Analysis of zz-sudoku-de-770757-base.sdk
Contents
Original Sudoku
level: medium
position: .2.4.7.5...8...4...1.5.3.8..36...71.5.......2.72...94..8.1.9.2...4...3...9.2.6.7. initial
Autosolve
position: .2.48715..58.124..41.5.328..36.2471554......2.72...94..8.1.9.2.264...391.9.2.6.7. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A1: 3,9 => CTR => A1: 6 * DIS # I1: 6 => CTR => I1: 3,9 * DIS # A2: 3,6 => CTR => A2: 7,9 * DIS # I3: 7,9 => CTR => I3: 6 * PRF # I3: 6 => SOL * PRF # A2: 6,9 => SOL * DIS # A2: 3,7 => CTR => A2: 6,9 * DIS # I2: 6,9 => CTR => I2: 3,7 * DIS # D5: 6,9 => CTR => D5: 3,7,8 * DIS # I3: 7 => CTR => I3: 6,9 * DIS # E5: 6,9 => CTR => E5: 7 * PRF # E5: 7 => SOL * DIS # I1: 3,6 => CTR => I1: 9 * DIS # I2: 3,6 => CTR => I2: 7,9 * DIS # A2: 3,6 => CTR => A2: 7,9 * DIS # F6: 1,8 => CTR => F6: 5 * PRF # F6: 5 => SOL * DIS # D5: 8,9 => CTR => D5: 3,6,7 * DIS # F6: 1,8 => CTR => F6: 5 * PRF # F6: 5 => SOL * DIS # I6: 6,8 => CTR => I6: 3 * PRF # I6: 3 => SOL * DIS # D5: 6,8 => CTR => D5: 3,7,9 * PRF # I6: 3,6 => SOL * DIS # I6: 8 => CTR => I6: 3,6 * PRF # D5: 3,6 => SOL * DIS # D5: 7,8,9 => CTR => D5: 3,6 * DIS # C7: 3,7 => CTR => C7: 5 * PRF # C7: 5 => SOL * DIS # A2: 3,7 => CTR => A2: 6,9 * PRF # A2: 6,9 => SOL * PRF # C9: 1,3 => SOL * DIS # C9: 5 => CTR => C9: 1,3 * DIS # D5: 7,8 => CTR => D5: 3,6,9 * PRF # D5: 3,6,9 => SOL * PRF # F6: 5,8 => SOL * DIS # F6: 1 => CTR => F6: 5,8 * CNT 37 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 # A1: 3,9 => CTR => A1: 6 * DIS A1: 6 # A2: 7 => CTR => A2: 3,9 * DIS A1: 6 + A2: 3,9 # D5: 6,9 => CTR => D5: 3,7,8 * DIS A1: 6 + A2: 3,9 + D5: 3,7,8 # E5: 6,9 => CTR => E5: 7 * PRF A1: 6 + A2: 3,9 + D5: 3,7,8 + E5: 7 => SOL * STA A1: 6 + A2: 3,9 + D5: 3,7,8 + E5: 7 * CNT 5 HDP CHAINS / 6 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .2.4.7.5...8...4...1.5.3.8..36...71.5.......2.72...94..8.1.9.2...4...3...9.2.6.7. | initial |
| .2.48715..58.124..41.5.328..36.2471554......2.72...94..8.1.9.2.264...391.9.2.6.7. | autosolve |
| 623487159958612437417593286836924715549371862172865943785139624264758391391246578 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (24) C1: 3,9 C3: 7,9 D2: 6,9 E3: 6,9 H2: 3,6 A4: 8,9 C5: 1,9 A6: 1,8 D4: 8,9 F5: 1,8 E6: 5,6 G5: 6,8 H5: 3,6 A7: 3,7 A9: 1,3 E7: 3,4 D8: 7,8 E8: 5,7 F8: 5,8 E9: 3,4 G7: 5,6 I7: 4,6 G9: 5,8 I9: 4,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C5,A6: 1.. / C5 = 1 => 0 pairs (X) / A6 = 1 => 0 pairs (_) F5,F6: 1.. / F5 = 1 => 0 pairs (*) / F6 = 1 => 0 pairs (X) A9,C9: 1.. / A9 = 1 => 0 pairs (X) / C9 = 1 => 0 pairs (_) C5,F5: 1.. / C5 = 1 => 0 pairs (X) / F5 = 1 => 0 pairs (_) A6,F6: 1.. / A6 = 1 => 0 pairs (*) / F6 = 1 => 0 pairs (X) A6,A9: 1.. / A6 = 1 => 0 pairs (*) / A9 = 1 => 0 pairs (X) C5,C9: 1.. / C5 = 1 => 0 pairs (X) / C9 = 1 => 0 pairs (_) D5,D6: 3.. / D5 = 3 => 0 pairs (*) / D6 = 3 => 0 pairs (X) H5,I6: 3.. / H5 = 3 => 0 pairs (X) / I6 = 3 => 0 pairs (_) E7,E9: 3.. / E7 = 3 => 0 pairs (*) / E9 = 3 => 0 pairs (X) D5,H5: 3.. / D5 = 3 => 0 pairs (*) / H5 = 3 => 0 pairs (X) D6,I6: 3.. / D6 = 3 => 0 pairs (X) / I6 = 3 => 0 pairs (_) H2,H5: 3.. / H2 = 3 => 0 pairs (*) / H5 = 3 => 0 pairs (X) E7,E9: 4.. / E7 = 4 => 0 pairs (X) / E9 = 4 => 0 pairs (_) I7,I9: 4.. / I7 = 4 => 0 pairs (*) / I9 = 4 => 0 pairs (X) E7,I7: 4.. / E7 = 4 => 0 pairs (X) / I7 = 4 => 0 pairs (_) E9,I9: 4.. / E9 = 4 => 0 pairs (*) / I9 = 4 => 0 pairs (X) E6,F6: 5.. / E6 = 5 => 0 pairs (X) / F6 = 5 => 0 pairs (_) C7,C9: 5.. / C7 = 5 => 0 pairs (*) / C9 = 5 => 0 pairs (X) E8,F8: 5.. / E8 = 5 => 0 pairs (*) / F8 = 5 => 0 pairs (X) G7,G9: 5.. / G7 = 5 => 0 pairs (X) / G9 = 5 => 0 pairs (_) C7,G7: 5.. / C7 = 5 => 0 pairs (*) / G7 = 5 => 0 pairs (X) C9,G9: 5.. / C9 = 5 => 0 pairs (X) / G9 = 5 => 0 pairs (_) E6,E8: 5.. / E6 = 5 => 0 pairs (X) / E8 = 5 => 0 pairs (_) F6,F8: 5.. / F6 = 5 => 0 pairs (*) / F8 = 5 => 0 pairs (X) A1,A2: 6.. / A1 = 6 => 25 pairs (_) / A2 = 6 => 0 pairs (X) D2,E3: 6.. / D2 = 6 => 0 pairs (*) / E3 = 6 => 0 pairs (X) G7,I7: 6.. / G7 = 6 => 0 pairs (*) / I7 = 6 => 0 pairs (X) A1,I1: 6.. / A1 = 6 => 25 pairs (_) / I1 = 6 => 0 pairs (X) E3,I3: 6.. / E3 = 6 => 0 pairs (X) / I3 = 6 => 0 pairs (_) G5,G7: 6.. / G5 = 6 => 0 pairs (X) / G7 = 6 => 0 pairs (_) H2,H5: 6.. / H2 = 6 => 0 pairs (X) / H5 = 6 => 0 pairs (_) A2,C3: 7.. / A2 = 7 => 0 pairs (X) / C3 = 7 => 24 pairs (_) I2,I3: 7.. / I2 = 7 => 24 pairs (_) / I3 = 7 => 0 pairs (X) D5,E5: 7.. / D5 = 7 => 0 pairs (X) / E5 = 7 => 0 pairs (_) A7,C7: 7.. / A7 = 7 => 24 pairs (_) / C7 = 7 => 0 pairs (X) D8,E8: 7.. / D8 = 7 => 0 pairs (*) / E8 = 7 => 0 pairs (X) A2,I2: 7.. / A2 = 7 => 0 pairs (X) / I2 = 7 => 24 pairs (_) C3,I3: 7.. / C3 = 7 => 24 pairs (_) / I3 = 7 => 0 pairs (X) A2,A7: 7.. / A2 = 7 => 0 pairs (X) / A7 = 7 => 24 pairs (_) C3,C7: 7.. / C3 = 7 => 24 pairs (_) / C7 = 7 => 0 pairs (X) D5,D8: 7.. / D5 = 7 => 0 pairs (X) / D8 = 7 => 0 pairs (_) E5,E8: 7.. / E5 = 7 => 0 pairs (*) / E8 = 7 => 0 pairs (X) A4,A6: 8.. / A4 = 8 => 0 pairs (*) / A6 = 8 => 0 pairs (X) G5,I6: 8.. / G5 = 8 => 0 pairs (*) / I6 = 8 => 0 pairs (X) D8,F8: 8.. / D8 = 8 => 0 pairs (X) / F8 = 8 => 0 pairs (_) G9,I9: 8.. / G9 = 8 => 0 pairs (X) / I9 = 8 => 0 pairs (_) A4,D4: 8.. / A4 = 8 => 0 pairs (*) / D4 = 8 => 0 pairs (X) G5,G9: 8.. / G5 = 8 => 0 pairs (*) / G9 = 8 => 0 pairs (X) I6,I9: 8.. / I6 = 8 => 0 pairs (X) / I9 = 8 => 0 pairs (_) D2,E3: 9.. / D2 = 9 => 0 pairs (X) / E3 = 9 => 0 pairs (_) A4,C5: 9.. / A4 = 9 => 0 pairs (X) / C5 = 9 => 0 pairs (_) A4,D4: 9.. / A4 = 9 => 0 pairs (X) / D4 = 9 => 0 pairs (_) E3,E5: 9.. / E3 = 9 => 0 pairs (*) / E5 = 9 => 0 pairs (X) * DURATION: 0:01:27.715094 START: 08:39:45.599587 END: 08:41:13.314681 2017-05-01 * CP COUNT: (54) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,A7,A9,C1,C3,C5,D2,D4,D8,E3,E6,E7,E8,E9,F5,F8,G5,G7,G9,H2,H5,I7,I9) * .2.48715..58.124..41.5.328..36.2471554......2.72...94..8.1.9.2.264...391.9.2.6.7. * PAIR C1: 3,9 BLK 1 A1: 3,9,6 # reduction candidate for 3,9 A1: 3,9 => CTR * .2.487156658912437417563289936824715541.....2.72...94..8.1.9.2.264...391.9.2.6.7. A1: 6 # 25 pairs A2: 3,9,6,7 # reduction candidate for 3,9 A2: 3,9 # 26 pairs * PAIR C1: 3,9 ROW 1 I1: 3,9,6 # reduction candidate for 3,9 I1: 6 => CTR * .2.487156658912437417563289936824715541.....2.72...94..8.1.9.2.264...391.9.2.6.7. I1: 3,9 # 25 pairs * PAIR C3: 7,9 BLK 1 A2: 7,9,3,6 # reduction candidate for 7,9 A2: 3,6 => CTR * .2.48715..589124.7417563289936824715541.....2.72...94.78.1.9.2.264...391.9.2.6.7. A2: 7,9 # 27 pairs * PAIR C3: 7,9 ROW 3 I3: 7,9,6 # reduction candidate for 7,9 I3: 7,9 => CTR * .2.48715..58.124..41.56328..36.2471554..9...2.72.5.94..8.1.9.2.264.75391.9.2.6.7. I3: 6 => SOLVED * 623487159958612437417593286836924715549371862172865943785139624264758391391246578 * PAIR D2: 6,9 ROW 2 A2: 6,9,3,7 # reduction candidate for 6,9 A2: 6,9 => SOLVED * 623487159958612437417593286836924715549371862172865943785139624264758391391246578 A2: 3,7 => CTR * 62.48715..58.124..41.5.328.936824715541.....2.72...94..8.1.9.2.264...391.9.2.6.7. I2: 6,9,3,7 # reduction candidate for 6,9 I2: 6,9 => CTR * .2.48715.758.1243.419563287936824715541.....2.72...94..8.1.9.2.264...391.9.2.6.7. I2: 3,7 # 25 pairs * PAIR D2: 6,9 COL D D5: 6,9,3,7,8 # reduction candidate for 6,9 D5: 6,9 => CTR * .2.48715..58.1246.41.5.328..36.2471554..7..32.723..94..8.1.9.2.264758391.9.2.6.7. D5: 3,7,8 # 24 pairs * PAIR E3: 6,9 ROW 3 I3: 6,9,7 # reduction candidate for 6,9 I3: 7 => CTR * .2.48715..58.124..41.563287.36.2471554..9...2.72.5.94..871.9526264.75391.952.6874 I3: 6,9 # 24 pairs * PAIR E3: 6,9 COL E E5: 6,9,7 # reduction candidate for 6,9 E5: 6,9 => CTR * .2.48715..586124..41.5.328..36.2471554.7...32.723..94..8.1.9.2.264875391.9.2.6.7. E5: 7 => SOLVED * 623487159958612437417593286836924715549371862172865943785139624264758391391246578 * PAIR H2: 3,6 BLK 3 I1: 3,6,9 # reduction candidate for 3,6 I1: 3,6 => CTR * .2.48715..58.124.74175.3289.36.2471554..9...2.72...94.78.1.9.2.264.75391.9.2.6.7. I1: 9 # 27 pairs I2: 3,6,7,9 # reduction candidate for 3,6 I2: 3,6 => CTR * .2.48715.7589124..419563287936824715541.....2.72...94..8.1.9.2.264...391.9.2.6.7. I2: 7,9 # 25 pairs * PAIR H2: 3,6 ROW 2 A2: 3,6,7,9 # reduction candidate for 3,6 A2: 3,6 => CTR * .2.48715..589124.7417563289936824715541.....2.72...94.78.1.9.2.264...391.9.2.6.7. A2: 7,9 # 27 pairs * PAIR A6: 1,8 ROW 6 F6: 1,8,5 # reduction candidate for 1,8 F6: 1,8 => CTR * 62.48715..586124..41.5.328..36.2471554.7...32.7235.946.8.1.9624264875391.9.246578 F6: 5 => SOLVED * 623487159958612437417593286836924715549371862172865943785139624264758391391246578 * PAIR D4: 8,9 BLK 5 D5: 8,9,3,6,7 # reduction candidate for 8,9 D5: 8,9 => CTR * .2.48715..586124..41.5.328..36.2471554..7..32.72365948.8.1.9.2.264758391.9.2.6874 D5: 3,6,7 # 24 pairs * PAIR F5: 1,8 BLK 5 F6: 1,8,5 # reduction candidate for 1,8 F6: 1,8 => CTR * 62.48715..586124..41.5.328..36.2471554.7...32.7235.946.8.1.9624264875391.9.246578 F6: 5 => SOLVED * 623487159958612437417593286836924715549371862172865943785139624264758391391246578 * PAIR G5: 6,8 BLK 6 I6: 6,8,3 # reduction candidate for 6,8 I6: 6,8 => CTR * .2.48715..58.1246.41.56328..36.2471554.6...32.723..94..8.1.9.2.264...391.9.2.6.7. I6: 3 => SOLVED * 623487159958612437417593286836924715549371862172865943785139624264758391391246578 * PAIR G5: 6,8 ROW 5 D5: 6,8,3,7,9 # reduction candidate for 6,8 D5: 6,8 => CTR * .2.48715..58.1246.41.5.328..36.2471554..7..32.723..94..8.1.9.2.264758391.9.2.6.7. D5: 3,7,9 # 24 pairs * PAIR H5: 3,6 BLK 6 I6: 3,6,8 # reduction candidate for 3,6 I6: 3,6 => SOLVED * 623487159958612437417593286836924715549371862172865943785139624264758391391246578 I6: 8 => CTR * .2.48715..586124..41.5.328..36.2471554.....32.72365948.8.1.9.2.264.58391.9.2.6874 * PAIR H5: 3,6 ROW 5 D5: 3,6,7,8,9 # reduction candidate for 3,6 D5: 3,6 => SOLVED * 623487159958612437417593286836924715549371862172865943785139624264758391391246578 D5: 7,8,9 => CTR * .2.48715..586124..41.5.328..36.2471554.....32.723..94..8.1.9.2.264...391.9.2.6.7. * PAIR A7: 3,7 BLK 7 C7: 3,7,5 # reduction candidate for 3,7 C7: 3,7 => CTR * 62.48715..58.1246.41.56328..36.24715541.98..2.72...94..8.1.9526264...391.952.6874 C7: 5 => SOLVED * 623487159958612437417593286836924715549371862172865943785139624264758391391246578 * PAIR A7: 3,7 COL A A2: 3,7,6,9 # reduction candidate for 3,7 A2: 3,7 => CTR * 62.48715..58.124..41.5.328.936824715541.....2.72...94..8.1.9.2.264...391.9.2.6.7. A2: 6,9 => SOLVED * 623487159958612437417593286836924715549371862172865943785139624264758391391246578 * PAIR A9: 1,3 BLK 7 C9: 1,3,5 # reduction candidate for 1,3 C9: 1,3 => SOLVED * 623487159958612437417593286836924715549371862172865943785139624264758391391246578 C9: 5 => CTR * .2.48715..58.124..41.5.328..36.24715541..8632872...94..8.1.9.2.264...391.9.2.6.7. * PAIR D8: 7,8 COL D D5: 7,8,3,6,9 # reduction candidate for 7,8 D5: 7,8 => CTR * .2.48715..586124..41.5.328..36.2471554.....32.723..94..8.1.9.2.264...391.9.2.6.7. D5: 3,6,9 => SOLVED * 623487159958612437417593286836924715549371862172865943785139624264758391391246578 * PAIR F8: 5,8 COL F F6: 5,8,1 # reduction candidate for 5,8 F6: 5,8 => SOLVED * 623487159958612437417593286836924715549371862172865943785139624264758391391246578 F6: 1 => CTR * .2.48715..58.124..41.5.328..36.24715541798..2.72.5194..8.1.9.2.264.7539119.2.6.7. * INCONCLUSIVE * SAVE PR GRAPH zz-sudoku-de-770757-base-pr-000.dot * REASONING * DIS # A1: 3,9 => CTR => A1: 6 * DIS # I1: 6 => CTR => I1: 3,9 * DIS # A2: 3,6 => CTR => A2: 7,9 * DIS # I3: 7,9 => CTR => I3: 6 * PRF # I3: 6 => SOL * PRF # A2: 6,9 => SOL * DIS # A2: 3,7 => CTR => A2: 6,9 * DIS # I2: 6,9 => CTR => I2: 3,7 * DIS # D5: 6,9 => CTR => D5: 3,7,8 * DIS # I3: 7 => CTR => I3: 6,9 * DIS # E5: 6,9 => CTR => E5: 7 * PRF # E5: 7 => SOL * DIS # I1: 3,6 => CTR => I1: 9 * DIS # I2: 3,6 => CTR => I2: 7,9 * DIS # A2: 3,6 => CTR => A2: 7,9 * DIS # F6: 1,8 => CTR => F6: 5 * PRF # F6: 5 => SOL * DIS # D5: 8,9 => CTR => D5: 3,6,7 * DIS # F6: 1,8 => CTR => F6: 5 * PRF # F6: 5 => SOL * DIS # I6: 6,8 => CTR => I6: 3 * PRF # I6: 3 => SOL * DIS # D5: 6,8 => CTR => D5: 3,7,9 * PRF # I6: 3,6 => SOL * DIS # I6: 8 => CTR => I6: 3,6 * PRF # D5: 3,6 => SOL * DIS # D5: 7,8,9 => CTR => D5: 3,6 * DIS # C7: 3,7 => CTR => C7: 5 * PRF # C7: 5 => SOL * DIS # A2: 3,7 => CTR => A2: 6,9 * PRF # A2: 6,9 => SOL * PRF # C9: 1,3 => SOL * DIS # C9: 5 => CTR => C9: 1,3 * DIS # D5: 7,8 => CTR => D5: 3,6,9 * PRF # D5: 3,6,9 => SOL * PRF # F6: 5,8 => SOL * DIS # F6: 1 => CTR => F6: 5,8 * CNT 37 HDP CHAINS / 49 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,A7,A9,C1,C3,C5,D2,D4,D8,E3,E6,E7,E8,E9,F5,F8,G5,G7,G9,H2,H5,I7,I9) * .2.48715..58.124..41.5.328..36.2471554......2.72...94..8.1.9.2.264...391.9.2.6.7. * PAIR C1: 3,9 BLK 1 A1: 3,9,6 # reduction candidate for 3,9 A1: 3,9 => CTR * .2.487156658912437417563289936824715541.....2.72...94..8.1.9.2.264...391.9.2.6.7. A2: 3,9,7 # reduction candidate for 3,9 A2: 3,9 # 26 pairs * RESTART * PAIR C1: 3,9 BLK 1 A2: 3,9,7 # reduction candidate for 3,9 A2: 7 => CTR * 6234871597589124..419563287936824715541.....2.72...94..8.1.9.2.264...391.9.2.6.7. * PAIR D2: 6,9 COL D D5: 6,9,3,7,8 # reduction candidate for 6,9 D5: 6,9 => CTR * 62.48715335891246741756328..36.2471554..7..32.723..94.78.1.9.2.264758391.9.2.6.7. * PAIR RESTART * PAIR E3: 6,9 COL E E5: 6,9,7 # reduction candidate for 6,9 E5: 6,9 => CTR * 62.487153358.124.74175.328..36.2471554.7...32.723..94.78.1.9.2.264875391.9.2.6.7. E5: 7 => SOLVED * 623487159958612437417593286836924715549371862172865943785139624264758391391246578 * DURATION: 0:00:08.414130 START: 08:41:59.650337 END: 08:42:08.064467 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-sudoku-de-770757-base-pr-001.dot * REASONING * DIS # A1: 3,9 => CTR => A1: 6 * DIS A1: 6 # A2: 7 => CTR => A2: 3,9 * DIS A1: 6 + A2: 3,9 # D5: 6,9 => CTR => D5: 3,7,8 * DIS A1: 6 + A2: 3,9 + D5: 3,7,8 # E5: 6,9 => CTR => E5: 7 * PRF A1: 6 + A2: 3,9 + D5: 3,7,8 + E5: 7 => SOL * STA A1: 6 + A2: 3,9 + D5: 3,7,8 + E5: 7 * CNT 5 HDP CHAINS / 6 HYP OPENED
Header Info
http://www.sudokus.de/770757.html sehr schwierig -------------------------------------------------- level: medium * PAIR REDUCTION .. * ROUND 1: .2.48715..58.124..41.5.328..36.2471554......2.72...94..8.1.9.2.264...391.9.2.6.7. C1: 3,9 A1: 3,6,9 # reduction candidate for 3,9 A1: 3,9 => CTR * .2.487156658912437417563289936824715541.....2.72...94..8.1.9.2.264...391.9.2.6.7. A2: 3,7,9 # reduction candidate for 3,9 A2: 7 => CTR * 6234871597589124..419563287936824715541.....2.72...94..8.1.9.2.264...391.9.2.6.7. D2: 6,9 D5: 3,6,7,8,9 # reduction candidate for 6,9 D5: 6,9 => CTR * 62.48715335891246741756328..36.2471554..7..32.723..94.78.1.9.2.264758391.9.2.6.7. E3: 6,9 E5: 6,7,9 # reduction candidate for 6,9 E5: 6,9 => CTR * 62.487153358.124.74175.328..36.2471554.7...32.723..94.78.1.9.2.264875391.9.2.6.7. E5: 7 => SOLVED * 623487159958612437417593286836924715549371862172865943785139624264758391391246578 * SOLVED! -------------------------------------------------- xy-wing C5: 1,9 D4: 8,9 F5: 1,8 * DISABLE VALUE:: E5 != 9 step 01 D4: 8,9 A4: 8,9 F5: 1,8 C5: 1,9 D4 = 8 => F5 = 1 => C5 = 9 D4 = 8 => A4 = 9 => CTR! => D4 != 8 * DISABLE VALUE:: D4 != 8 D4: 9 # naked single * DISABLE VALUE:: A4 != 9 A4: 8 # naked single * DISABLE VALUE:: A6 != 8 A6: 1 # naked single * DISABLE VALUE:: C5 != 1 C5: 9 # naked single * DISABLE VALUE:: F5 != 8 F5: 1 # naked single step 02
Solution
position: 623487159958612437417593286836924715549371862172865943785139624264758391391246578 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: 3,9 => CTR => A1: 6 * INC # A1: 6 => UNS * INC # A2: 3,9 => UNS * INC # I1: 3,9 => UNS * DIS # I1: 6 => CTR => I1: 3,9 * INC # A2: 7,9 => UNS * DIS # A2: 3,6 => CTR => A2: 7,9 * DIS # I3: 7,9 => CTR => I3: 6 * PRF # I3: 6 => SOL * PRF # A2: 6,9 => SOL * DIS # A2: 3,7 => CTR => A2: 6,9 * DIS # I2: 6,9 => CTR => I2: 3,7 * INC # I2: 3,7 => UNS * DIS # D5: 6,9 => CTR => D5: 3,7,8 * INC # D5: 3,7,8 => UNS * INC # I3: 6,9 => UNS * DIS # I3: 7 => CTR => I3: 6,9 * DIS # E5: 6,9 => CTR => E5: 7 * PRF # E5: 7 => SOL * DIS # I1: 3,6 => CTR => I1: 9 * INC # I1: 9 => UNS * DIS # I2: 3,6 => CTR => I2: 7,9 * INC # I2: 7,9 => UNS * DIS # A2: 3,6 => CTR => A2: 7,9 * INC # A2: 7,9 => UNS * DIS # F6: 1,8 => CTR => F6: 5 * PRF # F6: 5 => SOL * DIS # D5: 8,9 => CTR => D5: 3,6,7 * INC # D5: 3,6,7 => UNS * DIS # F6: 1,8 => CTR => F6: 5 * PRF # F6: 5 => SOL * DIS # I6: 6,8 => CTR => I6: 3 * PRF # I6: 3 => SOL * DIS # D5: 6,8 => CTR => D5: 3,7,9 * INC # D5: 3,7,9 => UNS * PRF # I6: 3,6 => SOL * DIS # I6: 8 => CTR => I6: 3,6 * PRF # D5: 3,6 => SOL * DIS # D5: 7,8,9 => CTR => D5: 3,6 * DIS # C7: 3,7 => CTR => C7: 5 * PRF # C7: 5 => SOL * DIS # A2: 3,7 => CTR => A2: 6,9 * PRF # A2: 6,9 => SOL * PRF # C9: 1,3 => SOL * DIS # C9: 5 => CTR => C9: 1,3 * DIS # D5: 7,8 => CTR => D5: 3,6,9 * PRF # D5: 3,6,9 => SOL * PRF # F6: 5,8 => SOL * DIS # F6: 1 => CTR => F6: 5,8 * CNT 49 HDP CHAINS / 49 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A1: 3,9 => CTR => A1: 6 * INC A1: 6 # A2: 3,9 => UNS * INC A1: 6 # A2: 3,9 => UNS * DIS A1: 6 # A2: 7 => CTR => A2: 3,9 * DIS A1: 6 + A2: 3,9 # D5: 6,9 => CTR => D5: 3,7,8 * DIS A1: 6 + A2: 3,9 + D5: 3,7,8 # E5: 6,9 => CTR => E5: 7 * PRF A1: 6 + A2: 3,9 + D5: 3,7,8 + E5: 7 => SOL * STA A1: 6 + A2: 3,9 + D5: 3,7,8 + E5: 7 * CNT 7 HDP CHAINS / 6 HYP OPENED