Analysis of zz-sudoku-de-602142-base.sdk
Contents
Original Sudoku
level: medium
position: 71.8.3.54.3.4.5.9.4.......8...7.1....5.....3....5.6...1.......7.7.3.9.6.56.1.4.23 initial
Autosolve
position: 71.8.3.54.3.41579.4.5..7318...7.1....57....3...15.6.7.1.3.....7.7.3.9.6.56.174.23 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C1: 6 => CTR => C1: 2,9 * DIS # E3: 2,9 => CTR => E3: 6 * DIS # B7: 4,8 => CTR => B7: 2,9 * DIS # E3: 2,9 => CTR => E3: 6 * DIS # C1: 6 => CTR => C1: 2,9 * PRF # E5: 2,9 => SOL * PRF # C1: 9 => SOL * PRF # E5: 2,9 => SOL * DIS # I5: 2,9 => CTR => I5: 1,6 * DIS # D3: 6 => CTR => D3: 2,9 * DIS # E4: 2,8 => CTR => E4: 3,4,9 * DIS # E5: 2,8 => CTR => E5: 4,9 * DIS # G5: 2,8 => CTR => G5: 1,4,6 * DIS # G4: 4,8 => CTR => G4: 2,5,6 * PRF # G5: 4,8 => SOL * DIS # C4: 4,8 => CTR => C4: 2,6 * DIS # E4: 4,8 => CTR => E4: 2,3,9 * DIS # I4: 2,9 => CTR => I4: 5,6 * DIS # I5: 2,9 => CTR => I5: 1,6 * DIS # C8: 2,8 => CTR => C8: 4 * DIS # E8: 5 => CTR => E8: 2,8 * DIS # A4: 2,8 => CTR => A4: 3,6,9 * DIS # A6: 2,8 => CTR => A6: 3,9 * DIS # B7: 2,4 => CTR => B7: 8,9 * DIS # E7: 2,6 => CTR => E7: 5,8 * PRF # D3: 9 => SOL * DIS # E7: 2,8 => CTR => E7: 5,6 * PRF # G7: 4,8 => SOL * DIS # G8: 4,8 => CTR => G8: 1,5 * DIS # B7: 4,8 => CTR => B7: 2,9 * DIS # G8: 4,8 => CTR => G8: 1,5 * DIS # G7: 4,5 => CTR => G7: 8,9 * CNT 32 HDP CHAINS / 89 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C1: 6 => CTR => C1: 2,9 * DIS C1: 2,9 # E3: 2,9 => CTR => E3: 6 * DIS C1: 2,9 + E3: 6 # B7: 4,8 => CTR => B7: 2,9 * PRF C1: 2,9 + E3: 6 + B7: 2,9 # E5: 2,9 => SOL * STA C1: 2,9 + E3: 6 + B7: 2,9 + E5: 2,9 * CNT 4 HDP CHAINS / 7 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 71.8.3.54.3.4.5.9.4.......8...7.1....5.....3....5.6...1.......7.7.3.9.6.56.1.4.23 | initial |
| 71.8.3.54.3.41579.4.5..7318...7.1....57....3...15.6.7.1.3.....7.7.3.9.6.56.174.23 | autosolve |
| 719823654836415792425967318942731586657298431381546279193652847274389165568174923 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) B3: 2,9 E1: 2,9 G1: 2,6 I2: 2,6 D5: 2,9 F5: 2,8 H4: 4,8 I6: 2,9 A8: 2,8 C9: 8,9 D7: 2,6 F7: 2,8 H7: 4,8 I8: 1,5 G9: 8,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G5,I5: 1.. / G5 = 1 => 16 pairs (_) / I5 = 1 => 15 pairs (_) G8,I8: 1.. / G8 = 1 => 15 pairs (_) / I8 = 1 => 16 pairs (_) G5,G8: 1.. / G5 = 1 => 16 pairs (_) / G8 = 1 => 15 pairs (_) I5,I8: 1.. / I5 = 1 => 15 pairs (_) / I8 = 1 => 16 pairs (_) G1,I2: 2.. / G1 = 2 => 0 pairs (X) / I2 = 2 => 19 pairs (_) F5,F7: 2.. / F5 = 2 => 0 pairs (X) / F7 = 2 => 15 pairs (_) A4,A6: 3.. / A4 = 3 => 15 pairs (_) / A6 = 3 => 15 pairs (_) E4,E6: 3.. / E4 = 3 => 15 pairs (_) / E6 = 3 => 15 pairs (_) A4,E4: 3.. / A4 = 3 => 15 pairs (_) / E4 = 3 => 15 pairs (_) A6,E6: 3.. / A6 = 3 => 15 pairs (_) / E6 = 3 => 15 pairs (_) B7,C8: 4.. / B7 = 4 => 0 pairs (X) / C8 = 4 => 15 pairs (_) E5,G5: 4.. / E5 = 4 => 15 pairs (_) / G5 = 4 => 0 pairs (*) C8,G8: 4.. / C8 = 4 => 15 pairs (_) / G8 = 4 => 0 pairs (X) C4,C8: 4.. / C4 = 4 => 0 pairs (X) / C8 = 4 => 15 pairs (_) H4,H7: 4.. / H4 = 4 => 0 pairs (X) / H7 = 4 => 16 pairs (_) G4,I4: 5.. / G4 = 5 => 15 pairs (_) / I4 = 5 => 16 pairs (_) E7,E8: 5.. / E7 = 5 => 17 pairs (_) / E8 = 5 => 0 pairs (X) E7,G7: 5.. / E7 = 5 => 17 pairs (_) / G7 = 5 => 0 pairs (X) I4,I8: 5.. / I4 = 5 => 16 pairs (_) / I8 = 5 => 15 pairs (_) D3,E3: 6.. / D3 = 6 => 0 pairs (X) / E3 = 6 => 15 pairs (_) G1,I2: 6.. / G1 = 6 => 19 pairs (_) / I2 = 6 => 0 pairs (X) D7,E7: 6.. / D7 = 6 => 15 pairs (_) / E7 = 6 => 0 pairs (X) C1,G1: 6.. / C1 = 6 => 0 pairs (X) / G1 = 6 => 19 pairs (_) D3,D7: 6.. / D3 = 6 => 0 pairs (X) / D7 = 6 => 15 pairs (_) E3,E7: 6.. / E3 = 6 => 15 pairs (_) / E7 = 6 => 0 pairs (X) A2,C2: 8.. / A2 = 8 => 22 pairs (_) / C2 = 8 => 17 pairs (_) C9,G9: 8.. / C9 = 8 => 0 pairs (*) / G9 = 8 => 0 pairs (X) F5,F7: 8.. / F5 = 8 => 15 pairs (_) / F7 = 8 => 0 pairs (X) H4,H7: 8.. / H4 = 8 => 16 pairs (_) / H7 = 8 => 0 pairs (X) C1,B3: 9.. / C1 = 9 => 0 pairs (*) / B3 = 9 => 0 pairs (X) B7,C9: 9.. / B7 = 9 => 0 pairs (*) / C9 = 9 => 0 pairs (X) G7,G9: 9.. / G7 = 9 => 17 pairs (_) / G9 = 9 => 0 pairs (*) C1,E1: 9.. / C1 = 9 => 0 pairs (*) / E1 = 9 => 0 pairs (X) B7,G7: 9.. / B7 = 9 => 0 pairs (*) / G7 = 9 => 0 pairs (X) C9,G9: 9.. / C9 = 9 => 17 pairs (_) / G9 = 9 => 0 pairs (*) B3,B7: 9.. / B3 = 9 => 17 pairs (_) / B7 = 9 => 0 pairs (*) C1,C9: 9.. / C1 = 9 => 0 pairs (*) / C9 = 9 => 0 pairs (X) D3,D5: 9.. / D3 = 9 => 0 pairs (*) / D5 = 9 => 0 pairs (X) * DURATION: 0:01:00.786189 START: 07:15:00.161990 END: 07:16:00.948179 2017-05-01 * CP COUNT: (38) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,B3,C9,D5,D7,E1,F5,F7,G1,G9,H4,H7,I2,I6,I8) * 71.8.3.54.3.41579.4.5..7318...7.1....57....3...15.6.7.1.3.....7.7.3.9.6.56.174.23 * PAIR B3: 2,9 BLK 1 C1: 2,9,6 # reduction candidate for 2,9 C1: 6 => CTR * 716893254.38415796495.67318.42731.8..5794..3.381526479123.5.947.743.9.6.569174823 C1: 2,9 # 19 pairs * PAIR B3: 2,9 ROW 3 D3: 2,9,6 # reduction candidate for 2,9 D3: 2,9 # 15 pairs E3: 2,9,6 # reduction candidate for 2,9 E3: 2,9 => CTR * 719823654.3.415792425697318..27.1.85.579.2136.815.6.7.1.3268547.74359.6156.174923 E3: 6 # 15 pairs * PAIR B3: 2,9 COL B B7: 2,9,4,8 # reduction candidate for 2,9 B7: 4,8 => CTR * 712893654638415792495267318..67.1.8.8579...3...15.6.7.183652947274389.6.569174823 B7: 2,9 # 19 pairs * PAIR E1: 2,9 BLK 2 D3: 2,9,6 # reduction candidate for 2,9 D3: 2,9 # 15 pairs E3: 2,9,6 # reduction candidate for 2,9 E3: 2,9 => CTR * 719823654.3.415792425697318..27.1.85.579.2136.815.6.7.1.3268547.74359.6156.174923 E3: 6 # 15 pairs * PAIR E1: 2,9 ROW 1 C1: 2,9,6 # reduction candidate for 2,9 C1: 6 => CTR * 716893254.38415796495.67318.42731.8..5794..3.381526479123.5.947.743.9.6.569174823 C1: 2,9 # 19 pairs * PAIR E1: 2,9 COL E E4: 2,9,3,4,8 # reduction candidate for 2,9 E4: 2,9 # 16 pairs E5: 2,9,4,8 # reduction candidate for 2,9 E5: 2,9 => SOLVED * 719823654836415792425967318942731586657298431381546279193652847274389165568174923 E5: 4,8 # 16 pairs E6: 2,9,3,4,8 # reduction candidate for 2,9 E6: 2,9 # 18 pairs * PAIR G1: 2,6 ROW 1 C1: 2,6,9 # reduction candidate for 2,6 C1: 9 => SOLVED * 719823654836415792425967318942731586657298431381546279193652847274389165568174923 C1: 2,6 # 17 pairs * PAIR G1: 2,6 COL G G4: 2,6,4,5,8 # reduction candidate for 2,6 G4: 2,6 # 18 pairs G5: 2,6,1,4,8 # reduction candidate for 2,6 G5: 2,6 # 17 pairs * PAIR I2: 2,6 ROW 2 A2: 2,6,8 # reduction candidate for 2,6 A2: 2,6 # 17 pairs C2: 2,6,8 # reduction candidate for 2,6 C2: 2,6 # 22 pairs * PAIR I2: 2,6 COL I I4: 2,6,5,9 # reduction candidate for 2,6 I4: 2,6 # 17 pairs I5: 2,6,1,9 # reduction candidate for 2,6 I5: 2,6 # 16 pairs * PAIR D5: 2,9 BLK 5 E4: 2,9,3,4,8 # reduction candidate for 2,9 E4: 2,9 # 16 pairs E5: 2,9,4,8 # reduction candidate for 2,9 E5: 2,9 => SOLVED * 719823654836415792425967318942731586657298431381546279193652847274389165568174923 E5: 4,8 # 16 pairs E6: 2,9,3,4,8 # reduction candidate for 2,9 E6: 2,9 # 18 pairs * PAIR D5: 2,9 ROW 5 A5: 2,9,6,8 # reduction candidate for 2,9 A5: 2,9 # 18 pairs I5: 2,9,1,6 # reduction candidate for 2,9 I5: 2,9 => CTR * 716893254.3.41579649526731892.7316856579481323815264791436.29.7.7.3.9561569174823 I5: 1,6 # 16 pairs * PAIR D5: 2,9 COL D D3: 2,9,6 # reduction candidate for 2,9 D3: 6 => CTR * 719823654.3.415792425697318..27.1.85.579.2136.815.6.7.1.3268547.74359.6156.174923 D3: 2,9 # 15 pairs * PAIR F5: 2,8 BLK 5 E4: 2,8,3,4,9 # reduction candidate for 2,8 E4: 2,8 => CTR * 71.8.3254.3.4157964.5..73183..7.15.9657.4..319.1536.721.3.5...7.7.3.916556.174.23 E4: 3,4,9 # 15 pairs E5: 2,8,4,9 # reduction candidate for 2,8 E5: 2,8 => CTR * 71.8.3654.364157924.5.673189.27315866579..431..15.62791.3.5..47.743.916556.174.23 E5: 4,9 # 16 pairs E6: 2,8,3,4,9 # reduction candidate for 2,8 E6: 2,8 # 15 pairs * PAIR F5: 2,8 ROW 5 A5: 2,8,6,9 # reduction candidate for 2,8 A5: 2,8 # 10 pairs G5: 2,8,1,4,6 # reduction candidate for 2,8 G5: 2,8 => CTR * 71.8936548364157924952673189..7315.66579482313.1526.79183652947274389165569174823 G5: 1,4,6 # 15 pairs * PAIR H4: 4,8 BLK 6 G4: 4,8,2,5,6 # reduction candidate for 4,8 G4: 4,8 => CTR * 712893654638415792495.27318926731..5.57.4.136.415.6279183..2947274389561569174823 G4: 2,5,6 # 15 pairs G5: 4,8,1,2,6 # reduction candidate for 4,8 G5: 4,8 => SOLVED * 719823654836415792425967318942731586657298431381546279193652847274389165568174923 G5: 1,2,6 # 15 pairs G6: 4,8,2 # reduction candidate for 4,8 G6: 4,8 # 16 pairs * PAIR H4: 4,8 ROW 4 B4: 4,8,2 # reduction candidate for 4,8 B4: 4,8 # 17 pairs C4: 4,8,2,6 # reduction candidate for 4,8 C4: 4,8 => CTR * 71.893.54.3.41579.495..7318.2.731.8.6579...3.3815.6.79143...9.7.7.3.9.6.569174823 C4: 2,6 # 16 pairs E4: 4,8,2,3,9 # reduction candidate for 4,8 E4: 4,8 => CTR * 71.8.3254.3.4157964.5..73183..7.15.9657....319.1536.721.3.5...7.7.3.916556.174.23 E4: 2,3,9 # 15 pairs * PAIR I6: 2,9 BLK 6 I4: 2,9,5,6 # reduction candidate for 2,9 I4: 2,9 => CTR * 716893254.3.4157964952673186..7315.9.5794.631..15.6.7.1.365...7.743.916556.174.23 I4: 5,6 # 18 pairs I5: 2,9,1,6 # reduction candidate for 2,9 I5: 2,9 => CTR * 716893254.3.41579649526731892.7316856579481323815264791436.29.7.7.3.9561569174823 I5: 1,6 # 16 pairs * PAIR I6: 2,9 ROW 6 A6: 2,9,3,8 # reduction candidate for 2,9 A6: 2,9 # 18 pairs E6: 2,9,3,4,8 # reduction candidate for 2,9 E6: 2,9 # 18 pairs * PAIR A8: 2,8 BLK 7 B7: 2,8,4,9 # reduction candidate for 2,8 B7: 2,8 # 17 pairs C8: 2,8,4 # reduction candidate for 2,8 C8: 2,8 => CTR * 71.8.3.54.3.41579.4.5..7318..47.1.8..57....3...15.6.7.143.....7.7.3.9.6.56.174.23 C8: 4 # 15 pairs * PAIR A8: 2,8 ROW 8 E8: 2,8,5 # reduction candidate for 2,8 E8: 5 => CTR * 719823654836415792425..73186.27.1..5.57.4.136..15.6.79193...547.74359861568174923 E8: 2,8 # 17 pairs * PAIR A8: 2,8 COL A A2: 2,8,6 # reduction candidate for 2,8 A2: 2,8 # 21 pairs A4: 2,8,3,6,9 # reduction candidate for 2,8 A4: 2,8 => CTR * 719823.54.3.41579.4.5..7318...731..9.57....3.3.1596.721.3.....7.7.3.9.6556.174.23 A4: 3,6,9 # 15 pairs A5: 2,8,6,9 # reduction candidate for 2,8 A5: 2,8 # 10 pairs A6: 2,8,3,9 # reduction candidate for 2,8 A6: 2,8 => CTR * 71.8.3.546384157924.59673183.6791..5957248.36..1536.791936.2..7.7.3.9.6.56.174.23 A6: 3,9 # 16 pairs * PAIR C9: 8,9 BLK 7 B7: 8,9,2,4 # reduction candidate for 8,9 B7: 2,4 => CTR * 71289365463841579.495267318.4.731.8..57982431381546279123658947874329165569174823 B7: 8,9 # 17 pairs * PAIR D7: 2,6 BLK 8 E7: 2,6,5,8 # reduction candidate for 2,6 E7: 2,6 => CTR * 719823654836415792425697318...7.1..5.57...136..15.6.79193.68547.74359861568174923 E7: 5,8 # 16 pairs * PAIR D7: 2,6 COL D D3: 2,6,9 # reduction candidate for 2,6 D3: 9 => SOLVED * 719823654836415792425967318942731586657298431381546279193652847274389165568174923 D3: 2,6 # 17 pairs * PAIR F7: 2,8 BLK 8 E7: 2,8,5,6 # reduction candidate for 2,8 E7: 2,8 => CTR * 7198236548364157924259673186.27.1..5.572.8136..15.6.79193682547.74359861568174923 E7: 5,6 # 16 pairs E8: 2,8,5 # reduction candidate for 2,8 E8: 2,8 # 17 pairs * PAIR F7: 2,8 ROW 7 B7: 2,8,4,9 # reduction candidate for 2,8 B7: 4,9 # 17 pairs B7: 2,8 # 17 pairs * PAIR H7: 4,8 BLK 9 G7: 4,8,5,9 # reduction candidate for 4,8 G7: 4,8 => SOLVED * 719823654836415792425967318942731586657298431381546279193652847274389165568174923 G7: 5,9 # 16 pairs G8: 4,8,1,5 # reduction candidate for 4,8 G8: 4,8 => CTR * 719823654836415792425..73186.27.1..5.57.4.136..15.6.79193...547.74359861568174923 G8: 1,5 # 17 pairs * PAIR H7: 4,8 ROW 7 B7: 4,8,2,9 # reduction candidate for 4,8 B7: 4,8 => CTR * 712893654638415792495267318..67.1.8.8579...3...15.6.7.183652947274389.6.569174823 B7: 2,9 # 19 pairs * PAIR I8: 1,5 BLK 9 G8: 1,5,4,8 # reduction candidate for 1,5 G8: 4,8 => CTR * 719823654836415792425..73186.27.1..5.57.4.136..15.6.79193...547.74359861568174923 G8: 1,5 # 17 pairs * PAIR G9: 8,9 BLK 9 G7: 8,9,4,5 # reduction candidate for 8,9 G7: 4,5 => CTR * 719823654836415792425..73189.27315.6657...8313.1586279193.....72743.9165568174923 G7: 8,9 # 19 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-sudoku-de-602142-base-pr-000.dot * REASONING * DIS # C1: 6 => CTR => C1: 2,9 * DIS # E3: 2,9 => CTR => E3: 6 * DIS # B7: 4,8 => CTR => B7: 2,9 * DIS # E3: 2,9 => CTR => E3: 6 * DIS # C1: 6 => CTR => C1: 2,9 * PRF # E5: 2,9 => SOL * PRF # C1: 9 => SOL * PRF # E5: 2,9 => SOL * DIS # I5: 2,9 => CTR => I5: 1,6 * DIS # D3: 6 => CTR => D3: 2,9 * DIS # E4: 2,8 => CTR => E4: 3,4,9 * DIS # E5: 2,8 => CTR => E5: 4,9 * DIS # G5: 2,8 => CTR => G5: 1,4,6 * DIS # G4: 4,8 => CTR => G4: 2,5,6 * PRF # G5: 4,8 => SOL * DIS # C4: 4,8 => CTR => C4: 2,6 * DIS # E4: 4,8 => CTR => E4: 2,3,9 * DIS # I4: 2,9 => CTR => I4: 5,6 * DIS # I5: 2,9 => CTR => I5: 1,6 * DIS # C8: 2,8 => CTR => C8: 4 * DIS # E8: 5 => CTR => E8: 2,8 * DIS # A4: 2,8 => CTR => A4: 3,6,9 * DIS # A6: 2,8 => CTR => A6: 3,9 * DIS # B7: 2,4 => CTR => B7: 8,9 * DIS # E7: 2,6 => CTR => E7: 5,8 * PRF # D3: 9 => SOL * DIS # E7: 2,8 => CTR => E7: 5,6 * PRF # G7: 4,8 => SOL * DIS # G8: 4,8 => CTR => G8: 1,5 * DIS # B7: 4,8 => CTR => B7: 2,9 * DIS # G8: 4,8 => CTR => G8: 1,5 * DIS # G7: 4,5 => CTR => G7: 8,9 * CNT 32 HDP CHAINS / 89 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,B3,C9,D5,D7,E1,F5,F7,G1,G9,H4,H7,I2,I6,I8) * 71.8.3.54.3.41579.4.5..7318...7.1....57....3...15.6.7.1.3.....7.7.3.9.6.56.174.23 * PAIR B3: 2,9 BLK 1 C1: 2,9,6 # reduction candidate for 2,9 C1: 6 => CTR * 716893254.38415796495.67318.42731.8..5794..3.381526479123.5.947.743.9.6.569174823 * PAIR B3: 2,9 ROW 3 D3: 2,9,6 # reduction candidate for 2,9 D3: 2,9 # 19 pairs E3: 2,9,6 # reduction candidate for 2,9 E3: 2,9 => CTR * 719823654.3.4157924256973189.2731....579...3...15.6.791.3268547.74359.6156.174923 * RESTART * PAIR B3: 2,9 COL B B7: 2,9,4,8 # reduction candidate for 2,9 B7: 4,8 => CTR * 712893654.384157924952673189.6731.858579...3.3.15.6.791.3652947274389.6.569174823 * PAIR RESTART * PAIR E1: 2,9 COL E E5: 2,9,4,8 # reduction candidate for 2,9 E5: 2,9 => SOLVED * 719823654836415792425967318942731586657298431381546279193652847274389165568174923 * DURATION: 0:00:08.511544 START: 07:17:21.087261 END: 07:17:29.598805 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-sudoku-de-602142-base-pr-001.dot * REASONING * DIS # C1: 6 => CTR => C1: 2,9 * DIS C1: 2,9 # E3: 2,9 => CTR => E3: 6 * DIS C1: 2,9 + E3: 6 # B7: 4,8 => CTR => B7: 2,9 * PRF C1: 2,9 + E3: 6 + B7: 2,9 # E5: 2,9 => SOL * STA C1: 2,9 + E3: 6 + B7: 2,9 + E5: 2,9 * CNT 4 HDP CHAINS / 7 HYP OPENED
Header Info
http://www.sudokus.de/602142.html sehr schwierig level: medium * PAIR REDUCTION .. * ROUND 1: 71.8.3.54.3.41579.4.5..7318...7.1....57....3...15.6.7.1.3.....7.7.3.9.6.56.174.23 B3: 2,9 C1: 2,6,9 # reduction candidate for 2,9 C1: 6 => CTR * 716893254.38415796495.67318.42731.8..5794..3.381526479123.5.947.743.9.6.569174823 D3: 2,6,9 # reduction candidate for 2,9 D3: 6 => CTR * 719823654.3.4157924256973189.2731....579...3...15.6.791.3268547.74359.6156.174923 B7: 2,4,8,9 # reduction candidate for 2,9 B7: 4,8 => CTR * 712893654.384157924952673189.6731.858579...3.3.15.6.791.3652947274389.6.569174823 E1: 2,9 E5: 2,4,8,9 # reduction candidate for 2,9 E5: 2,9 => SOLVED * 719823654836415792425967318942731586657298431381546279193652847274389165568174923 * SOLVED! -------------------------------------------------- * AUTO .. C3 = 5 # set value F3 = 7 # set value H3: 1 # naked single G3 = 3 # set value H3 = 1 # set value C7 = 3 # set value E9 = 7 # set value E2: 1.. # hidden single G2: 7.. # hidden single H6: 7.. # hidden single E2 = 1 # set value G2 = 7 # set value H6 = 7 # set value C5: 7.. # hidden single C5 = 7 # set value C6: 1.. # hidden single C6 = 1 # set value Q1,Q3: 6.. => E1 != 6 Q1,Q7: 9.. => B4,B6,C4 != 9 Q9: 9.. = G7,G9: 9.. => G4,G5,G6 != 9 * UNSOLVED! |:step:| 00 -------------------------------------------------- highlight 4 G8 = 4 => H4,B6,B7 = 4 => CTR => G8 != 4 highlight 8 C4 = 8 => A2,B7,E8,G9 = 8 => G4,H4,G5,G6 != 8 => CTR => C4 != 8 highlight 2 A5 = 2 => B7,E8,D3,F7 = 2 => CTR => A5 != 2 C2 = 2 => C4 = 6 => C1 != 6 C2 = 2 => I2 = 6 => G1 = !6 => C1 = 6 => CTR => C2 != 6 D5: 2,9 E5: 2,4,8,9 * DISABLE VALUE:: E5 != 4 G5: 4.. # hidden single * DISABLE VALUE:: E5 != 8 |:step:| 01 --------------------------------------------------
Solution
position: 719823654836415792425967318942731586657298431381546279193652847274389165568174923 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:
* INC # C1: 2,9 => UNS * DIS # C1: 6 => CTR => C1: 2,9 * INC # D3: 2,9 => UNS * DIS # E3: 2,9 => CTR => E3: 6 * INC # E3: 6 => UNS * INC # B7: 2,9 => UNS * DIS # B7: 4,8 => CTR => B7: 2,9 * INC # D3: 2,9 => UNS * DIS # E3: 2,9 => CTR => E3: 6 * INC # E3: 6 => UNS * INC # C1: 2,9 => UNS * DIS # C1: 6 => CTR => C1: 2,9 * INC # E4: 2,9 => UNS * PRF # E5: 2,9 => SOL * INC # E5: 4,8 => UNS * INC # E6: 2,9 => UNS * INC # C1: 2,6 => UNS * PRF # C1: 9 => SOL * INC # G4: 2,6 => UNS * INC # G5: 2,6 => UNS * INC # A2: 2,6 => UNS * INC # C2: 2,6 => UNS * INC # I4: 2,6 => UNS * INC # I5: 2,6 => UNS * INC # E4: 2,9 => UNS * PRF # E5: 2,9 => SOL * INC # E5: 4,8 => UNS * INC # E6: 2,9 => UNS * INC # A5: 2,9 => UNS * DIS # I5: 2,9 => CTR => I5: 1,6 * INC # I5: 1,6 => UNS * INC # D3: 2,9 => UNS * DIS # D3: 6 => CTR => D3: 2,9 * DIS # E4: 2,8 => CTR => E4: 3,4,9 * INC # E4: 3,4,9 => UNS * DIS # E5: 2,8 => CTR => E5: 4,9 * INC # E5: 4,9 => UNS * INC # E6: 2,8 => UNS * INC # A5: 2,8 => UNS * DIS # G5: 2,8 => CTR => G5: 1,4,6 * INC # G5: 1,4,6 => UNS * DIS # G4: 4,8 => CTR => G4: 2,5,6 * INC # G4: 2,5,6 => UNS * PRF # G5: 4,8 => SOL * INC # G5: 1,2,6 => UNS * INC # G6: 4,8 => UNS * INC # B4: 4,8 => UNS * DIS # C4: 4,8 => CTR => C4: 2,6 * INC # C4: 2,6 => UNS * DIS # E4: 4,8 => CTR => E4: 2,3,9 * INC # E4: 2,3,9 => UNS * DIS # I4: 2,9 => CTR => I4: 5,6 * INC # I4: 5,6 => UNS * DIS # I5: 2,9 => CTR => I5: 1,6 * INC # I5: 1,6 => UNS * INC # A6: 2,9 => UNS * INC # E6: 2,9 => UNS * INC # B7: 2,8 => UNS * DIS # C8: 2,8 => CTR => C8: 4 * INC # C8: 4 => UNS * INC # E8: 2,8 => UNS * DIS # E8: 5 => CTR => E8: 2,8 * INC # A2: 2,8 => UNS * DIS # A4: 2,8 => CTR => A4: 3,6,9 * INC # A4: 3,6,9 => UNS * INC # A5: 2,8 => UNS * DIS # A6: 2,8 => CTR => A6: 3,9 * INC # A6: 3,9 => UNS * INC # B7: 8,9 => UNS * DIS # B7: 2,4 => CTR => B7: 8,9 * DIS # E7: 2,6 => CTR => E7: 5,8 * INC # E7: 5,8 => UNS * INC # D3: 2,6 => UNS * PRF # D3: 9 => SOL * DIS # E7: 2,8 => CTR => E7: 5,6 * INC # E7: 5,6 => UNS * INC # E8: 2,8 => UNS * INC # B7: 2,8 => UNS * INC # B7: 4,9 => UNS * PRF # G7: 4,8 => SOL * INC # G7: 5,9 => UNS * DIS # G8: 4,8 => CTR => G8: 1,5 * INC # G8: 1,5 => UNS * DIS # B7: 4,8 => CTR => B7: 2,9 * INC # B7: 2,9 => UNS * INC # G8: 1,5 => UNS * DIS # G8: 4,8 => CTR => G8: 1,5 * INC # G7: 8,9 => UNS * DIS # G7: 4,5 => CTR => G7: 8,9 * CNT 89 HDP CHAINS / 89 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C1: 2,9 => UNS * DIS # C1: 6 => CTR => C1: 2,9 * INC C1: 2,9 # D3: 2,9 => UNS * DIS C1: 2,9 # E3: 2,9 => CTR => E3: 6 * INC C1: 2,9 + E3: 6 # B7: 2,9 => UNS * DIS C1: 2,9 + E3: 6 # B7: 4,8 => CTR => B7: 2,9 * PRF C1: 2,9 + E3: 6 + B7: 2,9 # E5: 2,9 => SOL * STA C1: 2,9 + E3: 6 + B7: 2,9 + E5: 2,9 * CNT 7 HDP CHAINS / 7 HYP OPENED