Analysis of zz-sudoku-de-739475-base.sdk
Contents
Original Sudoku
level: medium
position: .3.....1.2...1...97..3.9..2..85.31......2......34.65..1..8.5..73...4...5.7.....6. initial
Autosolve
position: .392...1.2..61...97.13.9..2.2859317...7128..39134765281.2865..73.67412.5.7.932.61 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # A1: 4,5 => SOL * DIS # B2: 4,5 => CTR => B2: 8 * PRF # B2: 8 => SOL * DIS # B3: 4,5 => CTR => B3: 6,8 * PRF # B3: 6,8 => SOL * PRF # H2: 4,5 => SOL * PRF # A1: 5,8 => SOL * DIS # A1: 4,6 => CTR => A1: 5,8 * PRF # G1: 4,7 => SOL * DIS # G1: 6,8 => CTR => G1: 4,7 * DIS # G2: 4,7 => CTR => G2: 3,8 * PRF # G2: 3,8 => SOL * DIS # B3: 5,8 => CTR => B3: 4,6 * DIS # G1: 4,6 => CTR => G1: 7,8 * DIS # A1: 4,6 => CTR => A1: 5,8 * PRF # A1: 5,8 => SOL * PRF # A5: 4,6 => SOL * DIS # A5: 5 => CTR => A5: 4,6 * DIS # B5: 4,6 => CTR => B5: 5 * PRF # B5: 5 => SOL * DIS # A1: 4,6 => CTR => A1: 5,8 * PRF # A1: 5,8 => SOL * PRF # G5: 4,6 => SOL * DIS # G5: 9 => CTR => G5: 4,6 * DIS # G5: 4,9 => CTR => G5: 6 * PRF # G5: 6 => SOL * DIS # H7: 4,9 => CTR => H7: 3 * PRF # H7: 3 => SOL * PRF # G7: 4,9 => SOL * DIS # G7: 3 => CTR => G7: 4,9 * DIS # H7: 4,9 => CTR => H7: 3 * PRF # H7: 3 => SOL * DIS # A9: 4,5 => CTR => A9: 8 * PRF # A9: 8 => SOL * PRF # A9: 4,8 => SOL * DIS # A9: 5 => CTR => A9: 4,8 * DIS # G1: 4,8 => CTR => G1: 6,7 * PRF # G1: 6,7 => SOL * DIS # G2: 4,8 => CTR => G2: 3,7 * PRF # G3: 4,8 => SOL * DIS # G3: 6 => CTR => G3: 4,8 * CNT 41 HDP CHAINS / 48 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # A1: 4,5 => SOL * STA A1: 4,5 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .3.....1.2...1...97..3.9..2..85.31......2......34.65..1..8.5..73...4...5.7.....6. | initial |
| .392...1.2..61...97.13.9..2.2859317...7128..39134765281.2865..73.67412.5.7.932.61 | autosolve |
| 539284716284617359761359842628593174457128693913476528142865937396741285875932461 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) C2: 4,5 E1: 5,8 F1: 4,7 F2: 4,7 E3: 5,8 I1: 4,6 A4: 4,6 I4: 4,6 H5: 4,9 B7: 4,9 B8: 8,9 C9: 4,5 H8: 8,9 G9: 4,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G2,H2: 3.. / G2 = 3 => 0 pairs (*) / H2 = 3 => 0 pairs (X) G7,H7: 3.. / G7 = 3 => 0 pairs (X) / H7 = 3 => 0 pairs (_) G2,G7: 3.. / G2 = 3 => 0 pairs (*) / G7 = 3 => 0 pairs (X) H2,H7: 3.. / H2 = 3 => 0 pairs (X) / H7 = 3 => 0 pairs (_) F1,F2: 4.. / F1 = 4 => 0 pairs (*) / F2 = 4 => 0 pairs (X) A4,I4: 4.. / A4 = 4 => 0 pairs (X) / I4 = 4 => 0 pairs (_) C2,C9: 4.. / C2 = 4 => 0 pairs (*) / C9 = 4 => 0 pairs (X) I1,I4: 4.. / I1 = 4 => 0 pairs (X) / I4 = 4 => 0 pairs (_) E1,E3: 5.. / E1 = 5 => 16 pairs (_) / E3 = 5 => 0 pairs (*) H2,H3: 5.. / H2 = 5 => 0 pairs (*) / H3 = 5 => 0 pairs (X) A5,B5: 5.. / A5 = 5 => 0 pairs (X) / B5 = 5 => 0 pairs (_) A9,C9: 5.. / A9 = 5 => 0 pairs (X) / C9 = 5 => 0 pairs (_) A1,E1: 5.. / A1 = 5 => 0 pairs (*) / E1 = 5 => 0 pairs (X) C2,C9: 5.. / C2 = 5 => 0 pairs (X) / C9 = 5 => 0 pairs (_) A1,B3: 6.. / A1 = 6 => 0 pairs (X) / B3 = 6 => 0 pairs (_) I4,G5: 6.. / I4 = 6 => 0 pairs (X) / G5 = 6 => 0 pairs (_) B3,G3: 6.. / B3 = 6 => 0 pairs (*) / G3 = 6 => 0 pairs (X) A4,I4: 6.. / A4 = 6 => 0 pairs (*) / I4 = 6 => 0 pairs (X) B3,B5: 6.. / B3 = 6 => 0 pairs (*) / B5 = 6 => 0 pairs (X) I1,I4: 6.. / I1 = 6 => 0 pairs (*) / I4 = 6 => 0 pairs (X) F1,F2: 7.. / F1 = 7 => 0 pairs (X) / F2 = 7 => 0 pairs (_) G1,G2: 7.. / G1 = 7 => 0 pairs (*) / G2 = 7 => 0 pairs (X) F1,G1: 7.. / F1 = 7 => 0 pairs (X) / G1 = 7 => 0 pairs (_) F2,G2: 7.. / F2 = 7 => 0 pairs (*) / G2 = 7 => 0 pairs (X) E1,E3: 8.. / E1 = 8 => 0 pairs (*) / E3 = 8 => 0 pairs (X) B8,A9: 8.. / B8 = 8 => 0 pairs (X) / A9 = 8 => 0 pairs (_) H8,G9: 8.. / H8 = 8 => 0 pairs (*) / G9 = 8 => 0 pairs (X) B8,H8: 8.. / B8 = 8 => 0 pairs (X) / H8 = 8 => 0 pairs (_) A9,G9: 8.. / A9 = 8 => 0 pairs (*) / G9 = 8 => 0 pairs (X) A1,A9: 8.. / A1 = 8 => 0 pairs (X) / A9 = 8 => 0 pairs (_) G5,H5: 9.. / G5 = 9 => 0 pairs (X) / H5 = 9 => 0 pairs (_) B7,B8: 9.. / B7 = 9 => 0 pairs (X) / B8 = 9 => 0 pairs (_) B8,H8: 9.. / B8 = 9 => 0 pairs (*) / H8 = 9 => 0 pairs (X) G5,G7: 9.. / G5 = 9 => 0 pairs (X) / G7 = 9 => 0 pairs (_) * DURATION: 0:00:56.582482 START: 08:24:03.475670 END: 08:25:00.058152 2017-05-01 * CP COUNT: (34) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B7,B8,C2,C9,E1,E3,F1,F2,G9,H5,H8,I1,I4) * .392...1.2..61...97.13.9..2.2859317...7128..39134765281.2865..73.67412.5.7.932.61 * PAIR C2: 4,5 BLK 1 A1: 4,5,6,8 # reduction candidate for 4,5 A1: 4,5 => SOLVED * 539284716284617359761359842628593174457128693913476528142865937396741285875932461 A1: 6,8 # 17 pairs B2: 4,5,8 # reduction candidate for 4,5 B2: 4,5 => CTR * .392547162..617..9761389452628593174..71286939134765281.28659.73.67412.5.7.932.61 B2: 8 => SOLVED * 539284716284617359761359842628593174457128693913476528142865937396741285875932461 B3: 4,5,6,8 # reduction candidate for 4,5 B3: 4,5 => CTR * 63925.81428.61473974138965242859317...7128..39134765281.2865..73.67412.5.7.932.61 B3: 6,8 => SOLVED * 539284716284617359761359842628593174457128693913476528142865937396741285875932461 * PAIR C2: 4,5 ROW 2 H2: 4,5,3,8 # reduction candidate for 4,5 H2: 4,5 => SOLVED * 539284716284617359761359842628593174457128693913476528142865937396741285875932461 H2: 3,8 # 16 pairs * PAIR E1: 5,8 ROW 1 A1: 5,8,4,6 # reduction candidate for 5,8 A1: 5,8 => SOLVED * 539284716284617359761359842628593174457128693913476528142865937396741285875932461 A1: 4,6 => CTR * .3925.81.28.61.7397.1389.52.2859317..57128..39134765281.28653.73967412.5.7.932.61 * PAIR F1: 4,7 ROW 1 G1: 4,7,6,8 # reduction candidate for 4,7 G1: 4,7 => SOLVED * 539284716284617359761359842628593174457128693913476528142865937396741285875932461 G1: 6,8 => CTR * .392.7.1.2..6147397.13.9.52.2859317...7128..39134765281.28653.73.674128587.932.61 * PAIR F2: 4,7 ROW 2 G2: 4,7,3,8 # reduction candidate for 4,7 G2: 4,7 => CTR * .392...1.2..61..397.13.9.52.2859317...7128..39134765281.28653.73.6741285875932461 G2: 3,8 => SOLVED * 539284716284617359761359842628593174457128693913476528142865937396741285875932461 * PAIR E3: 5,8 ROW 3 B3: 5,8,4,6 # reduction candidate for 5,8 B3: 5,8 => CTR * 63925.814284617..97.13.9..2.2859317...7128..39134765281.2865..73.67412.5.7.932.61 B3: 4,6 # 15 pairs H3: 5,8,4 # reduction candidate for 5,8 H3: 5,8 # 18 pairs * PAIR I1: 4,6 BLK 3 G1: 4,6,7,8 # reduction candidate for 4,6 G1: 4,6 => CTR * .392.7.1.2..6147397.13.9.52.2859317...7128..39134765281.28653.73.674128587.932.61 G1: 7,8 # 15 pairs G3: 4,6,8 # reduction candidate for 4,6 G3: 4,6 # 18 pairs * PAIR I1: 4,6 ROW 1 A1: 4,6,5,8 # reduction candidate for 4,6 A1: 4,6 => CTR * .3925.81.28.61.7397.1389.52.2859317..57128..39134765281.28653.73967412.5.7.932.61 A1: 5,8 => SOLVED * 539284716284617359761359842628593174457128693913476528142865937396741285875932461 * PAIR A4: 4,6 BLK 4 A5: 4,6,5 # reduction candidate for 4,6 A5: 4,6 => SOLVED * 539284716284617359761359842628593174457128693913476528142865937396741285875932461 A5: 5 => CTR * .392547162.4617..97613894526285931745471286939134765281928653473867412.5.75932.61 B5: 4,6,5 # reduction candidate for 4,6 B5: 4,6 => CTR * .392547162.4617..97613894526285931745471286939134765281928653473867412.5.75932.61 B5: 5 => SOLVED * 539284716284617359761359842628593174457128693913476528142865937396741285875932461 * PAIR A4: 4,6 COL A A1: 4,6,5,8 # reduction candidate for 4,6 A1: 4,6 => CTR * .3925.81.28.61.7397.1389.52.2859317..57128..39134765281.28653.73967412.5.7.932.61 A1: 5,8 => SOLVED * 539284716284617359761359842628593174457128693913476528142865937396741285875932461 * PAIR I4: 4,6 BLK 6 G5: 4,6,9 # reduction candidate for 4,6 G5: 4,6 => SOLVED * 539284716284617359761359842628593174457128693913476528142865937396741285875932461 G5: 9 => CTR * .392...142..6147397413.96.2.28593176..71289439134765281.2865..73.67412.5.7.932.61 * PAIR H5: 4,9 BLK 6 G5: 4,9,6 # reduction candidate for 4,9 G5: 4,9 => CTR * .392...142..6147397413.9652428593176.67128..3913476528192865..73.67412.5.7.932.61 G5: 6 => SOLVED * 539284716284617359761359842628593174457128693913476528142865937396741285875932461 * PAIR H5: 4,9 COL H H7: 4,9,3 # reduction candidate for 4,9 H7: 4,9 => CTR * .3925.8142..61..397.13.9.52.2859317...7128..39134765281.28653.73.6741285875932461 H7: 3 => SOLVED * 539284716284617359761359842628593174457128693913476528142865937396741285875932461 * PAIR B7: 4,9 ROW 7 G7: 4,9,3 # reduction candidate for 4,9 G7: 4,9 => SOLVED * 539284716284617359761359842628593174457128693913476528142865937396741285875932461 G7: 3 => CTR * .392...1.2..61...97.13.9..2.2859317...7128943913476528142865397396741285875932461 H7: 4,9,3 # reduction candidate for 4,9 H7: 4,9 => CTR * .3925.8142..61..397.13.9.52.2859317...7128..39134765281.28653.73.6741285875932461 H7: 3 => SOLVED * 539284716284617359761359842628593174457128693913476528142865937396741285875932461 * PAIR C9: 4,5 BLK 7 A9: 4,5,8 # reduction candidate for 4,5 A9: 4,5 => CTR * 83925..1.2..61...9761389452.28593174..71286939134765281.28659.73.67412.5.7.932.61 A9: 8 => SOLVED * 539284716284617359761359842628593174457128693913476528142865937396741285875932461 * PAIR G9: 4,8 ROW 9 A9: 4,8,5 # reduction candidate for 4,8 A9: 4,8 => SOLVED * 539284716284617359761359842628593174457128693913476528142865937396741285875932461 A9: 5 => CTR * 83925..1.2..61...9761389452.285931744571286939134765281.28659.73.67412.5.7.932.61 * PAIR G9: 4,8 COL G G1: 4,8,6,7 # reduction candidate for 4,8 G1: 4,8 => CTR * .392.7.1.2..6147397.13.9.52.2859317...7128..39134765281.28653.73.674128587.932.61 G1: 6,7 => SOLVED * 539284716284617359761359842628593174457128693913476528142865937396741285875932461 G2: 4,8,3,7 # reduction candidate for 4,8 G2: 4,8 => CTR * .392..71.2..617.397.13.9.52.2859317...7128..39134765281.28653.73.6741285875932461 G2: 3,7 # 15 pairs G3: 4,8,6 # reduction candidate for 4,8 G3: 4,8 => SOLVED * 539284716284617359761359842628593174457128693913476528142865937396741285875932461 G3: 6 => CTR * 63925.81428.6147397.13.96.2.28593176.67128..39134765281.2865..73.67412.5.7.932.61 * INCONCLUSIVE * SAVE PR GRAPH zz-sudoku-de-739475-base-pr-000.dot * REASONING * PRF # A1: 4,5 => SOL * DIS # B2: 4,5 => CTR => B2: 8 * PRF # B2: 8 => SOL * DIS # B3: 4,5 => CTR => B3: 6,8 * PRF # B3: 6,8 => SOL * PRF # H2: 4,5 => SOL * PRF # A1: 5,8 => SOL * DIS # A1: 4,6 => CTR => A1: 5,8 * PRF # G1: 4,7 => SOL * DIS # G1: 6,8 => CTR => G1: 4,7 * DIS # G2: 4,7 => CTR => G2: 3,8 * PRF # G2: 3,8 => SOL * DIS # B3: 5,8 => CTR => B3: 4,6 * DIS # G1: 4,6 => CTR => G1: 7,8 * DIS # A1: 4,6 => CTR => A1: 5,8 * PRF # A1: 5,8 => SOL * PRF # A5: 4,6 => SOL * DIS # A5: 5 => CTR => A5: 4,6 * DIS # B5: 4,6 => CTR => B5: 5 * PRF # B5: 5 => SOL * DIS # A1: 4,6 => CTR => A1: 5,8 * PRF # A1: 5,8 => SOL * PRF # G5: 4,6 => SOL * DIS # G5: 9 => CTR => G5: 4,6 * DIS # G5: 4,9 => CTR => G5: 6 * PRF # G5: 6 => SOL * DIS # H7: 4,9 => CTR => H7: 3 * PRF # H7: 3 => SOL * PRF # G7: 4,9 => SOL * DIS # G7: 3 => CTR => G7: 4,9 * DIS # H7: 4,9 => CTR => H7: 3 * PRF # H7: 3 => SOL * DIS # A9: 4,5 => CTR => A9: 8 * PRF # A9: 8 => SOL * PRF # A9: 4,8 => SOL * DIS # A9: 5 => CTR => A9: 4,8 * DIS # G1: 4,8 => CTR => G1: 6,7 * PRF # G1: 6,7 => SOL * DIS # G2: 4,8 => CTR => G2: 3,7 * PRF # G3: 4,8 => SOL * DIS # G3: 6 => CTR => G3: 4,8 * CNT 41 HDP CHAINS / 48 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B7,B8,C2,C9,E1,E3,F1,F2,G9,H5,H8,I1,I4) * .392...1.2..61...97.13.9..2.2859317...7128..39134765281.2865..73.67412.5.7.932.61 * PAIR C2: 4,5 BLK 1 A1: 4,5,6,8 # reduction candidate for 4,5 A1: 4,5 => SOLVED * 539284716284617359761359842628593174457128693913476528142865937396741285875932461 * DURATION: 0:00:02.010990 START: 08:25:51.092460 END: 08:25:53.103450 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-sudoku-de-739475-base-pr-001.dot * REASONING * PRF # A1: 4,5 => SOL * STA A1: 4,5 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokus.de/739475.html sehr schwierig -------------------------------------------------- level: medium * PAIR REDUCTION .. * ROUND 1: .392...1.2..61...97.13.9..2.2859317...7128..39134765281.2865..73.67412.5.7.932.61 C2: 4,5 A1: 4,5,6,8 # reduction candidate for 4,5 A1: 4,5 => SOLVED * 539284716284617359761359842628593174457128693913476528142865937396741285875932461 * SOLVED! -------------------------------------------------- |:step:| 00 -------------------------------------------------- * FORCE VALUE:: G7 = 3 => CTR * DISABLE VALUE:: G7 != 3 also * DISABLE VALUE:: B5 != 5 |:step:| 01 --------------------------------------------------
Solution
position: 539284716284617359761359842628593174457128693913476528142865937396741285875932461 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 # A1: 4,5 => SOL * INC # A1: 6,8 => UNS * DIS # B2: 4,5 => CTR => B2: 8 * PRF # B2: 8 => SOL * DIS # B3: 4,5 => CTR => B3: 6,8 * PRF # B3: 6,8 => SOL * PRF # H2: 4,5 => SOL * INC # H2: 3,8 => UNS * PRF # A1: 5,8 => SOL * DIS # A1: 4,6 => CTR => A1: 5,8 * PRF # G1: 4,7 => SOL * DIS # G1: 6,8 => CTR => G1: 4,7 * DIS # G2: 4,7 => CTR => G2: 3,8 * PRF # G2: 3,8 => SOL * DIS # B3: 5,8 => CTR => B3: 4,6 * INC # B3: 4,6 => UNS * INC # H3: 5,8 => UNS * DIS # G1: 4,6 => CTR => G1: 7,8 * INC # G1: 7,8 => UNS * INC # G3: 4,6 => UNS * DIS # A1: 4,6 => CTR => A1: 5,8 * PRF # A1: 5,8 => SOL * PRF # A5: 4,6 => SOL * DIS # A5: 5 => CTR => A5: 4,6 * DIS # B5: 4,6 => CTR => B5: 5 * PRF # B5: 5 => SOL * DIS # A1: 4,6 => CTR => A1: 5,8 * PRF # A1: 5,8 => SOL * PRF # G5: 4,6 => SOL * DIS # G5: 9 => CTR => G5: 4,6 * DIS # G5: 4,9 => CTR => G5: 6 * PRF # G5: 6 => SOL * DIS # H7: 4,9 => CTR => H7: 3 * PRF # H7: 3 => SOL * PRF # G7: 4,9 => SOL * DIS # G7: 3 => CTR => G7: 4,9 * DIS # H7: 4,9 => CTR => H7: 3 * PRF # H7: 3 => SOL * DIS # A9: 4,5 => CTR => A9: 8 * PRF # A9: 8 => SOL * PRF # A9: 4,8 => SOL * DIS # A9: 5 => CTR => A9: 4,8 * DIS # G1: 4,8 => CTR => G1: 6,7 * PRF # G1: 6,7 => SOL * DIS # G2: 4,8 => CTR => G2: 3,7 * INC # G2: 3,7 => UNS * PRF # G3: 4,8 => SOL * DIS # G3: 6 => CTR => G3: 4,8 * CNT 48 HDP CHAINS / 48 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # A1: 4,5 => SOL * STA A1: 4,5 * CNT 1 HDP CHAINS / 1 HYP OPENED