Analysis of zz-www.sudokuoftheday.co.uk-20060510-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006
level: medium
position: ...8...31...3.2...9..6..827.8..1..924........2....416.1.....7...32......7....9.8. initial
Autosolve
position: .2.8...31...3.2...9.36.182738..1.4924.....3752...341681....37...32....1.7..1.9283 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C1: 5,6 => CTR => C1: 4,7 * DIS # A2: 5,6 => CTR => A2: 8 * DIS # B2: 5,6 => CTR => B2: 1,7 * DIS # C2: 5,6 => CTR => C2: 1,7,8 * DIS # G1: 5,6 => CTR => G1: 9 * DIS # A8: 8 => CTR => A8: 5,6 * PRF # C1: 4,5 => SOL * DIS # C1: 6,7 => CTR => C1: 4,5 * DIS # B9: 6 => CTR => B9: 4,5 * PRF # E1: 5,7 => SOL * DIS # E2: 5,7 => CTR => E2: 9 * DIS # C1: 5,7 => CTR => C1: 4,6 * DIS # E1: 4,5 => CTR => E1: 7,9 * PRF # E1: 7,9 => SOL * DIS # D8: 5,7 => CTR => D8: 4 * PRF # E7: 5,6 => SOL * DIS # E8: 5,6 => CTR => E8: 7,8 * DIS # B9: 5,6 => CTR => B9: 4 * PRF # B9: 4 => SOL * PRF # C9: 5,6 => SOL * DIS # C9: 4 => CTR => C9: 5,6 * DIS # I8: 4,6 => CTR => I8: 9 * DIS # I2: 9 => CTR => I2: 4,6 * CNT 23 HDP CHAINS / 51 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C1: 5,6 => CTR => C1: 4,7 * DIS C1: 4,7 # A2: 5,6 => CTR => A2: 8 * DIS C1: 4,7 + A2: 8 # B2: 5,6 => CTR => B2: 1,7 * DIS C1: 4,7 + A2: 8 + B2: 1,7 # C2: 5,6 => CTR => C2: 1,7 * PRF C1: 4,7 + A2: 8 + B2: 1,7 + C2: 1,7 => SOL * STA C1: 4,7 + A2: 8 + B2: 1,7 + C2: 1,7 * CNT 5 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...8...31...3.2...9..6..827.8..1..924........2....416.1.....7...32......7....9.8. | initial |
| .2.8...31...3.2...9.36.182738..1.4924.....3752...341681....37...32....1.7..1.9283 | autosolve |
| 624875931817392546953641827385716492461928375279534168198263754532487619746159283 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (11) A1: 5,6 B3: 4,5 F1: 5,7 E3: 4,5 H2: 4,5 D4: 5,7 D5: 2,9 F5: 6,8 E9: 5,6 H7: 4,5 I7: 4,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B2,C2: 1.. / B2 = 1 => 16 pairs (_) / C2 = 1 => 15 pairs (_) B5,C5: 1.. / B5 = 1 => 15 pairs (_) / C5 = 1 => 16 pairs (_) B2,B5: 1.. / B2 = 1 => 16 pairs (_) / B5 = 1 => 15 pairs (_) C2,C5: 1.. / C2 = 1 => 15 pairs (_) / C5 = 1 => 16 pairs (_) D5,E5: 2.. / D5 = 2 => 20 pairs (_) / E5 = 2 => 15 pairs (_) D7,E7: 2.. / D7 = 2 => 15 pairs (_) / E7 = 2 => 20 pairs (_) D5,D7: 2.. / D5 = 2 => 20 pairs (_) / D7 = 2 => 15 pairs (_) E5,E7: 2.. / E5 = 2 => 15 pairs (_) / E7 = 2 => 20 pairs (_) C1,B3: 4.. / C1 = 4 => 0 pairs (*) / B3 = 4 => 0 pairs (X) E1,E3: 4.. / E1 = 4 => 0 pairs (X) / E3 = 4 => 0 pairs (_) H2,I2: 4.. / H2 = 4 => 13 pairs (_) / I2 = 4 => 0 pairs (X) B9,C9: 4.. / B9 = 4 => 0 pairs (*) / C9 = 4 => 0 pairs (X) D7,D8: 4.. / D7 = 4 => 0 pairs (X) / D8 = 4 => 14 pairs (_) C1,E1: 4.. / C1 = 4 => 0 pairs (*) / E1 = 4 => 0 pairs (X) B3,E3: 4.. / B3 = 4 => 0 pairs (X) / E3 = 4 => 0 pairs (_) D8,I8: 4.. / D8 = 4 => 14 pairs (_) / I8 = 4 => 0 pairs (X) B3,B9: 4.. / B3 = 4 => 0 pairs (X) / B9 = 4 => 0 pairs (_) C1,C9: 4.. / C1 = 4 => 0 pairs (*) / C9 = 4 => 0 pairs (X) H2,H7: 4.. / H2 = 4 => 13 pairs (_) / H7 = 4 => 0 pairs (X) H7,G8: 5.. / H7 = 5 => 13 pairs (_) / G8 = 5 => 0 pairs (X) B3,E3: 5.. / B3 = 5 => 0 pairs (*) / E3 = 5 => 0 pairs (X) H2,H7: 5.. / H2 = 5 => 0 pairs (X) / H7 = 5 => 13 pairs (_) C4,F4: 6.. / C4 = 6 => 20 pairs (_) / F4 = 6 => 15 pairs (_) B2,B6: 7.. / B2 = 7 => 0 pairs (X) / B6 = 7 => 15 pairs (_) A2,C2: 8.. / A2 = 8 => 14 pairs (_) / C2 = 8 => 0 pairs (X) E5,F5: 8.. / E5 = 8 => 17 pairs (_) / F5 = 8 => 11 pairs (_) C7,A8: 8.. / C7 = 8 => 14 pairs (_) / A8 = 8 => 0 pairs (X) C7,E7: 8.. / C7 = 8 => 14 pairs (_) / E7 = 8 => 0 pairs (X) A2,A8: 8.. / A2 = 8 => 14 pairs (_) / A8 = 8 => 0 pairs (X) C2,C7: 8.. / C2 = 8 => 0 pairs (X) / C7 = 8 => 14 pairs (_) F5,F8: 8.. / F5 = 8 => 11 pairs (_) / F8 = 8 => 17 pairs (_) E1,E2: 9.. / E1 = 9 => 0 pairs (X) / E2 = 9 => 24 pairs (_) D5,D6: 9.. / D5 = 9 => 15 pairs (_) / D6 = 9 => 20 pairs (_) B7,C7: 9.. / B7 = 9 => 13 pairs (_) / C7 = 9 => 0 pairs (X) G8,I8: 9.. / G8 = 9 => 0 pairs (X) / I8 = 9 => 15 pairs (_) E1,G1: 9.. / E1 = 9 => 0 pairs (X) / G1 = 9 => 24 pairs (_) I2,I8: 9.. / I2 = 9 => 0 pairs (X) / I8 = 9 => 15 pairs (_) * DURATION: 0:00:44.838188 START: 23:03:00.779982 END: 23:03:45.618170 2019-04-30 * CP COUNT: (37) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B3,D4,D5,E3,E9,F1,F5,H2,H7,I7) * .2.8...31...3.2...9.36.182738..1.4924.....3752...341681....37...32....1.7..1.9283 * PAIR A1: 5,6 BLK 1 C1: 5,6,4,7 # reduction candidate for 5,6 C1: 5,6 => CTR * 5268479318..392...94365182738..164924619283752...341681....37...3247..19754169283 C1: 4,7 # 12 pairs A2: 5,6,8 # reduction candidate for 5,6 A2: 5,6 => CTR * .278...31.18372...9.36.182738..1.4924.1.2837527..341681..2837..8324.7.1.7..1.9283 A2: 8 # 14 pairs B2: 5,6,1,7 # reduction candidate for 5,6 B2: 5,6 => CTR * .278...31..1372...9.36.182738..1.49241....37527..34168198..37...32....1.7..1.9283 B2: 1,7 # 12 pairs C2: 5,6,1,7,8 # reduction candidate for 5,6 C2: 5,6 => CTR * .278...3181.372...9.36.182738..1.4924.1...37527..341681.8..37...32....1.7..1.9283 C2: 1,7,8 # 11 pairs * PAIR A1: 5,6 ROW 1 G1: 5,6,9 # reduction candidate for 5,6 G1: 5,6 => CTR * .24897.31...352.4.95364182738..1.4924.....3752...341681....375.532.78.1.7461.9283 G1: 9 # 24 pairs * PAIR A1: 5,6 COL A A8: 5,6,8 # reduction candidate for 5,6 A8: 8 => CTR * .278...31.18372...9.36.182738..1.4924.1.2837527..341681..2837..8324.7.1.7..1.9283 A8: 5,6 # 14 pairs * PAIR B3: 4,5 BLK 1 C1: 4,5,6,7 # reduction candidate for 4,5 C1: 4,5 => SOLVED * 624875931817392546953641827385716492461928375279534168198263754532487619746159283 C1: 6,7 => CTR * 5268479318..392...94365182738..164924619283752...341681....37...32.7..197.4169283 * PAIR B3: 4,5 COL B B9: 4,5,6 # reduction candidate for 4,5 B9: 6 => CTR * .2.8...31...3.2...94365182738..1.4924.....3752...341681....37...32....1.76.1.9283 B9: 4,5 # 15 pairs * PAIR F1: 5,7 BLK 2 E1: 5,7,4,9 # reduction candidate for 5,7 E1: 5,7 => SOLVED * 624875931817392546953641827385716492461928375279534168198263754532487619746159283 E1: 4,9 # 12 pairs E2: 5,7,9 # reduction candidate for 5,7 E2: 5,7 => CTR * .24897.31...352.4.95364182738..1.4924.....3752...341681....375.532.78.1.7461.9283 E2: 9 # 24 pairs * PAIR F1: 5,7 ROW 1 C1: 5,7,4,6 # reduction candidate for 5,7 C1: 5,7 => CTR * 6258479318..392...94365182738..1.4924.....37525..341681....37...32.7..197.4169283 C1: 4,6 # 19 pairs * PAIR F1: 5,7 COL F F4: 5,7,6 # reduction candidate for 5,7 F4: 5,7 # 20 pairs F8: 5,7,6,8 # reduction candidate for 5,7 F8: 5,7 # 15 pairs * PAIR E3: 4,5 BLK 2 E1: 4,5,7,9 # reduction candidate for 4,5 E1: 4,5 => CTR * .2.8.79318..392...9.36.182738..154924...863752...341681.8..37...32478.197..169283 E1: 7,9 => SOLVED * 624875931817392546953641827385716492461928375279534168198263754532487619746159283 * PAIR D4: 5,7 BLK 5 F4: 5,7,6 # reduction candidate for 5,7 F4: 5,7 # 20 pairs D6: 5,7,9 # reduction candidate for 5,7 D6: 5,7 # 15 pairs * PAIR D4: 5,7 ROW 4 C4: 5,7,6 # reduction candidate for 5,7 C4: 6 # 20 pairs C4: 5,7 # 15 pairs * PAIR D4: 5,7 COL D D8: 5,7,4 # reduction candidate for 5,7 D8: 5,7 => CTR * .24897.318..35264995364182738.71549246.2..3752..934168198423756.32...91474.1.9283 D8: 4 # 14 pairs * PAIR F5: 6,8 BLK 5 E5: 6,8,2 # reduction candidate for 6,8 E5: 6,8 # 20 pairs E5: 2 # 15 pairs * PAIR F5: 6,8 COL F F8: 6,8,5,7 # reduction candidate for 6,8 F8: 6,8 # 20 pairs F8: 5,7 # 15 pairs * PAIR E9: 5,6 BLK 8 E7: 5,6,2,8 # reduction candidate for 5,6 E7: 5,6 => SOLVED * 624875931817392546953641827385716492461928375279534168198263754532487619746159283 E7: 2,8 # 12 pairs E8: 5,6,7,8 # reduction candidate for 5,6 E8: 5,6 => CTR * .2.8.5.31...3.2...95364182738..1.4924.....3752...341681....37..532.68914746159283 E8: 7,8 # 12 pairs F8: 5,6,7,8 # reduction candidate for 5,6 F8: 5,6 # 17 pairs * PAIR E9: 5,6 ROW 9 B9: 5,6,4 # reduction candidate for 5,6 B9: 5,6 => CTR * 5268479318..392...94365182738..164924619283752...341681....37...3247..19754169283 B9: 4 => SOLVED * 624875931817392546953641827385716492461928375279534168198263754532487619746159283 C9: 5,6,4 # reduction candidate for 5,6 C9: 5,6 => SOLVED * 624875931817392546953641827385716492461928375279534168198263754532487619746159283 C9: 4 => CTR * 5268479318..392...94365182738..164924619283752...341681....37...3247..19754169283 * PAIR H7: 4,5 ROW 7 D7: 4,5,2 # reduction candidate for 4,5 D7: 4,5 # 20 pairs D7: 2 # 15 pairs * PAIR I7: 4,6 BLK 9 I8: 4,6,9 # reduction candidate for 4,6 I8: 4,6 => CTR * .24897.31...35264995364182738..1.4924.....3752...341681....375.532.789167461.9283 I8: 9 # 15 pairs * PAIR I7: 4,6 COL I I2: 4,6,9 # reduction candidate for 4,6 I2: 9 => CTR * .24897.31...35264995364182738..1.4924.....3752...341681....375.532.789167461.9283 I2: 4,6 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060510-absurd-base-pr-000.dot * REASONING * DIS # C1: 5,6 => CTR => C1: 4,7 * DIS # A2: 5,6 => CTR => A2: 8 * DIS # B2: 5,6 => CTR => B2: 1,7 * DIS # C2: 5,6 => CTR => C2: 1,7,8 * DIS # G1: 5,6 => CTR => G1: 9 * DIS # A8: 8 => CTR => A8: 5,6 * PRF # C1: 4,5 => SOL * DIS # C1: 6,7 => CTR => C1: 4,5 * DIS # B9: 6 => CTR => B9: 4,5 * PRF # E1: 5,7 => SOL * DIS # E2: 5,7 => CTR => E2: 9 * DIS # C1: 5,7 => CTR => C1: 4,6 * DIS # E1: 4,5 => CTR => E1: 7,9 * PRF # E1: 7,9 => SOL * DIS # D8: 5,7 => CTR => D8: 4 * PRF # E7: 5,6 => SOL * DIS # E8: 5,6 => CTR => E8: 7,8 * DIS # B9: 5,6 => CTR => B9: 4 * PRF # B9: 4 => SOL * PRF # C9: 5,6 => SOL * DIS # C9: 4 => CTR => C9: 5,6 * DIS # I8: 4,6 => CTR => I8: 9 * DIS # I2: 9 => CTR => I2: 4,6 * CNT 23 HDP CHAINS / 51 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B3,D4,D5,E3,E9,F1,F5,H2,H7,I7) * .2.8...31...3.2...9.36.182738..1.4924.....3752...341681....37...32....1.7..1.9283 * PAIR A1: 5,6 BLK 1 C1: 5,6,4,7 # reduction candidate for 5,6 C1: 5,6 => CTR * 5268479318..392...94365182738..164924619283752...341681....37...3247..19754169283 A2: 5,6,8 # reduction candidate for 5,6 A2: 5,6 => CTR * .278...31.18372...9.36.182738..1.4924.1.2837527..341681..2837..8324.7.1.7..1.9283 B2: 5,6,1,7 # reduction candidate for 5,6 B2: 5,6 => CTR * .278...318.1372...9.36.182738..1.49241....37527..34168198..37...32....1.7..1.9283 C2: 5,6,1,7 # reduction candidate for 5,6 C2: 5,6 => CTR * .278...3181.372...9.36.182738..1.4924619283752795341681982.37...32487.1.7..1.9283 C2: 1,7 => SOLVED * 624875931817392546953641827385716492461928375279534168198263754532487619746159283 * DURATION: 0:00:03.581312 START: 23:04:20.225367 END: 23:04:23.806679 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060510-absurd-base-pr-001.dot * REASONING * DIS # C1: 5,6 => CTR => C1: 4,7 * DIS C1: 4,7 # A2: 5,6 => CTR => A2: 8 * DIS C1: 4,7 + A2: 8 # B2: 5,6 => CTR => B2: 1,7 * DIS C1: 4,7 + A2: 8 + B2: 1,7 # C2: 5,6 => CTR => C2: 1,7 * PRF C1: 4,7 + A2: 8 + B2: 1,7 + C2: 1,7 => SOL * STA C1: 4,7 + A2: 8 + B2: 1,7 + C2: 1,7 * CNT 5 HDP CHAINS / 4 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006, 20060510, absurd
Solution
position: 624875931817392546953641827385716492461928375279534168198263754532487619746159283 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 # C1: 5,6 => CTR => C1: 4,7 * INC # C1: 4,7 => UNS * DIS # A2: 5,6 => CTR => A2: 8 * INC # A2: 8 => UNS * DIS # B2: 5,6 => CTR => B2: 1,7 * INC # B2: 1,7 => UNS * DIS # C2: 5,6 => CTR => C2: 1,7,8 * INC # C2: 1,7,8 => UNS * DIS # G1: 5,6 => CTR => G1: 9 * INC # G1: 9 => UNS * INC # A8: 5,6 => UNS * DIS # A8: 8 => CTR => A8: 5,6 * PRF # C1: 4,5 => SOL * DIS # C1: 6,7 => CTR => C1: 4,5 * INC # B9: 4,5 => UNS * DIS # B9: 6 => CTR => B9: 4,5 * PRF # E1: 5,7 => SOL * INC # E1: 4,9 => UNS * DIS # E2: 5,7 => CTR => E2: 9 * INC # E2: 9 => UNS * DIS # C1: 5,7 => CTR => C1: 4,6 * INC # C1: 4,6 => UNS * INC # F4: 5,7 => UNS * INC # F8: 5,7 => UNS * DIS # E1: 4,5 => CTR => E1: 7,9 * PRF # E1: 7,9 => SOL * INC # F4: 5,7 => UNS * INC # D6: 5,7 => UNS * INC # C4: 5,7 => UNS * INC # C4: 6 => UNS * DIS # D8: 5,7 => CTR => D8: 4 * INC # D8: 4 => UNS * INC # E5: 6,8 => UNS * INC # E5: 2 => UNS * INC # F8: 6,8 => UNS * INC # F8: 5,7 => UNS * PRF # E7: 5,6 => SOL * INC # E7: 2,8 => UNS * DIS # E8: 5,6 => CTR => E8: 7,8 * INC # E8: 7,8 => UNS * INC # F8: 5,6 => UNS * DIS # B9: 5,6 => CTR => B9: 4 * PRF # B9: 4 => SOL * PRF # C9: 5,6 => SOL * DIS # C9: 4 => CTR => C9: 5,6 * INC # D7: 4,5 => UNS * INC # D7: 2 => UNS * DIS # I8: 4,6 => CTR => I8: 9 * INC # I8: 9 => UNS * INC # I2: 4,6 => UNS * DIS # I2: 9 => CTR => I2: 4,6 * CNT 51 HDP CHAINS / 51 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # C1: 5,6 => CTR => C1: 4,7 * DIS C1: 4,7 # A2: 5,6 => CTR => A2: 8 * DIS C1: 4,7 + A2: 8 # B2: 5,6 => CTR => B2: 1,7 * DIS C1: 4,7 + A2: 8 + B2: 1,7 # C2: 5,6 => CTR => C2: 1,7 * PRF C1: 4,7 + A2: 8 + B2: 1,7 + C2: 1,7 => SOL * STA C1: 4,7 + A2: 8 + B2: 1,7 + C2: 1,7 * CNT 5 HDP CHAINS / 4 HYP OPENED