Analysis of zz-www.sudokuoftheday.co.uk-20060406-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006
level: medium
position: .7.4.....9...28.1.....5.47..98......3156.4...74.....................23575....98.2 initial
Autosolve
position: .7.4....5954728613....5.47..98......3156.4...74..................9..23575....98.2 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # H1: 8 => CTR => H1: 2,9 * DIS # G5: 2,9 => CTR => G5: 7 * DIS # H1: 2 => CTR => H1: 8,9 * PRF # A7: 2,6 => SOL * DIS # C7: 2,6 => CTR => C7: 3,7 * DIS # H5: 8,9 => CTR => H5: 2 * DIS # E5: 7 => CTR => E5: 8,9 * DIS # I4: 1,6 => CTR => I4: 4 * DIS # I7: 4 => CTR => I7: 1,6 * DIS # A7: 6,8 => CTR => A7: 2,4 * DIS # B7: 6,8 => CTR => B7: 2,3 * DIS # A8: 6,8 => CTR => A8: 1,4 * PRF # E8: 6,8 => SOL * DIS # E8: 1,4 => CTR => E8: 6,8 * DIS # B3: 6,8 => CTR => B3: 2,3 * PRF # B7: 3,6 => SOL * DIS # C7: 3,6 => CTR => C7: 2,7 * DIS # C9: 3,6 => CTR => C9: 1,7 * DIS # E9: 3,6 => CTR => E9: 1,4,7 * DIS # B3: 3,6 => CTR => B3: 2,8 * DIS # E8: 1,8 => CTR => E8: 4,6 * DIS # A8: 1,8 => CTR => A8: 4,6 * PRF # A8: 4,6 => SOL * DIS # D6: 1,8 => CTR => D6: 2,3,5,9 * DIS # E9: 1,3 => CTR => E9: 4,6,7 * PRF # C9: 1,3 => SOL * DIS # C9: 6,7 => CTR => C9: 1,3 * DIS # D3: 1,3 => CTR => D3: 9 * DIS # D4: 1,3 => CTR => D4: 2,5 * DIS # D6: 1,3 => CTR => D6: 2,5,8,9 * DIS # E9: 4,6 => CTR => E9: 1,3,7 * PRF # E9: 1,3,7 => SOL * CNT 32 HDP CHAINS / 65 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # H1: 8 => CTR => H1: 2,9 * DIS H1: 2,9 # A3: 2,6 => CTR => A3: 1 * PRF H1: 2,9 + A3: 1 => SOL * STA H1: 2,9 + A3: 1 * CNT 3 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .7.4.....9...28.1.....5.47..98......3156.4...74.....................23575....98.2 | initial |
| .7.4....5954728613....5.47..98......3156.4...74..................9..23575....98.2 | autosolve |
| 876431295954728613123956478698217534315684729742593186237845961489162357561379842 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (12) G1: 2,9 I3: 8,9 A4: 2,6 C6: 2,6 I5: 8,9 I6: 1,6 B8: 6,8 B9: 3,6 D8: 1,8 D9: 1,3 G7: 1,9 H9: 4,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A8,C9: 1.. / A8 = 1 => 0 pairs (X) / C9 = 1 => 0 pairs (_) G7,I7: 1.. / G7 = 1 => 18 pairs (_) / I7 = 1 => 15 pairs (_) G1,H1: 2.. / G1 = 2 => 13 pairs (_) / H1 = 2 => 0 pairs (X) A4,C6: 2.. / A4 = 2 => 0 pairs (X) / C6 = 2 => 13 pairs (_) D4,D6: 2.. / D4 = 2 => 13 pairs (_) / D6 = 2 => 0 pairs (X) G5,H5: 2.. / G5 = 2 => 0 pairs (X) / H5 = 2 => 13 pairs (_) A4,D4: 2.. / A4 = 2 => 0 pairs (X) / D4 = 2 => 13 pairs (_) C6,D6: 2.. / C6 = 2 => 13 pairs (_) / D6 = 2 => 0 pairs (X) B3,B7: 2.. / B3 = 2 => 16 pairs (_) / B7 = 2 => 12 pairs (_) G1,G5: 2.. / G1 = 2 => 13 pairs (_) / G5 = 2 => 0 pairs (X) H1,H5: 2.. / H1 = 2 => 0 pairs (X) / H5 = 2 => 13 pairs (_) H4,H6: 3.. / H4 = 3 => 13 pairs (_) / H6 = 3 => 19 pairs (_) H4,I4: 4.. / H4 = 4 => 0 pairs (X) / I4 = 4 => 14 pairs (_) A7,A8: 4.. / A7 = 4 => 0 pairs (X) / A8 = 4 => 0 pairs (_) A8,E8: 4.. / A8 = 4 => 0 pairs (*) / E8 = 4 => 0 pairs (X) E9,H9: 4.. / E9 = 4 => 0 pairs (X) / H9 = 4 => 14 pairs (_) I4,I7: 4.. / I4 = 4 => 14 pairs (_) / I7 = 4 => 0 pairs (X) G4,G6: 5.. / G4 = 5 => 14 pairs (_) / G6 = 5 => 16 pairs (_) D7,F7: 5.. / D7 = 5 => 12 pairs (_) / F7 = 5 => 14 pairs (_) A4,C6: 6.. / A4 = 6 => 13 pairs (_) / C6 = 6 => 0 pairs (X) G4,G5: 7.. / G4 = 7 => 0 pairs (X) / G5 = 7 => 14 pairs (_) C7,C9: 7.. / C7 = 7 => 0 pairs (*) / C9 = 7 => 0 pairs (X) E5,G5: 7.. / E5 = 7 => 0 pairs (X) / G5 = 7 => 14 pairs (_) C9,E9: 7.. / C9 = 7 => 0 pairs (X) / E9 = 7 => 0 pairs (_) F4,F7: 7.. / F4 = 7 => 15 pairs (_) / F7 = 7 => 0 pairs (X) H1,I3: 8.. / H1 = 8 => 0 pairs (X) / I3 = 8 => 15 pairs (_) A1,H1: 8.. / A1 = 8 => 15 pairs (_) / H1 = 8 => 0 pairs (X) I3,I5: 8.. / I3 = 8 => 15 pairs (_) / I5 = 8 => 0 pairs (X) E1,D3: 9.. / E1 = 9 => 0 pairs (X) / D3 = 9 => 15 pairs (_) G7,H7: 9.. / G7 = 9 => 15 pairs (_) / H7 = 9 => 18 pairs (_) D3,I3: 9.. / D3 = 9 => 15 pairs (_) / I3 = 9 => 0 pairs (X) D3,D6: 9.. / D3 = 9 => 15 pairs (_) / D6 = 9 => 0 pairs (X) I3,I5: 9.. / I3 = 9 => 0 pairs (X) / I5 = 9 => 15 pairs (_) * DURATION: 0:00:38.170273 START: 22:11:18.055955 END: 22:11:56.226228 2019-04-30 * CP COUNT: (33) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B8,B9,C6,D8,D9,G1,G7,H9,I3,I5,I6) * .7.4....5954728613....5.47..98......3156.4...74..................9..23575....98.2 * PAIR G1: 2,9 BLK 3 H1: 2,9,8 # reduction candidate for 2,9 H1: 8 => CTR * .7.49.285954728613....5.4796982..7..31567492874298.5.....5.719.1.98.23575.7..98.2 H1: 2,9 # 15 pairs * PAIR G1: 2,9 COL G G5: 2,9,7 # reduction candidate for 2,9 G5: 2,9 => CTR * .7.4....5954728613....5.47..98..57.4315674...74..8.5.14825371961698423575371.9842 G5: 7 # 14 pairs * PAIR I3: 8,9 BLK 3 H1: 8,9,2 # reduction candidate for 8,9 H1: 2 => CTR * 87.4..925954728613...95.478.98..57..31567428974.89.5.....5.719.1.9..23575.7..98.2 H1: 8,9 # 13 pairs * PAIR A4: 2,6 COL A A3: 2,6,1,8 # reduction candidate for 2,6 A3: 2,6 # 15 pairs A7: 2,6,4,8 # reduction candidate for 2,6 A7: 2,6 => SOLVED * 876431295954728613123956478698217534315684729742593186237845961489162357561379842 A7: 4,8 # 13 pairs * PAIR C6: 2,6 COL C C3: 2,6,1,3 # reduction candidate for 2,6 C3: 2,6 # 15 pairs C7: 2,6,3,7 # reduction candidate for 2,6 C7: 2,6 => CTR * .7.4....5954728613.2.95.478298....643156.4.897462...31482...196169842357537169842 C7: 3,7 # 13 pairs * PAIR I5: 8,9 BLK 6 H5: 8,9,2 # reduction candidate for 8,9 H5: 8,9 => CTR * 87.4..925954728613...95.478.98..57..31567428974.89.5.....5.719.1.9..23575.7..98.2 H5: 2 # 13 pairs H6: 8,9,3,6 # reduction candidate for 8,9 H6: 8,9 # 15 pairs * PAIR I5: 8,9 ROW 5 E5: 8,9,7 # reduction candidate for 8,9 E5: 7 => CTR * .7.4....5954728613....5.47..98..57.4315674...74..8.5.14825371961698423575371.9842 E5: 8,9 # 14 pairs * PAIR I6: 1,6 BLK 6 I4: 1,6,4 # reduction candidate for 1,6 I4: 1,6 => CTR * .7.4....5954728613....5.47..98....4.3156.4...74.....3.........44.9..23575.13.98.2 I4: 4 # 14 pairs * PAIR I6: 1,6 COL I I7: 1,6,4 # reduction candidate for 1,6 I7: 4 => CTR * .7.4....5954728613....5.47..98......3156.4...74.............1944.9..23575.13.98.2 I7: 1,6 # 14 pairs * PAIR B8: 6,8 BLK 7 A7: 6,8,2,4 # reduction candidate for 6,8 A7: 6,8 => CTR * .7.4....5954728613....5.47..98..7..43156.472.74.........7.4....4.9..23575.1379842 A7: 2,4 # 13 pairs B7: 6,8,2,3 # reduction candidate for 6,8 B7: 6,8 => CTR * .7.4....5954728613.2.95.478298....643156.4.897462...31482...196169842357537169842 B7: 2,3 # 13 pairs A8: 6,8,1,4 # reduction candidate for 6,8 A8: 6,8 => CTR * .7.4....5954728613....5.47..98..7..43156.472.74.......4.7........9142357561379842 A8: 1,4 # 13 pairs * PAIR B8: 6,8 ROW 8 E8: 6,8,1,4 # reduction candidate for 6,8 E8: 6,8 => SOLVED * 876431295954728613123956478698217534315684729742593186237845961489162357561379842 E8: 1,4 => CTR * .7.4....5954728613.2.95.478298....643156.4.897462...31482...196169842357537169842 * PAIR B8: 6,8 COL B B3: 6,8,2,3 # reduction candidate for 6,8 B3: 6,8 => CTR * .7.4....5954728613....5.47..98......3156.4...74........2.......1.984235753.1.9842 B3: 2,3 # 15 pairs * PAIR B9: 3,6 BLK 7 B7: 3,6,2,8 # reduction candidate for 3,6 B7: 3,6 => SOLVED * 876431295954728613123956478698217534315684729742593186237845961489162357561379842 B7: 2,8 # 13 pairs C7: 3,6,2,7 # reduction candidate for 3,6 C7: 3,6 => CTR * .7.4....5954728613....5.47..98.....43156.4...74.......4........1.98423575.7..9842 C7: 2,7 # 13 pairs C9: 3,6,1,7 # reduction candidate for 3,6 C9: 3,6 => CTR * .7.4....5954728613....5.47..98..7..43156.472.74.......4.7......1.98423575...79842 C9: 1,7 # 13 pairs * PAIR B9: 3,6 ROW 9 E9: 3,6,1,4,7 # reduction candidate for 3,6 E9: 3,6 => CTR * .7.4....5954728613.2.95.478298....643156.4.897462...31482...196169842357537169842 E9: 1,4,7 # 12 pairs * PAIR B9: 3,6 COL B B3: 3,6,2,8 # reduction candidate for 3,6 B3: 3,6 => CTR * .7.4....5954728613....5.47..98......3156.4...74........2........891.23575.1379842 B3: 2,8 # 15 pairs * PAIR D8: 1,8 BLK 8 E8: 1,8,4,6 # reduction candidate for 1,8 E8: 1,8 => CTR * .7.4....5954728613....5.47..98......3156.4...74................469..2357531..98.2 E8: 4,6 # 13 pairs * PAIR D8: 1,8 ROW 8 A8: 1,8,4,6 # reduction candidate for 1,8 A8: 1,8 => CTR * .7.4....5954728613.2.95.478298....643156.4.897462...31482...196169842357537169842 A8: 4,6 => SOLVED * 876431295954728613123956478698217534315684729742593186237845961489162357561379842 * PAIR D8: 1,8 COL D D6: 1,8,2,3,5,9 # reduction candidate for 1,8 D6: 1,8 => CTR * 87.4....5954728613...95.4786982...343156.4..9742.935.....5......89162357561379842 D6: 2,3,5,9 # 12 pairs * PAIR D9: 1,3 BLK 8 E9: 1,3,4,6,7 # reduction candidate for 1,3 E9: 1,3 => CTR * .7.4....5954728613....5.47..98.....43156.4...74................1.9842357567..9842 E9: 4,6,7 # 12 pairs * PAIR D9: 1,3 ROW 9 C9: 1,3,6,7 # reduction candidate for 1,3 C9: 1,3 => SOLVED * 876431295954728613123956478698217534315684729742593186237845961489162357561379842 C9: 6,7 => CTR * .7.4....5954728613.2.95.478298....643156.4.897462...31482...196169842357537169842 * PAIR D9: 1,3 COL D D3: 1,3,9 # reduction candidate for 1,3 D3: 1,3 => CTR * .7.49.285954728613....5.4796982..7..31567492874298.5.....5.719.1.98.23575.7..98.2 D3: 9 # 15 pairs D4: 1,3,2,5 # reduction candidate for 1,3 D4: 1,3 => CTR * .7.4....5954728613...95.478298......3156.4..974629.581.825..19..698.23575371.98.2 D4: 2,5 # 13 pairs D6: 1,3,2,5,8,9 # reduction candidate for 1,3 D6: 1,3 => CTR * 87.4....5954728613...95.4786982...34315684729742.9..86.8.5....1.698.235753.1.98.2 D6: 2,5,8,9 # 12 pairs * PAIR G7: 1,9 COL G G6: 1,9,5 # reduction candidate for 1,9 G6: 5 # 16 pairs G6: 1,9 # 14 pairs * PAIR H9: 4,6 BLK 9 H7: 4,6,9 # reduction candidate for 4,6 H7: 4,6 # 15 pairs I7: 4,6,1 # reduction candidate for 4,6 I7: 4,6 # 18 pairs * PAIR H9: 4,6 ROW 9 E9: 4,6,1,3,7 # reduction candidate for 4,6 E9: 4,6 => CTR * .7.4....5954728613.2.95.478298....643156.4.897462...31482...196169842357537169842 E9: 1,3,7 => SOLVED * 876431295954728613123956478698217534315684729742593186237845961489162357561379842 * PAIR H9: 4,6 COL H H4: 4,6,3 # reduction candidate for 4,6 H4: 4,6 # 19 pairs H4: 3 # 13 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060406-absurd-base-pr-000.dot * REASONING * DIS # H1: 8 => CTR => H1: 2,9 * DIS # G5: 2,9 => CTR => G5: 7 * DIS # H1: 2 => CTR => H1: 8,9 * PRF # A7: 2,6 => SOL * DIS # C7: 2,6 => CTR => C7: 3,7 * DIS # H5: 8,9 => CTR => H5: 2 * DIS # E5: 7 => CTR => E5: 8,9 * DIS # I4: 1,6 => CTR => I4: 4 * DIS # I7: 4 => CTR => I7: 1,6 * DIS # A7: 6,8 => CTR => A7: 2,4 * DIS # B7: 6,8 => CTR => B7: 2,3 * DIS # A8: 6,8 => CTR => A8: 1,4 * PRF # E8: 6,8 => SOL * DIS # E8: 1,4 => CTR => E8: 6,8 * DIS # B3: 6,8 => CTR => B3: 2,3 * PRF # B7: 3,6 => SOL * DIS # C7: 3,6 => CTR => C7: 2,7 * DIS # C9: 3,6 => CTR => C9: 1,7 * DIS # E9: 3,6 => CTR => E9: 1,4,7 * DIS # B3: 3,6 => CTR => B3: 2,8 * DIS # E8: 1,8 => CTR => E8: 4,6 * DIS # A8: 1,8 => CTR => A8: 4,6 * PRF # A8: 4,6 => SOL * DIS # D6: 1,8 => CTR => D6: 2,3,5,9 * DIS # E9: 1,3 => CTR => E9: 4,6,7 * PRF # C9: 1,3 => SOL * DIS # C9: 6,7 => CTR => C9: 1,3 * DIS # D3: 1,3 => CTR => D3: 9 * DIS # D4: 1,3 => CTR => D4: 2,5 * DIS # D6: 1,3 => CTR => D6: 2,5,8,9 * DIS # E9: 4,6 => CTR => E9: 1,3,7 * PRF # E9: 1,3,7 => SOL * CNT 32 HDP CHAINS / 65 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B8,B9,C6,D8,D9,G1,G7,H9,I3,I5,I6) * .7.4....5954728613....5.47..98......3156.4...74..................9..23575....98.2 * PAIR G1: 2,9 BLK 3 H1: 2,9,8 # reduction candidate for 2,9 H1: 8 => CTR * .7.49.285954728613....5.4796982..7..31567492874298.5.....5.719.1.98.23575.7..98.2 * PAIR A4: 2,6 COL A A3: 2,6,1 # reduction candidate for 2,6 A3: 2,6 => CTR * 87.4..295954728613.2.95.478298.....431568472974..9..8.482......169842357537169842 A3: 1 => SOLVED * 876431295954728613123956478698217534315684729742593186237845961489162357561379842 * DURATION: 0:00:02.886003 START: 22:12:37.663399 END: 22:12:40.549402 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060406-absurd-base-pr-001.dot * REASONING * DIS # H1: 8 => CTR => H1: 2,9 * DIS H1: 2,9 # A3: 2,6 => CTR => A3: 1 * PRF H1: 2,9 + A3: 1 => SOL * STA H1: 2,9 + A3: 1 * CNT 3 HDP CHAINS / 3 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006, 20060406, absurd
Solution
position: 876431295954728613123956478698217534315684729742593186237845961489162357561379842 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 # H1: 2,9 => UNS * DIS # H1: 8 => CTR => H1: 2,9 * DIS # G5: 2,9 => CTR => G5: 7 * INC # G5: 7 => UNS * INC # H1: 8,9 => UNS * DIS # H1: 2 => CTR => H1: 8,9 * INC # A3: 2,6 => UNS * PRF # A7: 2,6 => SOL * INC # A7: 4,8 => UNS * INC # C3: 2,6 => UNS * DIS # C7: 2,6 => CTR => C7: 3,7 * INC # C7: 3,7 => UNS * DIS # H5: 8,9 => CTR => H5: 2 * INC # H5: 2 => UNS * INC # H6: 8,9 => UNS * INC # E5: 8,9 => UNS * DIS # E5: 7 => CTR => E5: 8,9 * DIS # I4: 1,6 => CTR => I4: 4 * INC # I4: 4 => UNS * INC # I7: 1,6 => UNS * DIS # I7: 4 => CTR => I7: 1,6 * DIS # A7: 6,8 => CTR => A7: 2,4 * INC # A7: 2,4 => UNS * DIS # B7: 6,8 => CTR => B7: 2,3 * INC # B7: 2,3 => UNS * DIS # A8: 6,8 => CTR => A8: 1,4 * INC # A8: 1,4 => UNS * PRF # E8: 6,8 => SOL * DIS # E8: 1,4 => CTR => E8: 6,8 * DIS # B3: 6,8 => CTR => B3: 2,3 * INC # B3: 2,3 => UNS * PRF # B7: 3,6 => SOL * INC # B7: 2,8 => UNS * DIS # C7: 3,6 => CTR => C7: 2,7 * INC # C7: 2,7 => UNS * DIS # C9: 3,6 => CTR => C9: 1,7 * INC # C9: 1,7 => UNS * DIS # E9: 3,6 => CTR => E9: 1,4,7 * INC # E9: 1,4,7 => UNS * DIS # B3: 3,6 => CTR => B3: 2,8 * INC # B3: 2,8 => UNS * DIS # E8: 1,8 => CTR => E8: 4,6 * INC # E8: 4,6 => UNS * DIS # A8: 1,8 => CTR => A8: 4,6 * PRF # A8: 4,6 => SOL * DIS # D6: 1,8 => CTR => D6: 2,3,5,9 * INC # D6: 2,3,5,9 => UNS * DIS # E9: 1,3 => CTR => E9: 4,6,7 * INC # E9: 4,6,7 => UNS * PRF # C9: 1,3 => SOL * DIS # C9: 6,7 => CTR => C9: 1,3 * DIS # D3: 1,3 => CTR => D3: 9 * INC # D3: 9 => UNS * DIS # D4: 1,3 => CTR => D4: 2,5 * INC # D4: 2,5 => UNS * DIS # D6: 1,3 => CTR => D6: 2,5,8,9 * INC # D6: 2,5,8,9 => UNS * INC # G6: 1,9 => UNS * INC # G6: 5 => UNS * INC # H7: 4,6 => UNS * INC # I7: 4,6 => UNS * DIS # E9: 4,6 => CTR => E9: 1,3,7 * PRF # E9: 1,3,7 => SOL * INC # H4: 4,6 => UNS * INC # H4: 3 => UNS * CNT 65 HDP CHAINS / 65 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # H1: 2,9 => UNS * DIS # H1: 8 => CTR => H1: 2,9 * DIS H1: 2,9 # A3: 2,6 => CTR => A3: 1 * PRF H1: 2,9 + A3: 1 => SOL * STA H1: 2,9 + A3: 1 * CNT 4 HDP CHAINS / 3 HYP OPENED