Analysis of xx-top500-311-base.sdk
Contents
Original Sudoku
level: medium
position: .3.7...4.1...9..............2.68.........21........5.98.1.........4...6.5........ initial
Autosolve
position: 23.7...4.1...9.............925681......9521866183..5298.1.........4...6.5........ autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # G1: 6,9 => CTR => G1: 8 * DIS # F2: 5,8 => CTR => F2: 3,4,6 * DIS # I2: 5,8 => CTR => I2: 2,3,7 * DIS # D3: 5,8 => CTR => D3: 1,2 * DIS # F3: 5,8 => CTR => F3: 3,4,6 * DIS # E3: 1,6 => CTR => E3: 2,3,4 * DIS # E9: 1,6 => CTR => E9: 2,3,7 * DIS # H3: 3,7 => CTR => H3: 1,5,9 * DIS # H7: 3,7 => CTR => H7: 5,9 * DIS # H9: 3,7 => CTR => H9: 1,9 * DIS # E8: 3,7 => CTR => E8: 1,2 * DIS # F8: 3,7 => CTR => F8: 5,8,9 * DIS # I8: 3,7 => CTR => I8: 1,2,5,8 * DIS # F8: 7,9 => CTR => F8: 3,5,8 * DIS # I7: 2,5 => CTR => I7: 3,4,7 * DIS # D3: 2,5 => CTR => D3: 1,8 * CNT 16 HDP CHAINS / 56 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # G1: 6,9 => CTR => G1: 8 * DIS G1: 8 # A5: 3 => CTR => A5: 4,7 * PRF G1: 8 + A5: 4,7 # I4: 3,7 => SOL * STA G1: 8 + A5: 4,7 + I4: 3,7 * CNT 3 HDP CHAINS / 6 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .3.7...4.1...9..............2.68.........21........5.98.1.........4...6.5........ | initial |
| 23.7...4.1...9.............925681......9521866183..5298.1.........4...6.5........ | autosolve |
| 239765841157894632486123957925681473743952186618347529871536294392418765564279318 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (12) C1: 6,9 B2: 5,8 A3: 4,7 B3: 5,8 E1: 1,6 B5: 4,7 E6: 4,7 F6: 4,7 H4: 3,7 A8: 3,7 B8: 7,9 D7: 2,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E1,I1: 1.. / E1 = 1 => 0 pairs (X) / I1 = 1 => 13 pairs (_) E8,I8: 1.. / E8 = 1 => 13 pairs (_) / I8 = 1 => 0 pairs (X) D3,D9: 1.. / D3 = 1 => 13 pairs (_) / D9 = 1 => 0 pairs (X) H3,H9: 1.. / H3 = 1 => 0 pairs (X) / H9 = 1 => 13 pairs (_) C8,C9: 2.. / C8 = 2 => 12 pairs (_) / C9 = 2 => 19 pairs (_) A5,C5: 3.. / A5 = 3 => 11 pairs (_) / C5 = 3 => 13 pairs (_) A5,A8: 3.. / A5 = 3 => 11 pairs (_) / A8 = 3 => 13 pairs (_) E6,F6: 4.. / E6 = 4 => 10 pairs (_) / F6 = 4 => 0 pairs (X) G4,I4: 4.. / G4 = 4 => 13 pairs (_) / I4 = 4 => 13 pairs (_) C2,F2: 4.. / C2 = 4 => 13 pairs (_) / F2 = 4 => 11 pairs (_) A3,A5: 4.. / A3 = 4 => 13 pairs (_) / A5 = 4 => 13 pairs (_) E3,E6: 4.. / E3 = 4 => 0 pairs (X) / E6 = 4 => 10 pairs (_) B2,B3: 5.. / B2 = 5 => 14 pairs (_) / B3 = 5 => 13 pairs (_) F1,I1: 5.. / F1 = 5 => 13 pairs (_) / I1 = 5 => 0 pairs (X) F8,I8: 5.. / F8 = 5 => 0 pairs (X) / I8 = 5 => 13 pairs (_) B7,B9: 6.. / B7 = 6 => 12 pairs (_) / B9 = 6 => 12 pairs (_) E6,F6: 7.. / E6 = 7 => 0 pairs (X) / F6 = 7 => 10 pairs (_) B2,B3: 8.. / B2 = 8 => 13 pairs (_) / B3 = 8 => 14 pairs (_) C1,C3: 9.. / C1 = 9 => 12 pairs (_) / C3 = 9 => 0 pairs (X) C1,G1: 9.. / C1 = 9 => 12 pairs (_) / G1 = 9 => 0 pairs (X) * DURATION: 0:00:27.714719 START: 13:37:22.112559 END: 13:37:49.827278 2017-05-04 * CP COUNT: (20) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A8,B2,B3,B5,B8,C1,D7,E1,E6,F6,H4) * 23.7...4.1...9.............925681......9521866183..5298.1.........4...6.5........ * PAIR C1: 6,9 BLK 1 C3: 6,9,4,7 # reduction candidate for 6,9 C3: 6,9 # 14 pairs C3: 4,7 # 11 pairs * PAIR C1: 6,9 ROW 1 G1: 6,9,8 # reduction candidate for 6,9 G1: 6,9 => CTR * 23.71..4.1...9...........1.925681......9521866183..5298.1.........4.58615..1.8... G1: 8 # 13 pairs * PAIR B2: 5,8 ROW 2 D2: 5,8,2 # reduction candidate for 5,8 D2: 5,8 # 16 pairs F2: 5,8,3,4,6 # reduction candidate for 5,8 F2: 5,8 => CTR * 2397.58411542986..7861..952925681...4739521866183..5298.15.6.9.39.4172655....9.1. F2: 3,4,6 # 12 pairs I2: 5,8,2,3,7 # reduction candidate for 5,8 I2: 5,8 => CTR * 23.7.5.4.15.29...8.8.1...5.925681......9521866183..5298.15...9....41..655..8...1. I2: 2,3,7 # 12 pairs * PAIR A3: 4,7 BLK 1 C2: 4,7,6 # reduction candidate for 4,7 C2: 4,7 # 14 pairs C3: 4,7,6,9 # reduction candidate for 4,7 C3: 4,7 # 11 pairs * PAIR A3: 4,7 COL A A5: 4,7,3 # reduction candidate for 4,7 A5: 4,7 # 13 pairs A5: 3 # 11 pairs * PAIR B3: 5,8 ROW 3 D3: 5,8,1,2 # reduction candidate for 5,8 D3: 5,8 => CTR * 23.71..4.1...9...........1.925681......9521866183..5298.1.........4.58615..1.8... D3: 1,2 # 13 pairs F3: 5,8,3,4,6 # reduction candidate for 5,8 F3: 5,8 => CTR * 2397.58411..89.............925681......9521866183..5298.15........4...655.......8 F3: 3,4,6 # 12 pairs I3: 5,8,1,2,3,7 # reduction candidate for 5,8 I3: 5,8 # 14 pairs * PAIR E1: 1,6 BLK 2 E3: 1,6,2,3,4 # reduction candidate for 1,6 E3: 1,6 => CTR * 23.7.5.4.1...9.............925681......9521866183475298.15........41..655..8..... E3: 2,3,4 # 12 pairs * PAIR E1: 1,6 COL E E9: 1,6,2,3,7 # reduction candidate for 1,6 E9: 1,6 => CTR * 23.71..4.1...9...........1.925681......9521866183..5298.1.........4.58615..168... E9: 2,3,7 # 12 pairs * PAIR B5: 4,7 BLK 4 A5: 4,7,3 # reduction candidate for 4,7 A5: 4,7 # 13 pairs C5: 4,7,3 # reduction candidate for 4,7 C5: 4,7 # 11 pairs * PAIR B5: 4,7 COL B B7: 4,7,6,9 # reduction candidate for 4,7 B7: 4,7 # 12 pairs B9: 4,7,6,9 # reduction candidate for 4,7 B9: 4,7 # 12 pairs * PAIR H4: 3,7 BLK 6 G4: 3,7,4 # reduction candidate for 3,7 G4: 3,7 # 13 pairs I4: 3,7,4 # reduction candidate for 3,7 I4: 3,7 # 13 pairs * PAIR H4: 3,7 COL H H2: 3,7,5 # reduction candidate for 3,7 H2: 3,7 # 15 pairs H3: 3,7,1,5,9 # reduction candidate for 3,7 H3: 3,7 => CTR * 23976584118.29..5..5.1.89.2925681......9521866183..5298.15...9....41..655..8...1. H3: 1,5,9 # 12 pairs H7: 3,7,5,9 # reduction candidate for 3,7 H7: 3,7 => CTR * 2397658411...9.......1...9.925681......9521866183..5298.15........418.655..2...18 H7: 5,9 # 13 pairs H9: 3,7,1,9 # reduction candidate for 3,7 H9: 3,7 => CTR * 23.71..4.1...9..5..5.....1.925681......9521866183..5298.15...9....4...6.5..1..... H9: 1,9 # 13 pairs * PAIR A8: 3,7 BLK 7 C8: 3,7,2 # reduction candidate for 3,7 C8: 3,7 # 19 pairs C9: 3,7,2,4 # reduction candidate for 3,7 C9: 3,7 # 15 pairs * PAIR A8: 3,7 ROW 8 E8: 3,7,1,2 # reduction candidate for 3,7 E8: 3,7 => CTR * 23.71..4.1...9...........1.925681......9521866183..5298.1.........4.58615..1.8... E8: 1,2 # 13 pairs F8: 3,7,5,8,9 # reduction candidate for 3,7 F8: 3,7 => CTR * 23.7.5.4.1...9.............925681......9521866183..5298.15........41.8655........ F8: 5,8,9 # 12 pairs G8: 3,7,2,8,9 # reduction candidate for 3,7 G8: 3,7 # 13 pairs I8: 3,7,1,2,5,8 # reduction candidate for 3,7 I8: 3,7 => CTR * 23.7...4.1...9.............925681......9521866183..5298.1.........41586.5........ I8: 1,2,5,8 # 12 pairs * PAIR A8: 3,7 COL A A5: 3,7,4 # reduction candidate for 3,7 A5: 4 # 13 pairs A5: 3,7 # 13 pairs * PAIR B8: 7,9 BLK 7 B7: 7,9,4,6 # reduction candidate for 7,9 B7: 7,9 # 10 pairs B9: 7,9,4,6 # reduction candidate for 7,9 B9: 7,9 # 10 pairs * PAIR B8: 7,9 ROW 8 F8: 7,9,3,5,8 # reduction candidate for 7,9 F8: 7,9 => CTR * 23.7.5.4.1...9.............925681......9521866183..5298.15........41.8655........ F8: 3,5,8 # 12 pairs G8: 7,9,2,3,8 # reduction candidate for 7,9 G8: 7,9 # 16 pairs * PAIR D7: 2,5 ROW 7 I7: 2,5,3,4,7 # reduction candidate for 2,5 I7: 2,5 => CTR * 2397658411..89.2...8.12.6..925681......9521866183..5298.15....2..2418.655..2...18 I7: 3,4,7 # 12 pairs * PAIR D7: 2,5 COL D D2: 2,5,8 # reduction candidate for 2,5 D2: 2,5 # 15 pairs D3: 2,5,1,8 # reduction candidate for 2,5 D3: 2,5 => CTR * 23.71..4.15.89.....8.....1.925681......9521866183..5298.1....5....4.58615..1.8.9. D3: 1,8 # 13 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-311-base-pr-000.dot * REASONING * DIS # G1: 6,9 => CTR => G1: 8 * DIS # F2: 5,8 => CTR => F2: 3,4,6 * DIS # I2: 5,8 => CTR => I2: 2,3,7 * DIS # D3: 5,8 => CTR => D3: 1,2 * DIS # F3: 5,8 => CTR => F3: 3,4,6 * DIS # E3: 1,6 => CTR => E3: 2,3,4 * DIS # E9: 1,6 => CTR => E9: 2,3,7 * DIS # H3: 3,7 => CTR => H3: 1,5,9 * DIS # H7: 3,7 => CTR => H7: 5,9 * DIS # H9: 3,7 => CTR => H9: 1,9 * DIS # E8: 3,7 => CTR => E8: 1,2 * DIS # F8: 3,7 => CTR => F8: 5,8,9 * DIS # I8: 3,7 => CTR => I8: 1,2,5,8 * DIS # F8: 7,9 => CTR => F8: 3,5,8 * DIS # I7: 2,5 => CTR => I7: 3,4,7 * DIS # D3: 2,5 => CTR => D3: 1,8 * CNT 16 HDP CHAINS / 56 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A8,B2,B3,B5,B8,C1,D7,E1,E6,F6,H4) * 23.7...4.1...9.............925681......9521866183..5298.1.........4...6.5........ * PAIR C1: 6,9 BLK 1 C3: 6,9,4,7 # reduction candidate for 6,9 C3: 6,9 # 14 pairs C3: 4,7 # 11 pairs * PAIR C1: 6,9 ROW 1 G1: 6,9,8 # reduction candidate for 6,9 G1: 6,9 => CTR * 23.71..4.1...9...........1.925681......9521866183..5298.1.........4.58615..1.8... * PAIR RESTART * PAIR A3: 4,7 COL A A5: 4,7,3 # reduction candidate for 4,7 A5: 3 => CTR * 23976584115.89.6.2486123957925681.7.3..9521866183475298.15.629.792418365563279.18 * PAIR RESTART * PAIR H4: 3,7 BLK 6 I4: 3,7,4 # reduction candidate for 3,7 I4: 3,7 => SOLVED * 239765841157894632486123957925681473743952186618347529871536294392418765564279318 * DURATION: 0:00:08.929040 START: 13:38:29.567834 END: 13:38:38.496874 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-311-base-pr-001.dot * REASONING * DIS # G1: 6,9 => CTR => G1: 8 * DIS G1: 8 # A5: 3 => CTR => A5: 4,7 * PRF G1: 8 + A5: 4,7 # I4: 3,7 => SOL * STA G1: 8 + A5: 4,7 + I4: 3,7 * CNT 3 HDP CHAINS / 6 HYP OPENED
Header Info
Top 500 Minimum 17 311 solution: 239765841157894632486123957925681473743952186618347529871536294392418765564279318 info: 2771 FNBHWXY S8.f 18055 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 239765841157894632486123957925681473743952186618347529871536294392418765564279318 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 # C3: 6,9 => UNS * INC # C3: 4,7 => UNS * DIS # G1: 6,9 => CTR => G1: 8 * INC # G1: 8 => UNS * INC # D2: 5,8 => UNS * DIS # F2: 5,8 => CTR => F2: 3,4,6 * INC # F2: 3,4,6 => UNS * DIS # I2: 5,8 => CTR => I2: 2,3,7 * INC # I2: 2,3,7 => UNS * INC # C2: 4,7 => UNS * INC # C3: 4,7 => UNS * INC # A5: 4,7 => UNS * INC # A5: 3 => UNS * DIS # D3: 5,8 => CTR => D3: 1,2 * INC # D3: 1,2 => UNS * DIS # F3: 5,8 => CTR => F3: 3,4,6 * INC # F3: 3,4,6 => UNS * INC # I3: 5,8 => UNS * DIS # E3: 1,6 => CTR => E3: 2,3,4 * INC # E3: 2,3,4 => UNS * DIS # E9: 1,6 => CTR => E9: 2,3,7 * INC # E9: 2,3,7 => UNS * INC # A5: 4,7 => UNS * INC # C5: 4,7 => UNS * INC # B7: 4,7 => UNS * INC # B9: 4,7 => UNS * INC # G4: 3,7 => UNS * INC # I4: 3,7 => UNS * INC # H2: 3,7 => UNS * DIS # H3: 3,7 => CTR => H3: 1,5,9 * INC # H3: 1,5,9 => UNS * DIS # H7: 3,7 => CTR => H7: 5,9 * INC # H7: 5,9 => UNS * DIS # H9: 3,7 => CTR => H9: 1,9 * INC # H9: 1,9 => UNS * INC # C8: 3,7 => UNS * INC # C9: 3,7 => UNS * DIS # E8: 3,7 => CTR => E8: 1,2 * INC # E8: 1,2 => UNS * DIS # F8: 3,7 => CTR => F8: 5,8,9 * INC # F8: 5,8,9 => UNS * INC # G8: 3,7 => UNS * DIS # I8: 3,7 => CTR => I8: 1,2,5,8 * INC # I8: 1,2,5,8 => UNS * INC # A5: 3,7 => UNS * INC # A5: 4 => UNS * INC # B7: 7,9 => UNS * INC # B9: 7,9 => UNS * DIS # F8: 7,9 => CTR => F8: 3,5,8 * INC # F8: 3,5,8 => UNS * INC # G8: 7,9 => UNS * DIS # I7: 2,5 => CTR => I7: 3,4,7 * INC # I7: 3,4,7 => UNS * INC # D2: 2,5 => UNS * DIS # D3: 2,5 => CTR => D3: 1,8 * INC # D3: 1,8 => UNS * CNT 56 HDP CHAINS / 56 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C3: 6,9 => UNS * INC # C3: 4,7 => UNS * DIS # G1: 6,9 => CTR => G1: 8 * INC G1: 8 # A5: 4,7 => UNS * DIS G1: 8 # A5: 3 => CTR => A5: 4,7 * PRF G1: 8 + A5: 4,7 # I4: 3,7 => SOL * STA G1: 8 + A5: 4,7 + I4: 3,7 * CNT 6 HDP CHAINS / 6 HYP OPENED