Analysis of zz-sudoku-de-706185-base.sdk
Contents
Original Sudoku
level: medium
position: .4...812...3....57....1.4.3...25...4.7.....6.4...67...3.8.2....72....5...598...1. initial
Autosolve
position: .4...812.1.3..2.57....1.4.3...25..74.7..8..6.4...67...318.2..4.724...5.86598...12 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A3: 5,9 => CTR => A3: 2,8 * DIS # D1: 5,9 => CTR => D1: 3,6,7 * DIS # A5: 2 => CTR => A5: 5,9 * DIS # D2: 6 => CTR => D2: 4,9 * PRF # G2: 6,9 => SOL * DIS # G2: 8 => CTR => G2: 6,9 * DIS # D1: 6,9 => CTR => D1: 3,5,7 * DIS # G2: 8,9 => CTR => G2: 6 * PRF # G2: 6 => SOL * DIS # A3: 8,9 => CTR => A3: 2,5 * DIS # H6: 3 => CTR => H6: 8,9 * DIS # B4: 8,9 => CTR => B4: 3,6 * DIS # A3: 8,9 => CTR => A3: 2,5 * DIS # C5: 2 => CTR => C5: 1,5 * PRF # C6: 2 => SOL * DIS # D7: 5,9 => CTR => D7: 7 * PRF # F3: 6 => SOL * DIS # E1: 3,9 => CTR => E1: 7 * DIS # E9: 7 => CTR => E9: 3,4 * DIS # F5: 1,9 => CTR => F5: 3,4 * DIS # G7: 7 => CTR => G7: 6,9 * PRF # H6: 3,9 => SOL * DIS # H6: 8 => CTR => H6: 3,9 * DIS # E9: 4 => CTR => E9: 3,7 * CNT 24 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 # A3: 5,9 => CTR => A3: 2,8 * DIS A3: 2,8 # D1: 5,9 => CTR => D1: 3,6,7 * DIS A3: 2,8 + D1: 3,6,7 # A5: 2 => CTR => A5: 5,9 * DIS A3: 2,8 + D1: 3,6,7 + A5: 5,9 # D2: 6 => CTR => D2: 4,9 * PRF A3: 2,8 + D1: 3,6,7 + A5: 5,9 + D2: 4,9 # H6: 8,9 => SOL * STA A3: 2,8 + D1: 3,6,7 + A5: 5,9 + D2: 4,9 + H6: 8,9 * CNT 5 HDP CHAINS / 7 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .4...812...3....57....1.4.3...25...4.7.....6.4...67...3.8.2....72....5...598...1. | initial |
| .4...812.1.3..2.57....1.4.3...25..74.7..8..6.4...67...318.2..4.724...5.86598...12 | autosolve |
| 546378129183942657297516483861259374975483261432167895318725946724691538659834712 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) A1: 5,9 E2: 4,9 I1: 6,9 H3: 8,9 A4: 8,9 C4: 1,6 I5: 1,5 I6: 1,5 F7: 5,9 D8: 1,6 E8: 3,9 F8: 1,6 F9: 3,4 I7: 6,9 H8: 3,9 G9: 3,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) I5,I6: 1.. / I5 = 1 => 16 pairs (_) / I6 = 1 => 19 pairs (_) D8,F8: 1.. / D8 = 1 => 21 pairs (_) / F8 = 1 => 0 pairs (*) C4,F4: 1.. / C4 = 1 => 0 pairs (*) / F4 = 1 => 0 pairs (X) A3,C3: 2.. / A3 = 2 => 18 pairs (_) / C3 = 2 => 0 pairs (X) G5,G6: 2.. / G5 = 2 => 0 pairs (*) / G6 = 2 => 0 pairs (X) C6,G6: 2.. / C6 = 2 => 0 pairs (*) / G6 = 2 => 0 pairs (X) A3,A5: 2.. / A3 = 2 => 18 pairs (_) / A5 = 2 => 0 pairs (X) D1,E1: 3.. / D1 = 3 => 20 pairs (_) / E1 = 3 => 0 pairs (X) B4,B6: 3.. / B4 = 3 => 24 pairs (_) / B6 = 3 => 18 pairs (_) H8,G9: 3.. / H8 = 3 => 18 pairs (_) / G9 = 3 => 0 pairs (X) E8,H8: 3.. / E8 = 3 => 0 pairs (X) / H8 = 3 => 18 pairs (_) H6,H8: 3.. / H6 = 3 => 0 pairs (X) / H8 = 3 => 18 pairs (_) D2,E2: 4.. / D2 = 4 => 0 pairs (X) / E2 = 4 => 20 pairs (_) D5,F5: 4.. / D5 = 4 => 20 pairs (_) / F5 = 4 => 0 pairs (X) E9,F9: 4.. / E9 = 4 => 0 pairs (X) / F9 = 4 => 20 pairs (_) D2,D5: 4.. / D2 = 4 => 0 pairs (X) / D5 = 4 => 20 pairs (_) E2,E9: 4.. / E2 = 4 => 20 pairs (_) / E9 = 4 => 0 pairs (X) F5,F9: 4.. / F5 = 4 => 0 pairs (X) / F9 = 4 => 20 pairs (_) I5,I6: 5.. / I5 = 5 => 19 pairs (_) / I6 = 5 => 16 pairs (_) D7,F7: 5.. / D7 = 5 => 0 pairs (X) / F7 = 5 => 21 pairs (_) C6,I6: 5.. / C6 = 5 => 19 pairs (_) / I6 = 5 => 16 pairs (_) F3,F7: 5.. / F3 = 5 => 0 pairs (X) / F7 = 5 => 21 pairs (_) I1,G2: 6.. / I1 = 6 => 0 pairs (X) / G2 = 6 => 0 pairs (_) B4,C4: 6.. / B4 = 6 => 0 pairs (*) / C4 = 6 => 0 pairs (X) D8,F8: 6.. / D8 = 6 => 0 pairs (*) / F8 = 6 => 0 pairs (X) G7,I7: 6.. / G7 = 6 => 0 pairs (X) / I7 = 6 => 0 pairs (_) F3,F8: 6.. / F3 = 6 => 0 pairs (*) / F8 = 6 => 0 pairs (X) G2,G7: 6.. / G2 = 6 => 0 pairs (*) / G7 = 6 => 0 pairs (X) I1,I7: 6.. / I1 = 6 => 0 pairs (X) / I7 = 6 => 0 pairs (_) C1,C3: 7.. / C1 = 7 => 0 pairs (X) / C3 = 7 => 21 pairs (_) D7,E9: 7.. / D7 = 7 => 18 pairs (_) / E9 = 7 => 0 pairs (X) G7,G9: 7.. / G7 = 7 => 0 pairs (X) / G9 = 7 => 18 pairs (_) C3,D3: 7.. / C3 = 7 => 21 pairs (_) / D3 = 7 => 0 pairs (X) D7,G7: 7.. / D7 = 7 => 18 pairs (_) / G7 = 7 => 0 pairs (X) E9,G9: 7.. / E9 = 7 => 0 pairs (X) / G9 = 7 => 18 pairs (_) E1,E9: 7.. / E1 = 7 => 18 pairs (_) / E9 = 7 => 0 pairs (X) G2,H3: 8.. / G2 = 8 => 0 pairs (X) / H3 = 8 => 0 pairs (_) B2,G2: 8.. / B2 = 8 => 0 pairs (*) / G2 = 8 => 0 pairs (X) A3,A4: 8.. / A3 = 8 => 0 pairs (X) / A4 = 8 => 17 pairs (_) H3,H6: 8.. / H3 = 8 => 0 pairs (*) / H6 = 8 => 0 pairs (X) E8,H8: 9.. / E8 = 9 => 18 pairs (_) / H8 = 9 => 0 pairs (X) I1,I7: 9.. / I1 = 9 => 0 pairs (*) / I7 = 9 => 0 pairs (X) * DURATION: 0:01:06.865837 START: 08:03:44.391341 END: 08:04:51.257178 2017-05-01 * CP COUNT: (42) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A4,C4,D8,E2,E8,F7,F8,F9,G9,H3,H8,I1,I5,I6,I7) * .4...812.1.3..2.57....1.4.3...25..74.7..8..6.4...67...318.2..4.724...5.86598...12 * PAIR A1: 5,9 BLK 1 A3: 5,9,2,8 # reduction candidate for 5,9 A3: 5,9 => CTR * .4...812.1.3..2.57..271.4.38..25..7427..8..6.4...6728.318.2.746724...5.86598...12 A3: 2,8 # 17 pairs * PAIR A1: 5,9 ROW 1 D1: 5,9,3,6,7 # reduction candidate for 5,9 D1: 5,9 => CTR * .4..3812.1.3..2.57...71.4.3...25..74.7..8..6.4...67...318.2.746724.9.5.86598...12 D1: 3,6,7 # 16 pairs * PAIR A1: 5,9 COL A A5: 5,9,2 # reduction candidate for 5,9 A5: 2 => CTR * .4763812.1.3..2.57..271.4.3...25..7427..8..6.4...672..318.2.746724...598659874312 A5: 5,9 # 18 pairs * PAIR E2: 4,9 BLK 2 D2: 4,9,6 # reduction candidate for 4,9 D2: 6 => CTR * .4..781261.3642.57..7.1.4.3..6251.74.7.483.6.4..967.8.318725649724196538659834712 D2: 4,9 # 21 pairs * PAIR I1: 6,9 BLK 3 G2: 6,9,8 # reduction candidate for 6,9 G2: 6,9 => SOLVED * 546378129183942657297516483861259374975483261432167895318725946724691538659834712 G2: 8 => CTR * .4..781261.3.42857..7.1.493..6251.74.7.48936.4..36728.31872.649724.9.5386598..712 * PAIR I1: 6,9 ROW 1 D1: 6,9,3,5,7 # reduction candidate for 6,9 D1: 6,9 => CTR * .4..3812.1.3..2.57...7154.3...25..74.7..8..6.4...67...318529.4.724...5.86598...12 D1: 3,5,7 # 16 pairs * PAIR H3: 8,9 BLK 3 G2: 8,9,6 # reduction candidate for 8,9 G2: 8,9 => CTR * .453781261.3.42.572.75194838.6251.7457.48396.4...67...318725649724196538659834712 G2: 6 => SOLVED * 546378129183942657297516483861259374975483261432167895318725946724691538659834712 * PAIR H3: 8,9 ROW 3 A3: 8,9,2,5 # reduction candidate for 8,9 A3: 8,9 => CTR * .4...812.1.3..2.57..27154.3...25..7427..8..6.4...672..318529746724.36598659874312 A3: 2,5 # 18 pairs B3: 8,9,6 # reduction candidate for 8,9 B3: 8,9 # 20 pairs * PAIR H3: 8,9 COL H H6: 8,9,3 # reduction candidate for 8,9 H6: 3 => CTR * .4.3.8129183..2.57....1.4838..25..74.7..8..6.4...6783.318.2..4.724.3.5986598.4312 H6: 8,9 # 18 pairs * PAIR A4: 8,9 BLK 4 B4: 8,9,3,6 # reduction candidate for 8,9 B4: 8,9 => CTR * .4..7812.1.3..2857..7.1.493..6251374.7..8.96.43.96728.31872..4.7241.65386598..712 B4: 3,6 # 17 pairs B6: 8,9,3 # reduction candidate for 8,9 B6: 8,9 # 24 pairs * PAIR A4: 8,9 ROW 4 G4: 8,9,3 # reduction candidate for 8,9 G4: 8,9 # 19 pairs G4: 3 # 19 pairs * PAIR A4: 8,9 COL A A3: 8,9,2,5 # reduction candidate for 8,9 A3: 8,9 => CTR * .4...812.1.3..2.57..27154.3...25..7427..8..6.4...672..318529746724.36598659874312 A3: 2,5 # 18 pairs * PAIR I5: 1,5 ROW 5 C5: 1,5,2 # reduction candidate for 1,5 C5: 2 => CTR * .4.3781261639428572875164938.625..74.72.8..6.4...6728.318725649724.9.538659834712 C5: 1,5 # 19 pairs * PAIR I6: 1,5 ROW 6 C6: 1,5,2 # reduction candidate for 1,5 C6: 2 => SOLVED * 546378129183942657297516483861259374975483261432167895318725946724691538659834712 C6: 1,5 # 19 pairs * PAIR F7: 5,9 BLK 8 D7: 5,9,7 # reduction candidate for 5,9 D7: 5,9 => CTR * .4...81291.3..2.57....1.4.3...25..74.7..8..6.4...67...318.2.746724...598659874312 D7: 7 # 18 pairs * PAIR F7: 5,9 COL F F3: 5,9,6 # reduction candidate for 5,9 F3: 6 => SOLVED * 546378129183942657297516483861259374975483261432167895318725946724691538659834712 F3: 5,9 # 21 pairs * PAIR E8: 3,9 COL E E1: 3,9,7 # reduction candidate for 3,9 E1: 3,9 => CTR * .4...812.1.3.42.57....1.4.3...25..74.7.483.6.4...67.3.318.2.746724.3.598659874312 E1: 7 # 18 pairs * PAIR F9: 3,4 BLK 8 E9: 3,4,7 # reduction candidate for 3,4 E9: 7 => CTR * .4...812.1.3.42.57....1.4.3...25..74.7.483.6.4...67.3.318.2.746724.3.598659874312 E9: 3,4 # 18 pairs * PAIR F9: 3,4 COL F F5: 3,4,1,9 # reduction candidate for 3,4 F5: 1,9 => CTR * .4.37812.1.3.428572875164938.125397497248136.43..6728.318725.4.724.9.538659834712 F5: 3,4 # 18 pairs * PAIR I7: 6,9 BLK 9 G7: 6,9,7 # reduction candidate for 6,9 G7: 7 => CTR * .4...8129183..2657....1.4838..25..74.7..8..6.4...678..318.2.746724...598659874312 G7: 6,9 # 18 pairs * PAIR H8: 3,9 COL H H6: 3,9,8 # reduction candidate for 3,9 H6: 3,9 => SOLVED * 546378129183942657297516483861259374975483261432167895318725946724691538659834712 H6: 8 => CTR * .4.3781261.39428572875164938.6251.74.7..8..6.4...67.8.318725649724.9.538659834712 * PAIR G9: 3,7 ROW 9 E9: 3,7,4 # reduction candidate for 3,7 E9: 4 => CTR * .4..7812.1.3..2.57..7.1.4.3...25..74.7..8..6.4...67...318725.4.724...5.86598...12 E9: 3,7 # 20 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-sudoku-de-706185-base-pr-000.dot * REASONING * DIS # A3: 5,9 => CTR => A3: 2,8 * DIS # D1: 5,9 => CTR => D1: 3,6,7 * DIS # A5: 2 => CTR => A5: 5,9 * DIS # D2: 6 => CTR => D2: 4,9 * PRF # G2: 6,9 => SOL * DIS # G2: 8 => CTR => G2: 6,9 * DIS # D1: 6,9 => CTR => D1: 3,5,7 * DIS # G2: 8,9 => CTR => G2: 6 * PRF # G2: 6 => SOL * DIS # A3: 8,9 => CTR => A3: 2,5 * DIS # H6: 3 => CTR => H6: 8,9 * DIS # B4: 8,9 => CTR => B4: 3,6 * DIS # A3: 8,9 => CTR => A3: 2,5 * DIS # C5: 2 => CTR => C5: 1,5 * PRF # C6: 2 => SOL * DIS # D7: 5,9 => CTR => D7: 7 * PRF # F3: 6 => SOL * DIS # E1: 3,9 => CTR => E1: 7 * DIS # E9: 7 => CTR => E9: 3,4 * DIS # F5: 1,9 => CTR => F5: 3,4 * DIS # G7: 7 => CTR => G7: 6,9 * PRF # H6: 3,9 => SOL * DIS # H6: 8 => CTR => H6: 3,9 * DIS # E9: 4 => CTR => E9: 3,7 * CNT 24 HDP CHAINS / 46 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A4,C4,D8,E2,E8,F7,F8,F9,G9,H3,H8,I1,I5,I6,I7) * .4...812.1.3..2.57....1.4.3...25..74.7..8..6.4...67...318.2..4.724...5.86598...12 * PAIR A1: 5,9 BLK 1 A3: 5,9,2,8 # reduction candidate for 5,9 A3: 5,9 => CTR * .4...812.1.3..2.57..271.4.38..25..7427..8..6.4...6728.318.2.746724...5.86598...12 * PAIR A1: 5,9 ROW 1 D1: 5,9,3,6,7 # reduction candidate for 5,9 D1: 5,9 => CTR * .4..3812.1.3..2.57...71.4.3...25..74.7..8..6.4...67...318.2.746724.9.5.86598...12 * PAIR A1: 5,9 COL A A5: 5,9,2 # reduction candidate for 5,9 A5: 2 => CTR * 54...812.1.3..2.578.27154939..25..7427..8.96.4..96728.318529746724...5.86598...12 * PAIR RESTART * PAIR E2: 4,9 BLK 2 D2: 4,9,6 # reduction candidate for 4,9 D2: 6 => CTR * 945.78126183642957267.1.4838.625137457.48..6.4...67...318.2.6497241965386598.4712 * PAIR H3: 8,9 COL H H6: 8,9,3 # reduction candidate for 8,9 H6: 8,9 => SOLVED * 546378129183942657297516483861259374975483261432167895318725946724691538659834712 * DURATION: 0:00:09.388454 START: 08:05:33.750617 END: 08:05:43.139071 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-sudoku-de-706185-base-pr-001.dot * REASONING * DIS # A3: 5,9 => CTR => A3: 2,8 * DIS A3: 2,8 # D1: 5,9 => CTR => D1: 3,6,7 * DIS A3: 2,8 + D1: 3,6,7 # A5: 2 => CTR => A5: 5,9 * DIS A3: 2,8 + D1: 3,6,7 + A5: 5,9 # D2: 6 => CTR => D2: 4,9 * PRF A3: 2,8 + D1: 3,6,7 + A5: 5,9 + D2: 4,9 # H6: 8,9 => SOL * STA A3: 2,8 + D1: 3,6,7 + A5: 5,9 + D2: 4,9 + H6: 8,9 * CNT 5 HDP CHAINS / 7 HYP OPENED
Header Info
http://www.sudokus.de/706185.html sehr schwierig -------------------------------------------------- level: medium * PAIR REDUCTION .. * ROUND 1: .4...812.1.3..2.57....1.4.3...25..74.7..8..6.4...67...318.2..4.724...5.86598...12 A1: 5,9 A3: 2,5,8,9 # reduction candidate for 5,9 A3: 5,9 => CTR * .4...812.1.3..2.57..271.4.38..25..7427..8..6.4...6728.318.2.746724...5.86598...12 D1: 3,5,6,7,9 # reduction candidate for 5,9 D1: 5,9 => CTR * .4..3812.1.3..2.57...71.4.3...25..74.7..8..6.4...67...318.2.746724.9.5.86598...12 A5: 2,5,9 # reduction candidate for 5,9 A5: 2 => CTR * 54...812.1.3..2.578.27154939..25..7427..8.96.4..96728.318529746724...5.86598...12 E2: 4,9 D2: 4,6,9 # reduction candidate for 4,9 D2: 6 => CTR * 945.78126183642957267.1.4838.625137457.48..6.4...67...318.2.6497241965386598.4712 I1: 6,9 H3: 8,9 H6: 3,8,9 # reduction candidate for 8,9 H6: 8,9 => SOLVED * 546378129183942657297516483861259374975483261432167895318725946724691538659834712 * SOLVED! --------------------------------------------------
Solution
position: 546378129183942657297516483861259374975483261432167895318725946724691538659834712 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 # A3: 5,9 => CTR => A3: 2,8 * INC # A3: 2,8 => UNS * DIS # D1: 5,9 => CTR => D1: 3,6,7 * INC # D1: 3,6,7 => UNS * INC # A5: 5,9 => UNS * DIS # A5: 2 => CTR => A5: 5,9 * INC # D2: 4,9 => UNS * DIS # D2: 6 => CTR => D2: 4,9 * PRF # G2: 6,9 => SOL * DIS # G2: 8 => CTR => G2: 6,9 * DIS # D1: 6,9 => CTR => D1: 3,5,7 * INC # D1: 3,5,7 => UNS * DIS # G2: 8,9 => CTR => G2: 6 * PRF # G2: 6 => SOL * DIS # A3: 8,9 => CTR => A3: 2,5 * INC # A3: 2,5 => UNS * INC # B3: 8,9 => UNS * INC # H6: 8,9 => UNS * DIS # H6: 3 => CTR => H6: 8,9 * DIS # B4: 8,9 => CTR => B4: 3,6 * INC # B4: 3,6 => UNS * INC # B6: 8,9 => UNS * INC # G4: 8,9 => UNS * INC # G4: 3 => UNS * DIS # A3: 8,9 => CTR => A3: 2,5 * INC # A3: 2,5 => UNS * INC # C5: 1,5 => UNS * DIS # C5: 2 => CTR => C5: 1,5 * INC # C6: 1,5 => UNS * PRF # C6: 2 => SOL * DIS # D7: 5,9 => CTR => D7: 7 * INC # D7: 7 => UNS * INC # F3: 5,9 => UNS * PRF # F3: 6 => SOL * DIS # E1: 3,9 => CTR => E1: 7 * INC # E1: 7 => UNS * INC # E9: 3,4 => UNS * DIS # E9: 7 => CTR => E9: 3,4 * INC # F5: 3,4 => UNS * DIS # F5: 1,9 => CTR => F5: 3,4 * INC # G7: 6,9 => UNS * DIS # G7: 7 => CTR => G7: 6,9 * PRF # H6: 3,9 => SOL * DIS # H6: 8 => CTR => H6: 3,9 * INC # E9: 3,7 => UNS * DIS # E9: 4 => CTR => E9: 3,7 * CNT 46 HDP CHAINS / 46 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A3: 5,9 => CTR => A3: 2,8 * DIS A3: 2,8 # D1: 5,9 => CTR => D1: 3,6,7 * INC A3: 2,8 + D1: 3,6,7 # A5: 5,9 => UNS * DIS A3: 2,8 + D1: 3,6,7 # A5: 2 => CTR => A5: 5,9 * INC A3: 2,8 + D1: 3,6,7 + A5: 5,9 # D2: 4,9 => UNS * DIS A3: 2,8 + D1: 3,6,7 + A5: 5,9 # D2: 6 => CTR => D2: 4,9 * PRF A3: 2,8 + D1: 3,6,7 + A5: 5,9 + D2: 4,9 # H6: 8,9 => SOL * STA A3: 2,8 + D1: 3,6,7 + A5: 5,9 + D2: 4,9 + H6: 8,9 * CNT 7 HDP CHAINS / 7 HYP OPENED