Analysis of xx-top500-040-base.sdk
Contents
Original Sudoku
level: medium
position: 64...23.....5........1.....1.57.........3.2..8...............17.3..4...........5. initial
Autosolve
position: 641.723.5...5..1...5.1..7..1.572..34....352.182341.57....35..17537.41....1.2.7.53 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D8: 8,9 => CTR => D8: 6 * DIS # H2: 8,9 => CTR => H2: 2,4,6 * PRF # H3: 8,9 => SOL * DIS # H8: 8,9 => CTR => H8: 2,6 * PRF # F4: 6,9 => SOL * PRF # F4: 6,9 => SOL * PRF # F7: 8 => SOL * PRF # H5: 6,9 => SOL * DIS # C9: 4,9 => CTR => C9: 6,8 * DIS # D8: 8,9 => CTR => D8: 6 * DIS # G9: 8,9 => CTR => G9: 4,6 * CNT 11 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:
* DIS # D8: 8,9 => CTR => D8: 6 * DIS D8: 6 # H2: 8,9 => CTR => H2: 2,4,6 * PRF D8: 6 + H2: 2,4,6 # H3: 8,9 => SOL * STA D8: 6 + H2: 2,4,6 + H3: 8,9 * CNT 3 HDP CHAINS / 9 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 64...23.....5........1.....1.57.........3.2..8...............17.3..4...........5. | initial |
| 641.723.5...5..1...5.1..7..1.572..34....352.182341.57....35..17537.41....1.2.7.53 | autosolve |
| 641972385789563142352184796165729834974835261823416579296358417537641928418297653 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) D1: 8,9 F2: 3,4 F3: 3,4 H1: 8,9 B4: 6,9 F6: 6,9 I6: 6,9 A9: 4,9 E9: 8,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A7,C7: 2.. / A7 = 2 => 10 pairs (_) / C7 = 2 => 20 pairs (_) H8,I8: 2.. / H8 = 2 => 9 pairs (_) / I8 = 2 => 0 pairs (X) A2,A3: 3.. / A2 = 3 => 15 pairs (_) / A3 = 3 => 7 pairs (_) F2,F3: 3.. / F2 = 3 => 7 pairs (_) / F3 = 3 => 15 pairs (_) A2,F2: 3.. / A2 = 3 => 15 pairs (_) / F2 = 3 => 7 pairs (_) A3,F3: 3.. / A3 = 3 => 7 pairs (_) / F3 = 3 => 15 pairs (_) F2,F3: 4.. / F2 = 4 => 15 pairs (_) / F3 = 4 => 7 pairs (_) H2,H3: 4.. / H2 = 4 => 7 pairs (_) / H3 = 4 => 15 pairs (_) A5,C5: 4.. / A5 = 4 => 16 pairs (_) / C5 = 4 => 11 pairs (_) G7,G9: 4.. / G7 = 4 => 10 pairs (_) / G9 = 4 => 19 pairs (_) F2,H2: 4.. / F2 = 4 => 15 pairs (_) / H2 = 4 => 7 pairs (_) F3,H3: 4.. / F3 = 4 => 7 pairs (_) / H3 = 4 => 15 pairs (_) E2,E3: 6.. / E2 = 6 => 10 pairs (_) / E3 = 6 => 10 pairs (_) F7,D8: 6.. / F7 = 6 => 0 pairs (X) / D8 = 6 => 15 pairs (_) F6,I6: 6.. / F6 = 6 => 0 pairs (*) / I6 = 6 => 0 pairs (X) C9,G9: 6.. / C9 = 6 => 16 pairs (_) / G9 = 6 => 14 pairs (_) D5,D8: 6.. / D5 = 6 => 0 pairs (X) / D8 = 6 => 15 pairs (_) A2,B2: 7.. / A2 = 7 => 9 pairs (_) / B2 = 7 => 15 pairs (_) A5,B5: 7.. / A5 = 7 => 15 pairs (_) / B5 = 7 => 9 pairs (_) A2,A5: 7.. / A2 = 7 => 9 pairs (_) / A5 = 7 => 15 pairs (_) B2,B5: 7.. / B2 = 7 => 15 pairs (_) / B5 = 7 => 9 pairs (_) F4,D5: 8.. / F4 = 8 => 13 pairs (_) / D5 = 8 => 0 pairs (*) G4,H5: 8.. / G4 = 8 => 0 pairs (*) / H5 = 8 => 0 pairs (X) D1,H1: 8.. / D1 = 8 => 13 pairs (_) / H1 = 8 => 0 pairs (*) F4,G4: 8.. / F4 = 8 => 13 pairs (_) / G4 = 8 => 0 pairs (*) D5,H5: 8.. / D5 = 8 => 0 pairs (*) / H5 = 8 => 0 pairs (X) B2,B7: 8.. / B2 = 8 => 13 pairs (_) / B7 = 8 => 15 pairs (_) F4,F7: 8.. / F4 = 8 => 13 pairs (_) / F7 = 8 => 0 pairs (*) D1,H1: 9.. / D1 = 9 => 0 pairs (*) / H1 = 9 => 0 pairs (X) F6,I6: 9.. / F6 = 9 => 15 pairs (_) / I6 = 9 => 0 pairs (*) * DURATION: 0:00:54.520662 START: 04:02:05.217925 END: 04:02:59.738587 2017-05-04 * CP COUNT: (30) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B4,D1,E9,F2,F3,F6,H1,I6) * 641.723.5...5..1...5.1..7..1.572..34....352.182341.57....35..17537.41....1.2.7.53 * PAIR D1: 8,9 BLK 2 E2: 8,9,6 # reduction candidate for 8,9 E2: 8,9 # 10 pairs E3: 8,9,6 # reduction candidate for 8,9 E3: 8,9 # 10 pairs * PAIR D1: 8,9 COL D D5: 8,9,6 # reduction candidate for 8,9 D5: 8,9 # 15 pairs D8: 8,9,6 # reduction candidate for 8,9 D8: 8,9 => CTR * 641872395...5..1...5.1..7..165728934...635281823419576...356.17537941628916287453 D8: 6 # 15 pairs * PAIR H1: 8,9 BLK 3 H2: 8,9,2,4,6 # reduction candidate for 8,9 H2: 8,9 => CTR * 641.723.537.5.41...5.1.374.1.572..347.4.35261823416579.8.359.17537641.2..1.2.7.53 H2: 2,4,6 # 9 pairs I2: 8,9,2,6 # reduction candidate for 8,9 I2: 8,9 # 11 pairs H3: 8,9,2,4,6 # reduction candidate for 8,9 H3: 8,9 => SOLVED * 641972385789563142352184796165729834974835261823416579296358417537641928418297653 H3: 2,4,6 # 9 pairs I3: 8,9,2,6 # reduction candidate for 8,9 I3: 8,9 # 11 pairs * PAIR H1: 8,9 COL H H5: 8,9,6 # reduction candidate for 8,9 H5: 8,9 # 11 pairs H8: 8,9,2,6 # reduction candidate for 8,9 H8: 8,9 => CTR * 641872395...5..1...5.1..7..1.5728934....3528182341.57....35..17537.41..2.1.2.7.53 H8: 2,6 # 10 pairs * PAIR B4: 6,9 BLK 4 B5: 6,9,7 # reduction candidate for 6,9 B5: 6,9 # 15 pairs C5: 6,9,4 # reduction candidate for 6,9 C5: 6,9 # 16 pairs * PAIR B4: 6,9 ROW 4 F4: 6,9,8 # reduction candidate for 6,9 F4: 6,9 => SOLVED * 641972385789563142352184796165729834974835261823416579296358417537641928418297653 F4: 8 # 13 pairs G4: 6,9,8 # reduction candidate for 6,9 G4: 6,9 # 13 pairs * PAIR B4: 6,9 COL B B7: 6,9,8 # reduction candidate for 6,9 B7: 8 # 15 pairs B7: 6,9 # 13 pairs * PAIR F6: 6,9 BLK 5 F4: 6,9,8 # reduction candidate for 6,9 F4: 6,9 => SOLVED * 641972385789563142352184796165729834974835261823416579296358417537641928418297653 F4: 8 # 13 pairs D5: 6,9,8 # reduction candidate for 6,9 D5: 6,9 # 13 pairs * PAIR F6: 6,9 COL F F7: 6,9,8 # reduction candidate for 6,9 F7: 8 => SOLVED * 641972385789563142352184796165729834974835261823416579296358417537641928418297653 F7: 6,9 # 13 pairs * PAIR I6: 6,9 BLK 6 G4: 6,9,8 # reduction candidate for 6,9 G4: 6,9 # 13 pairs H5: 6,9,8 # reduction candidate for 6,9 H5: 6,9 => SOLVED * 641972385789563142352184796165729834974835261823416579296358417537641928418297653 H5: 8 # 13 pairs * PAIR I6: 6,9 COL I I2: 6,9,2,8 # reduction candidate for 6,9 I2: 6,9 # 12 pairs I3: 6,9,2,8 # reduction candidate for 6,9 I3: 6,9 # 12 pairs I8: 6,9,2,8 # reduction candidate for 6,9 I8: 6,9 # 17 pairs * PAIR A9: 4,9 BLK 7 A7: 4,9,2 # reduction candidate for 4,9 A7: 4,9 # 20 pairs C7: 4,9,2,6,8 # reduction candidate for 4,9 C7: 4,9 # 13 pairs C9: 4,9,6,8 # reduction candidate for 4,9 C9: 4,9 => CTR * 641872395...5..1...5.1..7..1.5728934...9352.182341.57....35.417537641....1.287653 C9: 6,8 # 10 pairs * PAIR A9: 4,9 ROW 9 G9: 4,9,6,8 # reduction candidate for 4,9 G9: 4,9 # 16 pairs G9: 6,8 # 12 pairs * PAIR A9: 4,9 COL A A5: 4,9,7 # reduction candidate for 4,9 A5: 7 # 15 pairs A5: 4,9 # 9 pairs * PAIR E9: 8,9 BLK 8 F7: 8,9,6 # reduction candidate for 8,9 F7: 8,9 # 15 pairs D8: 8,9,6 # reduction candidate for 8,9 D8: 8,9 => CTR * 641872395...5..1...5.1..7..165728934...635281823419576...356.17537941628916287453 D8: 6 # 15 pairs * PAIR E9: 8,9 ROW 9 C9: 8,9,4,6 # reduction candidate for 8,9 C9: 8,9 # 16 pairs G9: 8,9,4,6 # reduction candidate for 8,9 G9: 8,9 => CTR * 641872395...5..1...5.1..7..165728934..4635281823419576...3564175379416..4162.7853 G9: 4,6 # 10 pairs * PAIR E9: 8,9 COL E E2: 8,9,6 # reduction candidate for 8,9 E2: 8,9 # 10 pairs E3: 8,9,6 # reduction candidate for 8,9 E3: 8,9 # 10 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-040-base-pr-000.dot * REASONING * DIS # D8: 8,9 => CTR => D8: 6 * DIS # H2: 8,9 => CTR => H2: 2,4,6 * PRF # H3: 8,9 => SOL * DIS # H8: 8,9 => CTR => H8: 2,6 * PRF # F4: 6,9 => SOL * PRF # F4: 6,9 => SOL * PRF # F7: 8 => SOL * PRF # H5: 6,9 => SOL * DIS # C9: 4,9 => CTR => C9: 6,8 * DIS # D8: 8,9 => CTR => D8: 6 * DIS # G9: 8,9 => CTR => G9: 4,6 * CNT 11 HDP CHAINS / 48 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B4,D1,E9,F2,F3,F6,H1,I6) * 641.723.5...5..1...5.1..7..1.572..34....352.182341.57....35..17537.41....1.2.7.53 * PAIR D1: 8,9 BLK 2 E2: 8,9,6 # reduction candidate for 8,9 E2: 8,9 # 10 pairs E3: 8,9,6 # reduction candidate for 8,9 E3: 8,9 # 10 pairs * PAIR D1: 8,9 COL D D5: 8,9,6 # reduction candidate for 8,9 D5: 8,9 # 15 pairs D8: 8,9,6 # reduction candidate for 8,9 D8: 8,9 => CTR * 641872395...5..1...5.1..7..165728934...635281823419576...356.17537941628916287453 * RESTART * PAIR RESTART * PAIR D1: 8,9 BLK 2 E2: 8,9,6 # reduction candidate for 8,9 E2: 8,9 # 16 pairs E3: 8,9,6 # reduction candidate for 8,9 E3: 8,9 # 16 pairs * PAIR H1: 8,9 BLK 3 H2: 8,9,2,4,6 # reduction candidate for 8,9 H2: 8,9 => CTR * 641.723.537.5.41...5.1.374.165729834794835261823416579.8.35..17537641928.1.2.7.53 I2: 8,9,2,6 # reduction candidate for 8,9 I2: 8,9 # 17 pairs H3: 8,9,2,4,6 # reduction candidate for 8,9 H3: 8,9 => SOLVED * 641972385789563142352184796165729834974835261823416579296358417537641928418297653 * DURATION: 0:00:10.216353 START: 04:03:47.132033 END: 04:03:57.348386 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-040-base-pr-001.dot * REASONING * DIS # D8: 8,9 => CTR => D8: 6 * DIS D8: 6 # H2: 8,9 => CTR => H2: 2,4,6 * PRF D8: 6 + H2: 2,4,6 # H3: 8,9 => SOL * STA D8: 6 + H2: 2,4,6 + H3: 8,9 * CNT 3 HDP CHAINS / 9 HYP OPENED
Header Info
Top 500 Minimum 17 040 solution: 641972385789563142352184796165729834974835261823416579296358417537641928418297653 info: 1370 FNBHWXY S8.f 35909 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 641972385789563142352184796165729834974835261823416579296358417537641928418297653 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 # E2: 8,9 => UNS * INC # E3: 8,9 => UNS * INC # D5: 8,9 => UNS * DIS # D8: 8,9 => CTR => D8: 6 * INC # D8: 6 => UNS * DIS # H2: 8,9 => CTR => H2: 2,4,6 * INC # H2: 2,4,6 => UNS * INC # I2: 8,9 => UNS * PRF # H3: 8,9 => SOL * INC # H3: 2,4,6 => UNS * INC # I3: 8,9 => UNS * INC # H5: 8,9 => UNS * DIS # H8: 8,9 => CTR => H8: 2,6 * INC # H8: 2,6 => UNS * INC # B5: 6,9 => UNS * INC # C5: 6,9 => UNS * PRF # F4: 6,9 => SOL * INC # F4: 8 => UNS * INC # G4: 6,9 => UNS * INC # B7: 6,9 => UNS * INC # B7: 8 => UNS * PRF # F4: 6,9 => SOL * INC # F4: 8 => UNS * INC # D5: 6,9 => UNS * INC # F7: 6,9 => UNS * PRF # F7: 8 => SOL * INC # G4: 6,9 => UNS * PRF # H5: 6,9 => SOL * INC # H5: 8 => UNS * INC # I2: 6,9 => UNS * INC # I3: 6,9 => UNS * INC # I8: 6,9 => UNS * INC # A7: 4,9 => UNS * INC # C7: 4,9 => UNS * DIS # C9: 4,9 => CTR => C9: 6,8 * INC # C9: 6,8 => UNS * INC # G9: 4,9 => UNS * INC # G9: 6,8 => UNS * INC # A5: 4,9 => UNS * INC # A5: 7 => UNS * INC # F7: 8,9 => UNS * DIS # D8: 8,9 => CTR => D8: 6 * INC # D8: 6 => UNS * INC # C9: 8,9 => UNS * DIS # G9: 8,9 => CTR => G9: 4,6 * INC # G9: 4,6 => UNS * INC # E2: 8,9 => UNS * INC # E3: 8,9 => UNS * CNT 48 HDP CHAINS / 48 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # E2: 8,9 => UNS * INC # E3: 8,9 => UNS * INC # D5: 8,9 => UNS * DIS # D8: 8,9 => CTR => D8: 6 * INC D8: 6 # E2: 8,9 => UNS * INC D8: 6 # E3: 8,9 => UNS * DIS D8: 6 # H2: 8,9 => CTR => H2: 2,4,6 * INC D8: 6 + H2: 2,4,6 # I2: 8,9 => UNS * PRF D8: 6 + H2: 2,4,6 # H3: 8,9 => SOL * STA D8: 6 + H2: 2,4,6 + H3: 8,9 * CNT 9 HDP CHAINS / 9 HYP OPENED