # set value F4: 5 # naked single E2: 7 # naked single D2: 4.. # hidden single D5: 2.. # hidden single I4: 2.. # hidden single F8: 4.. # hidden single |:step:| 01 --------------------------------------------------
Solution
position: 219586374563471829847392156791845632684237591352169487476953218138724965925618743 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 # D8: 4,7 => SOL * DIS # D8: 2 => CTR => D8: 4,7 * INC # E8: 4,7 => UNS * PRF # E8: 2,5 => SOL * PRF # E4: 4,5 => SOL * DIS # E4: 2 => CTR => E4: 4,5 * PRF # F8: 4,5 => SOL * DIS # F8: 7 => CTR => F8: 4,5 * INC # D8: 2,7 => UNS * DIS # D8: 4 => CTR => D8: 2,7 * INC # F8: 5,7 => UNS * PRF # F8: 4 => SOL * INC # E4: 2,5 => UNS * PRF # E4: 4 => SOL * PRF # E8: 2,5 => SOL * INC # E8: 4,7 => UNS * INC # E4: 2,5 => UNS * PRF # E4: 4 => SOL * PRF # E8: 2,5 => SOL * INC # E8: 4,7 => UNS * CNT 20 HDP CHAINS / 20 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # D8: 4,7 => SOL * STA D8: 4,7 * CNT 1 HDP CHAINS / 1 HYP OPENED