Analysis of zz-sudoku-de-772112-base.sdk
Contents
Original Sudoku
level: medium
position: 16..7.5.8..3.....44....6.9...52.8...9...5...3...3.12...8.9....13.....8..5.7.8..62 initial
Autosolve
position: 16947.5.8..3..96.44....6.97.35248...9..657483...3912..28.9....13..7..8..5.718..62 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A6: 7,8 => CTR => A6: 6 * PRF # A6: 6 => SOL * PRF # A6: 6,7 => SOL * DIS # A6: 8 => CTR => A6: 6,7 * DIS # G4: 1,7 => CTR => G4: 9 * PRF # G4: 9 => SOL * PRF # H7: 5,7 => SOL * PRF # C8: 4,6 => SOL * DIS # C8: 1 => CTR => C8: 4,6 * DIS # B8: 4,9 => CTR => B8: 1 * PRF # B8: 1 => SOL * PRF # F7: 3,4 => SOL * DIS # H7: 3,7 => CTR => H7: 4,5 * PRF # H7: 4,5 => SOL * PRF # H7: 4,5 => SOL * DIS # H7: 3,7 => CTR => H7: 4,5 * PRF # F8: 4,5 => SOL * DIS # F8: 2 => CTR => F8: 4,5 * CNT 18 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:
* DIS # A6: 7,8 => CTR => A6: 6 * PRF A6: 6 => SOL * STA A6: 6 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 16..7.5.8..3.....44....6.9...52.8...9...5...3...3.12...8.9....13.....8..5.7.8..62 | initial |
| 16947.5.8..3..96.44....6.97.35248...9..657483...3912..28.9....13..7..8..5.718..62 | autosolve |
| 169472538873519624452836197735248916921657483648391275284963751316725849597184362 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (30) A2: 7,8 B2: 5,7 B3: 2,5 C3: 2,8 F1: 2,3 D2: 5,8 E2: 1,2 D3: 5,8 E3: 1,3 H1: 2,3 H2: 1,2 G3: 1,3 A4: 6,7 B5: 1,2 C5: 1,2 B6: 4,7 C6: 4,8 H4: 1,7 I4: 6,9 H6: 5,7 I6: 5,6 C7: 4,6 B9: 4,9 E7: 3,6 E8: 2,6 F9: 3,4 G7: 3,7 H8: 4,5 I8: 5,9 G9: 3,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E2,E3: 1.. / E2 = 1 => 0 pairs (*) / E3 = 1 => 0 pairs (X) H2,G3: 1.. / H2 = 1 => 0 pairs (X) / G3 = 1 => 0 pairs (_) B5,C5: 1.. / B5 = 1 => 0 pairs (X) / C5 = 1 => 0 pairs (_) G4,H4: 1.. / G4 = 1 => 0 pairs (X) / H4 = 1 => 0 pairs (_) B8,C8: 1.. / B8 = 1 => 0 pairs (*) / C8 = 1 => 0 pairs (X) E2,H2: 1.. / E2 = 1 => 0 pairs (*) / H2 = 1 => 0 pairs (X) E3,G3: 1.. / E3 = 1 => 0 pairs (X) / G3 = 1 => 0 pairs (_) B5,B8: 1.. / B5 = 1 => 0 pairs (X) / B8 = 1 => 0 pairs (_) C5,C8: 1.. / C5 = 1 => 0 pairs (*) / C8 = 1 => 0 pairs (X) G3,G4: 1.. / G3 = 1 => 0 pairs (*) / G4 = 1 => 0 pairs (X) H2,H4: 1.. / H2 = 1 => 0 pairs (X) / H4 = 1 => 0 pairs (_) B3,C3: 2.. / B3 = 2 => 0 pairs (X) / C3 = 2 => 0 pairs (_) F1,E2: 2.. / F1 = 2 => 0 pairs (*) / E2 = 2 => 0 pairs (X) H1,H2: 2.. / H1 = 2 => 0 pairs (X) / H2 = 2 => 0 pairs (_) B5,C5: 2.. / B5 = 2 => 0 pairs (*) / C5 = 2 => 0 pairs (X) E8,F8: 2.. / E8 = 2 => 0 pairs (*) / F8 = 2 => 0 pairs (X) F1,H1: 2.. / F1 = 2 => 0 pairs (*) / H1 = 2 => 0 pairs (X) E2,H2: 2.. / E2 = 2 => 0 pairs (X) / H2 = 2 => 0 pairs (_) B3,B5: 2.. / B3 = 2 => 0 pairs (X) / B5 = 2 => 0 pairs (_) C3,C5: 2.. / C3 = 2 => 0 pairs (*) / C5 = 2 => 0 pairs (X) E2,E8: 2.. / E2 = 2 => 0 pairs (X) / E8 = 2 => 0 pairs (_) F1,F8: 2.. / F1 = 2 => 0 pairs (*) / F8 = 2 => 0 pairs (X) F1,E3: 3.. / F1 = 3 => 0 pairs (X) / E3 = 3 => 0 pairs (_) H1,G3: 3.. / H1 = 3 => 0 pairs (*) / G3 = 3 => 0 pairs (X) F1,H1: 3.. / F1 = 3 => 0 pairs (X) / H1 = 3 => 0 pairs (_) E3,G3: 3.. / E3 = 3 => 0 pairs (*) / G3 = 3 => 0 pairs (X) F9,G9: 3.. / F9 = 3 => 0 pairs (X) / G9 = 3 => 0 pairs (_) E3,E7: 3.. / E3 = 3 => 0 pairs (*) / E7 = 3 => 0 pairs (X) H1,H7: 3.. / H1 = 3 => 0 pairs (*) / H7 = 3 => 0 pairs (X) B6,C6: 4.. / B6 = 4 => 0 pairs (*) / C6 = 4 => 0 pairs (X) H7,H8: 4.. / H7 = 4 => 0 pairs (X) / H8 = 4 => 32 pairs (_) B9,F9: 4.. / B9 = 4 => 0 pairs (X) / F9 = 4 => 0 pairs (_) B2,B3: 5.. / B2 = 5 => 0 pairs (X) / B3 = 5 => 0 pairs (_) D2,D3: 5.. / D2 = 5 => 0 pairs (*) / D3 = 5 => 0 pairs (X) H6,I6: 5.. / H6 = 5 => 0 pairs (X) / I6 = 5 => 0 pairs (_) F7,F8: 5.. / F7 = 5 => 31 pairs (_) / F8 = 5 => 0 pairs (*) B2,D2: 5.. / B2 = 5 => 0 pairs (X) / D2 = 5 => 0 pairs (_) B3,D3: 5.. / B3 = 5 => 0 pairs (*) / D3 = 5 => 0 pairs (X) F7,H7: 5.. / F7 = 5 => 31 pairs (_) / H7 = 5 => 0 pairs (*) I6,I8: 5.. / I6 = 5 => 0 pairs (*) / I8 = 5 => 0 pairs (X) A4,A6: 6.. / A4 = 6 => 0 pairs (X) / A6 = 6 => 0 pairs (_) I4,I6: 6.. / I4 = 6 => 0 pairs (*) / I6 = 6 => 0 pairs (X) C7,C8: 6.. / C7 = 6 => 0 pairs (X) / C8 = 6 => 0 pairs (_) E7,E8: 6.. / E7 = 6 => 0 pairs (*) / E8 = 6 => 0 pairs (X) A4,I4: 6.. / A4 = 6 => 0 pairs (X) / I4 = 6 => 0 pairs (_) A6,I6: 6.. / A6 = 6 => 0 pairs (*) / I6 = 6 => 0 pairs (X) C7,E7: 6.. / C7 = 6 => 0 pairs (X) / E7 = 6 => 0 pairs (_) C8,E8: 6.. / C8 = 6 => 0 pairs (*) / E8 = 6 => 0 pairs (X) A2,B2: 7.. / A2 = 7 => 0 pairs (X) / B2 = 7 => 0 pairs (_) G7,H7: 7.. / G7 = 7 => 30 pairs (_) / H7 = 7 => 0 pairs (X) B2,B6: 7.. / B2 = 7 => 0 pairs (*) / B6 = 7 => 0 pairs (X) G4,G7: 7.. / G4 = 7 => 0 pairs (X) / G7 = 7 => 30 pairs (_) A2,C3: 8.. / A2 = 8 => 0 pairs (*) / C3 = 8 => 0 pairs (X) D2,D3: 8.. / D2 = 8 => 0 pairs (X) / D3 = 8 => 0 pairs (_) A6,C6: 8.. / A6 = 8 => 0 pairs (X) / C6 = 8 => 0 pairs (_) A2,D2: 8.. / A2 = 8 => 0 pairs (*) / D2 = 8 => 0 pairs (X) C3,D3: 8.. / C3 = 8 => 0 pairs (X) / D3 = 8 => 0 pairs (_) A2,A6: 8.. / A2 = 8 => 0 pairs (*) / A6 = 8 => 0 pairs (X) C3,C6: 8.. / C3 = 8 => 0 pairs (X) / C6 = 8 => 0 pairs (_) G4,I4: 9.. / G4 = 9 => 0 pairs (*) / I4 = 9 => 0 pairs (X) B8,B9: 9.. / B8 = 9 => 0 pairs (X) / B9 = 9 => 0 pairs (_) I8,G9: 9.. / I8 = 9 => 0 pairs (*) / G9 = 9 => 0 pairs (X) B8,I8: 9.. / B8 = 9 => 0 pairs (X) / I8 = 9 => 0 pairs (_) B9,G9: 9.. / B9 = 9 => 0 pairs (*) / G9 = 9 => 0 pairs (X) G4,G9: 9.. / G4 = 9 => 0 pairs (*) / G9 = 9 => 0 pairs (X) I4,I8: 9.. / I4 = 9 => 0 pairs (X) / I8 = 9 => 0 pairs (_) * DURATION: 0:01:56.432082 START: 08:42:22.954354 END: 08:44:19.386436 2017-05-01 * CP COUNT: (66) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A4,B2,B3,B5,B6,B9,C3,C5,C6,C7,D2,D3,E2,E3,E7,E8,F1,F9,G3,G7,G9,H1,H2,H4,H6,H8,I4,I6,I8) * 16947.5.8..3..96.44....6.97.35248...9..657483...3912..28.9....13..7..8..5.718..62 * PAIR A2: 7,8 COL A A6: 7,8,6 # reduction candidate for 7,8 A6: 7,8 => CTR * 16947.5.8..3..96.44....6.97635248..99..657483...3912.628.9....1391762845547183.62 A6: 6 => SOLVED * 169472538873519624452836197735248916921657483648391275284963751316725849597184362 * PAIR A4: 6,7 BLK 4 A6: 6,7,8 # reduction candidate for 6,7 A6: 6,7 => SOLVED * 169472538873519624452836197735248916921657483648391275284963751316725849597184362 A6: 8 => CTR * 16947.5.8..3..96.44....6.97635248..99..6574838743912562869357.13..7..8..5.718..62 * PAIR H4: 1,7 BLK 6 G4: 1,7,9 # reduction candidate for 1,7 G4: 1,7 => CTR * 16947.5.8..3..96.44....6.97.35248..99..657483...3912.628.9....1391762845547183.62 G4: 9 => SOLVED * 169472538873519624452836197735248916921657483648391275284963751316725849597184362 * PAIR H6: 5,7 COL H H7: 5,7,3,4 # reduction candidate for 5,7 H7: 5,7 => SOLVED * 169472538873519624452836197735248916921657483648391275284963751316725849597184362 H7: 3,4 # 32 pairs * PAIR C7: 4,6 BLK 7 C8: 4,6,1 # reduction candidate for 4,6 C8: 4,6 => SOLVED * 169472538873519624452836197735248916921657483648391275284963751316725849597184362 C8: 1 => CTR * 16947.5.8..3..96.44....6.97.35248...9..657483...3912..28693.7.13.17628..5.7184362 * PAIR B9: 4,9 BLK 7 B8: 4,9,1 # reduction candidate for 4,9 B8: 4,9 => CTR * 169473528..3.29614428516397.352481799126574838743912562869357413.17628..5.718..62 B8: 1 => SOLVED * 169472538873519624452836197735248916921657483648391275284963751316725849597184362 * PAIR F9: 3,4 BLK 8 F7: 3,4,5 # reduction candidate for 3,4 F7: 3,4 => SOLVED * 169472538873519624452836197735248916921657483648391275284963751316725849597184362 F7: 5 # 31 pairs * PAIR G7: 3,7 BLK 9 H7: 3,7,4,5 # reduction candidate for 3,7 H7: 3,7 => CTR * 16947.5.8..3..96.44....6.97.35248...9..657483...3912..28.9.5..13..7..8455.7184.62 H7: 4,5 => SOLVED * 169472538873519624452836197735248916921657483648391275284963751316725849597184362 * PAIR H8: 4,5 BLK 9 H7: 4,5,3,7 # reduction candidate for 4,5 H7: 4,5 => SOLVED * 169472538873519624452836197735248916921657483648391275284963751316725849597184362 H7: 3,7 => CTR * 16947.5.8..3..96.44....6.97.35248...9..657483...3912..28.9.5..13..7..8455.7184.62 * PAIR H8: 4,5 ROW 8 F8: 4,5,2 # reduction candidate for 4,5 F8: 4,5 => SOLVED * 169472538873519624452836197735248916921657483648391275284963751316725849597184362 F8: 2 => CTR * 16947.5.8..3..96.44....6.97.35248...9..657483...3912..28.9.5..13..7.28..5.7184362 * INCONCLUSIVE * SAVE PR GRAPH zz-sudoku-de-772112-base-pr-000.dot * REASONING * DIS # A6: 7,8 => CTR => A6: 6 * PRF # A6: 6 => SOL * PRF # A6: 6,7 => SOL * DIS # A6: 8 => CTR => A6: 6,7 * DIS # G4: 1,7 => CTR => G4: 9 * PRF # G4: 9 => SOL * PRF # H7: 5,7 => SOL * PRF # C8: 4,6 => SOL * DIS # C8: 1 => CTR => C8: 4,6 * DIS # B8: 4,9 => CTR => B8: 1 * PRF # B8: 1 => SOL * PRF # F7: 3,4 => SOL * DIS # H7: 3,7 => CTR => H7: 4,5 * PRF # H7: 4,5 => SOL * PRF # H7: 4,5 => SOL * DIS # H7: 3,7 => CTR => H7: 4,5 * PRF # F8: 4,5 => SOL * DIS # F8: 2 => CTR => F8: 4,5 * CNT 18 HDP CHAINS / 20 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A4,B2,B3,B5,B6,B9,C3,C5,C6,C7,D2,D3,E2,E3,E7,E8,F1,F9,G3,G7,G9,H1,H2,H4,H6,H8,I4,I6,I8) * 16947.5.8..3..96.44....6.97.35248...9..657483...3912..28.9....13..7..8..5.718..62 * PAIR A2: 7,8 COL A A6: 7,8,6 # reduction candidate for 7,8 A6: 7,8 => CTR * 16947.5.8..3..96.44....6.97635248..99..657483...3912.628.9....1391762845547183.62 A6: 6 => SOLVED * 169472538873519624452836197735248916921657483648391275284963751316725849597184362 * DURATION: 0:00:03.089118 START: 08:44:43.741565 END: 08:44:46.830683 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-sudoku-de-772112-base-pr-001.dot * REASONING * DIS # A6: 7,8 => CTR => A6: 6 * PRF A6: 6 => SOL * STA A6: 6 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokus.de/772112.html sehr schwierig -------------------------------------------------- level: medium * PAIR REDUCTION .. * ROUND 1: 16947.5.8..3..96.44....6.97.35248...9..657483...3912..28.9....13..7..8..5.718..62 A2: 7,8 A6: 6,7,8 # reduction candidate for 7,8 A6: 7,8 => CTR * 16947.5.8..3..96.44....6.97635248..99..657483...3912.628.9....1391762845547183.62 A6: 6 => SOLVED * 169472538873519624452836197735248916921657483648391275284963751316725849597184362 * SOLVED! -------------------------------------------------- |:step:| 00 -------------------------------------------------- xwing |:guess:| highlight 7 H6 != 7 => A2,B2,A6,B6: 7.. => A4 != 7 H6 != 7 => CTR => H6 = 7 * AUTO .. * SOLVED! |:step:| 01 --------------------------------------------------
Solution
position: 169472538873519624452836197735248916921657483648391275284963751316725849597184362 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 # A6: 7,8 => CTR => A6: 6 * PRF # A6: 6 => SOL * PRF # A6: 6,7 => SOL * DIS # A6: 8 => CTR => A6: 6,7 * DIS # G4: 1,7 => CTR => G4: 9 * PRF # G4: 9 => SOL * PRF # H7: 5,7 => SOL * INC # H7: 3,4 => UNS * PRF # C8: 4,6 => SOL * DIS # C8: 1 => CTR => C8: 4,6 * DIS # B8: 4,9 => CTR => B8: 1 * PRF # B8: 1 => SOL * PRF # F7: 3,4 => SOL * INC # F7: 5 => UNS * DIS # H7: 3,7 => CTR => H7: 4,5 * PRF # H7: 4,5 => SOL * PRF # H7: 4,5 => SOL * DIS # H7: 3,7 => CTR => H7: 4,5 * PRF # F8: 4,5 => SOL * DIS # F8: 2 => CTR => F8: 4,5 * CNT 20 HDP CHAINS / 20 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A6: 7,8 => CTR => A6: 6 * PRF A6: 6 => SOL * STA A6: 6 * CNT 2 HDP CHAINS / 1 HYP OPENED