Analysis of zz-sudoku-de-720321-base.sdk
Contents
Original Sudoku
level: medium
position: 6..1.3..8.2.7.9.3...3...2....73.69..5.......7..94.85....1...8...7.8.1.2.8..5.7..9 initial
Autosolve
position: 694123758125789.3.783645291.1735698.5.8912..7..947851..512.487..768.1.258.25.71.9 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # G5: 4,6 => CTR => G5: 3 * PRF # G5: 3 => SOL * PRF # I6: 6 => SOL * PRF # B5: 3,6 => SOL * DIS # B5: 4 => CTR => B5: 3,6 * PRF # I6: 3,6 => SOL * DIS # I6: 2 => CTR => I6: 3,6 * DIS # G5: 4,6 => CTR => G5: 3 * PRF # G5: 3 => SOL * PRF # B5: 4,6 => SOL * DIS # B5: 3 => CTR => B5: 4,6 * PRF # A8: 3,9 => SOL * DIS # A8: 4 => CTR => A8: 3,9 * DIS # E7: 3,9 => CTR => E7: 6 * PRF # E7: 6 => SOL * DIS # A8: 9 => CTR => A8: 3,4 * PRF # B5: 6 => SOL * DIS # E7: 3,9 => CTR => E7: 6 * PRF # E7: 6 => SOL * PRF # A8: 3,9 => SOL * DIS # A8: 4 => CTR => A8: 3,9 * DIS # E7: 9 => CTR => E7: 3,6 * DIS # E7: 9 => CTR => E7: 3,6 * PRF # I6: 3,6 => SOL * DIS # I6: 2 => CTR => I6: 3,6 * DIS # A8: 9 => CTR => A8: 3,4 * PRF # G5: 3,4 => SOL * DIS # G5: 6 => CTR => G5: 3,4 * CNT 28 HDP CHAINS / 34 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # G5: 4,6 => CTR => G5: 3 * PRF G5: 3 => SOL * STA G5: 3 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 6..1.3..8.2.7.9.3...3...2....73.69..5.......7..94.85....1...8...7.8.1.2.8..5.7..9 | initial |
| 694123758125789.3.783645291.1735698.5.8912..7..947851..512.487..768.1.258.25.71.9 | autosolve |
| 694123758125789634783645291417356982568912347239478516951264873376891425842537169 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) G2: 4,6 I2: 4,6 A4: 2,4 A6: 2,3 B6: 3,6 I4: 2,4 H5: 4,6 A7: 3,9 B9: 3,4 E8: 3,9 E9: 3,6 I7: 3,6 G8: 3,4 H9: 4,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A4,A6: 2.. / A4 = 2 => 0 pairs (X) / A6 = 2 => 0 pairs (_) I4,I6: 2.. / I4 = 2 => 0 pairs (*) / I6 = 2 => 0 pairs (X) A4,I4: 2.. / A4 = 2 => 0 pairs (X) / I4 = 2 => 0 pairs (_) A6,I6: 2.. / A6 = 2 => 0 pairs (*) / I6 = 2 => 0 pairs (X) G5,I6: 3.. / G5 = 3 => 0 pairs (*) / I6 = 3 => 0 pairs (X) I7,G8: 3.. / I7 = 3 => 0 pairs (*) / G8 = 3 => 0 pairs (X) B5,G5: 3.. / B5 = 3 => 0 pairs (X) / G5 = 3 => 0 pairs (_) B9,E9: 3.. / B9 = 3 => 0 pairs (X) / E9 = 3 => 0 pairs (_) G5,G8: 3.. / G5 = 3 => 0 pairs (*) / G8 = 3 => 0 pairs (X) I6,I7: 3.. / I6 = 3 => 0 pairs (X) / I7 = 3 => 0 pairs (_) G2,I2: 4.. / G2 = 4 => 0 pairs (X) / I2 = 4 => 0 pairs (_) A4,B5: 4.. / A4 = 4 => 0 pairs (*) / B5 = 4 => 0 pairs (X) A8,B9: 4.. / A8 = 4 => 0 pairs (X) / B9 = 4 => 0 pairs (_) G8,H9: 4.. / G8 = 4 => 0 pairs (*) / H9 = 4 => 0 pairs (X) A4,I4: 4.. / A4 = 4 => 0 pairs (*) / I4 = 4 => 0 pairs (X) A8,G8: 4.. / A8 = 4 => 0 pairs (X) / G8 = 4 => 0 pairs (_) B9,H9: 4.. / B9 = 4 => 0 pairs (*) / H9 = 4 => 0 pairs (X) A4,A8: 4.. / A4 = 4 => 0 pairs (*) / A8 = 4 => 0 pairs (X) B5,B9: 4.. / B5 = 4 => 0 pairs (X) / B9 = 4 => 0 pairs (_) H5,H9: 4.. / H5 = 4 => 0 pairs (*) / H9 = 4 => 0 pairs (X) I2,I4: 4.. / I2 = 4 => 0 pairs (*) / I4 = 4 => 0 pairs (X) G2,I2: 6.. / G2 = 6 => 0 pairs (*) / I2 = 6 => 0 pairs (X) B5,B6: 6.. / B5 = 6 => 0 pairs (*) / B6 = 6 => 0 pairs (X) E7,E9: 6.. / E7 = 6 => 0 pairs (*) / E9 = 6 => 0 pairs (X) I7,H9: 6.. / I7 = 6 => 0 pairs (X) / H9 = 6 => 0 pairs (_) B6,I6: 6.. / B6 = 6 => 15 pairs (_) / I6 = 6 => 0 pairs (*) E7,I7: 6.. / E7 = 6 => 0 pairs (*) / I7 = 6 => 0 pairs (X) E9,H9: 6.. / E9 = 6 => 0 pairs (X) / H9 = 6 => 0 pairs (_) G2,G5: 6.. / G2 = 6 => 0 pairs (*) / G5 = 6 => 0 pairs (X) H5,H9: 6.. / H5 = 6 => 0 pairs (X) / H9 = 6 => 0 pairs (_) A7,A8: 9.. / A7 = 9 => 14 pairs (_) / A8 = 9 => 0 pairs (X) E7,E8: 9.. / E7 = 9 => 0 pairs (X) / E8 = 9 => 14 pairs (_) A7,E7: 9.. / A7 = 9 => 14 pairs (_) / E7 = 9 => 0 pairs (X) A8,E8: 9.. / A8 = 9 => 0 pairs (X) / E8 = 9 => 14 pairs (_) * DURATION: 0:00:57.515536 START: 08:17:24.645805 END: 08:18:22.161341 2017-05-01 * CP COUNT: (34) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,A7,B6,B9,E8,E9,G2,G8,H5,H9,I2,I4,I7) * 694123758125789.3.783645291.1735698.5.8912..7..947851..512.487..768.1.258.25.71.9 * PAIR G2: 4,6 COL G G5: 4,6,3 # reduction candidate for 4,6 G5: 4,6 => CTR * 694123758125789.3.783645291.1735698.538912..7269478513.512.4876.768.13258425.71.9 G5: 3 => SOLVED * 694123758125789634783645291417356982568912347239478516951264873376891425842537169 * PAIR A6: 2,3 ROW 6 I6: 2,3,6 # reduction candidate for 2,3 I6: 6 => SOLVED * 694123758125789634783645291417356982568912347239478516951264873376891425842537169 I6: 2,3 # 15 pairs * PAIR B6: 3,6 BLK 4 B5: 3,6,4 # reduction candidate for 3,6 B5: 3,6 => SOLVED * 694123758125789634783645291417356982568912347239478516951264873376891425842537169 B5: 4 => CTR * 694123758125789.3.783645291.1735698.548912367.69478512.512.487..768.1.258.25.71.9 * PAIR B6: 3,6 ROW 6 I6: 3,6,2 # reduction candidate for 3,6 I6: 3,6 => SOLVED * 694123758125789634783645291417356982568912347239478516951264873376891425842537169 I6: 2 => CTR * 694123758125789.3.783645291.1735698.5.8912367.69478512.512.487..768.1.258.25.71.9 * PAIR H5: 4,6 BLK 6 G5: 4,6,3 # reduction candidate for 4,6 G5: 4,6 => CTR * 694123758125789.3.783645291.1735698.538912..7269478513.512.4876.768.13258425.71.9 G5: 3 => SOLVED * 694123758125789634783645291417356982568912347239478516951264873376891425842537169 * PAIR H5: 4,6 ROW 5 B5: 4,6,3 # reduction candidate for 4,6 B5: 4,6 => SOLVED * 694123758125789634783645291417356982568912347239478516951264873376891425842537169 B5: 3 => CTR * 694123758125789.3.783645291417356982538912..7269478513.512.4876.768.1.258.25.71.9 * PAIR A7: 3,9 BLK 7 A8: 3,9,4 # reduction candidate for 3,9 A8: 3,9 => SOLVED * 694123758125789634783645291417356982568912347239478516951264873376891425842537169 A8: 4 => CTR * 694123758125789.3.783645291.1735698.5.8912..7..947851.9512.487.4768913258325.71.9 * PAIR A7: 3,9 ROW 7 E7: 3,9,6 # reduction candidate for 3,9 E7: 3,9 => CTR * 694123758125789.3.783645291.1735698.5.8912..7..947851..512.4876.768.13258.2567149 E7: 6 => SOLVED * 694123758125789634783645291417356982568912347239478516951264873376891425842537169 * PAIR B9: 3,4 BLK 7 A8: 3,4,9 # reduction candidate for 3,4 A8: 9 => CTR * 694123758125789.3.7836452914173569825.8912..72.947851.351294876.768.1.258.25.71.9 A8: 3,4 # 14 pairs * PAIR B9: 3,4 COL B B5: 3,4,6 # reduction candidate for 3,4 B5: 6 => SOLVED * 694123758125789634783645291417356982568912347239478516951264873376891425842537169 B5: 3,4 # 15 pairs * PAIR E8: 3,9 BLK 8 E7: 3,9,6 # reduction candidate for 3,9 E7: 3,9 => CTR * 694123758125789.3.783645291.1735698.5.8912..7..947851..512.4876.768.13258.2567149 E7: 6 => SOLVED * 694123758125789634783645291417356982568912347239478516951264873376891425842537169 * PAIR E8: 3,9 ROW 8 A8: 3,9,4 # reduction candidate for 3,9 A8: 3,9 => SOLVED * 694123758125789634783645291417356982568912347239478516951264873376891425842537169 A8: 4 => CTR * 694123758125789.3.783645291.1735698.5.8912..7..947851.9512.487.4768913258325.71.9 * PAIR E9: 3,6 BLK 8 E7: 3,6,9 # reduction candidate for 3,6 E7: 9 => CTR * 694123758125789.3.783645291.1735698.5.8912..7..947851..51294876976831.258.25.71.9 E7: 3,6 # 14 pairs * PAIR I7: 3,6 ROW 7 E7: 3,6,9 # reduction candidate for 3,6 E7: 9 => CTR * 694123758125789.3.783645291.1735698.5.8912..7..947851..51294876976831.258.25.71.9 E7: 3,6 # 14 pairs * PAIR I7: 3,6 COL I I6: 3,6,2 # reduction candidate for 3,6 I6: 3,6 => SOLVED * 694123758125789634783645291417356982568912347239478516951264873376891425842537169 I6: 2 => CTR * 694123758125789.3.783645291.1735698.5.8912367.69478512.512.487..768.1.258.25.71.9 * PAIR G8: 3,4 ROW 8 A8: 3,4,9 # reduction candidate for 3,4 A8: 9 => CTR * 694123758125789.3.7836452914173569825.8912..72.947851.351294876.768.1.258.25.71.9 A8: 3,4 # 14 pairs * PAIR G8: 3,4 COL G G5: 3,4,6 # reduction candidate for 3,4 G5: 3,4 => SOLVED * 694123758125789634783645291417356982568912347239478516951264873376891425842537169 G5: 6 => CTR * 694123758125789.3.783645291.1735698.538912647269478513.512.487..768.1.258.25.71.9 * INCONCLUSIVE * SAVE PR GRAPH zz-sudoku-de-720321-base-pr-000.dot * REASONING * DIS # G5: 4,6 => CTR => G5: 3 * PRF # G5: 3 => SOL * PRF # I6: 6 => SOL * PRF # B5: 3,6 => SOL * DIS # B5: 4 => CTR => B5: 3,6 * PRF # I6: 3,6 => SOL * DIS # I6: 2 => CTR => I6: 3,6 * DIS # G5: 4,6 => CTR => G5: 3 * PRF # G5: 3 => SOL * PRF # B5: 4,6 => SOL * DIS # B5: 3 => CTR => B5: 4,6 * PRF # A8: 3,9 => SOL * DIS # A8: 4 => CTR => A8: 3,9 * DIS # E7: 3,9 => CTR => E7: 6 * PRF # E7: 6 => SOL * DIS # A8: 9 => CTR => A8: 3,4 * PRF # B5: 6 => SOL * DIS # E7: 3,9 => CTR => E7: 6 * PRF # E7: 6 => SOL * PRF # A8: 3,9 => SOL * DIS # A8: 4 => CTR => A8: 3,9 * DIS # E7: 9 => CTR => E7: 3,6 * DIS # E7: 9 => CTR => E7: 3,6 * PRF # I6: 3,6 => SOL * DIS # I6: 2 => CTR => I6: 3,6 * DIS # A8: 9 => CTR => A8: 3,4 * PRF # G5: 3,4 => SOL * DIS # G5: 6 => CTR => G5: 3,4 * CNT 28 HDP CHAINS / 34 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,A7,B6,B9,E8,E9,G2,G8,H5,H9,I2,I4,I7) * 694123758125789.3.783645291.1735698.5.8912..7..947851..512.487..768.1.258.25.71.9 * PAIR G2: 4,6 COL G G5: 4,6,3 # reduction candidate for 4,6 G5: 4,6 => CTR * 694123758125789.3.783645291.1735698.538912..7269478513.512.4876.768.13258425.71.9 G5: 3 => SOLVED * 694123758125789634783645291417356982568912347239478516951264873376891425842537169 * DURATION: 0:00:02.843322 START: 08:19:00.082094 END: 08:19:02.925416 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-sudoku-de-720321-base-pr-001.dot * REASONING * DIS # G5: 4,6 => CTR => G5: 3 * PRF G5: 3 => SOL * STA G5: 3 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokus.de/720321.html sehr schwierig -------------------------------------------------- level: medium * PAIR REDUCTION .. * ROUND 1: 694123758125789.3.783645291.1735698.5.8912..7..947851..512.487..768.1.258.25.71.9 G2: 4,6 G5: 3,4,6 # reduction candidate for 4,6 G5: 4,6 => CTR * 694123758125789.3.783645291.1735698.538912..7269478513.512.4876.768.13258425.71.9 G5: 3 => SOLVED * 694123758125789634783645291417356982568912347239478516951264873376891425842537169 * SOLVED! -------------------------------------------------- |:step:| 00 -------------------------------------------------- pair quad |:guess:| highlight 3,9 A7,E8,A8,E7: 3,9.. => A8 = 4 or E7 = 6 # pair quad E7 != 6 => CTR * DISABLE VALUE:: E7 != 6 * AUTO .. E9: 6.. # hidden single I7: 6.. # hidden single E9: 6 # naked single E7,E8: 3,9.. => E9 != 3,9 # naked pair I7: 6 # naked single A7,E7: 3,9.. => I7 != 3,9 # naked pair G8: 3.. # hidden single B9: 3.. # hidden single I6: 3.. # hidden single I6 = 3 # set value A6: 2 # naked single B6: 6 # naked single I7 = 6 # set value H9: 4 # naked single I2: 4 # naked single G8 = 3 # set value E8: 9 # naked single B9 = 3 # set value A7: 9 # naked single E9 = 6 # set value H9 = 4 # set value H5: 6 # naked single G2: 6.. # hidden single I4: 2.. # hidden single A8: 4.. # hidden single E7: 3.. # hidden single B5: 4.. # hidden single A4..C6 != 3 => CTR => A8 != 4 * DISABLE VALUE:: A8 != 4 |:step:| 01 -------------------------------------------------- * AUTO .. B9: 4.. # hidden single G8: 4.. # hidden single A4: 4.. # hidden single B9: 4 # naked single A7,A8: 3,9.. => B9 != 3,9 # naked pair G8: 4 # naked single A8,E8: 3,9.. => G8 != 3,9 # naked pair A6: 2 # naked single A7,A8: 3,9.. => A6 != 3,9 # naked pair I7: 3.. # hidden single E9: 3.. # hidden single G5: 3.. # hidden single A4 = 4 # set value I4: 2 # naked single I4 = 2 # set value G5 = 3 # set value I6: 6 # naked single B5: 6 # naked single A6 = 2 # set value I6 = 6 # set value H5: 4 # naked single I2: 4 # naked single I7: 3 # naked single B6: 3 # naked single I7 = 3 # set value A7: 9 # naked single G8 = 4 # set value H9: 6 # naked single G2: 6 # naked single B9 = 4 # set value E9 = 3 # set value E8: 9 # naked single H9 = 6 # set value A8: 3.. # hidden single E7: 6.. # hidden single G2 = 6 # set value I2 = 4 # set value B5 = 6 # set value H5 = 4 # set value B6 = 3 # set value A7 = 9 # set value A8: 3 # naked single E7: 6 # naked single E7 = 6 # set value A8 = 3 # set value E8 = 9 # set value * SOLVED!
Solution
position: 694123758125789634783645291417356982568912347239478516951264873376891425842537169 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 # G5: 4,6 => CTR => G5: 3 * PRF # G5: 3 => SOL * INC # I6: 2,3 => UNS * PRF # I6: 6 => SOL * PRF # B5: 3,6 => SOL * DIS # B5: 4 => CTR => B5: 3,6 * PRF # I6: 3,6 => SOL * DIS # I6: 2 => CTR => I6: 3,6 * DIS # G5: 4,6 => CTR => G5: 3 * PRF # G5: 3 => SOL * PRF # B5: 4,6 => SOL * DIS # B5: 3 => CTR => B5: 4,6 * PRF # A8: 3,9 => SOL * DIS # A8: 4 => CTR => A8: 3,9 * DIS # E7: 3,9 => CTR => E7: 6 * PRF # E7: 6 => SOL * INC # A8: 3,4 => UNS * DIS # A8: 9 => CTR => A8: 3,4 * INC # B5: 3,4 => UNS * PRF # B5: 6 => SOL * DIS # E7: 3,9 => CTR => E7: 6 * PRF # E7: 6 => SOL * PRF # A8: 3,9 => SOL * DIS # A8: 4 => CTR => A8: 3,9 * INC # E7: 3,6 => UNS * DIS # E7: 9 => CTR => E7: 3,6 * INC # E7: 3,6 => UNS * DIS # E7: 9 => CTR => E7: 3,6 * PRF # I6: 3,6 => SOL * DIS # I6: 2 => CTR => I6: 3,6 * INC # A8: 3,4 => UNS * DIS # A8: 9 => CTR => A8: 3,4 * PRF # G5: 3,4 => SOL * DIS # G5: 6 => CTR => G5: 3,4 * CNT 34 HDP CHAINS / 34 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # G5: 4,6 => CTR => G5: 3 * PRF G5: 3 => SOL * STA G5: 3 * CNT 2 HDP CHAINS / 1 HYP OPENED