Analysis of xx-top500-339-base.sdk
Contents
Original Sudoku
level: medium
position: ....23..71.....6......5....63.....1..27.........4..8..8..6.............3.......2. initial
Autosolve
position: ....23..71.....6......56...638....1.427.........4..8..8..6.............3.......2. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C2: 5,9 => CTR => C2: 2,3 * DIS # D4: 7,9 => CTR => D4: 2,5 * DIS # F4: 7,9 => CTR => F4: 2,5 * DIS # E2: 7,9 => CTR => E2: 4,8 * DIS # E7: 7,9 => CTR => E7: 1,3,4 * DIS # E5: 3,8 => CTR => E5: 1,6 * DIS # D9: 5,7,9 => CTR => D9: 3,8 * DIS # E5: 1,8 => CTR => E5: 3,6 * PRF # E5: 3,6 => SOL * PRF # E5: 3,6 => SOL * DIS # E5: 1,8 => CTR => E5: 3,6 * PRF # H6: 3,6 => SOL * DIS # H6: 7 => CTR => H6: 3,6 * DIS # F4: 2,7 => CTR => F4: 5,9 * DIS # F8: 2,7 => CTR => F8: 1,4,5,8,9 * DIS # G4: 2,4 => CTR => G4: 7 * PRF # G4: 7 => SOL * DIS # I3: 2,4 => CTR => I3: 1,8,9 * DIS # F8: 2,7 => CTR => F8: 1,4,5,8,9 * DIS # A3: 2,7 => CTR => A3: 3 * PRF # A3: 3 => SOL * DIS # E9: 3,7 => CTR => E9: 1,4,8,9 * PRF # A3: 3,7 => SOL * DIS # A3: 2 => CTR => A3: 3,7 * CNT 24 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 # C2: 5,9 => CTR => C2: 2,3 * DIS C2: 2,3 # D4: 7,9 => CTR => D4: 2,5 * DIS C2: 2,3 + D4: 2,5 # F4: 7,9 => CTR => F4: 2,5 * PRF C2: 2,3 + D4: 2,5 + F4: 2,5 => SOL * STA C2: 2,3 + D4: 2,5 + F4: 2,5 * CNT 4 HDP CHAINS / 15 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....23..71.....6......5....63.....1..27.........4..8..8..6.............3.......2. | initial |
| ....23..71.....6......56...638....1.427.........4..8..8..6.............3.......2. | autosolve |
| 586923147192784635374156298638295714427861359915437862853642971261579483749318526 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) A1: 5,9 A6: 5,9 E4: 7,9 D5: 3,8 F5: 1,8 E6: 3,6 F6: 2,7 I4: 2,4 I6: 2,6 A8: 2,7 A9: 3,7 H8: 6,8 I9: 6,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D1,D3: 1.. / D1 = 1 => 13 pairs (_) / D3 = 1 => 14 pairs (_) B6,C6: 1.. / B6 = 1 => 14 pairs (_) / C6 = 1 => 14 pairs (_) E5,F5: 1.. / E5 = 1 => 0 pairs (X) / F5 = 1 => 12 pairs (_) D1,G1: 1.. / D1 = 1 => 13 pairs (_) / G1 = 1 => 14 pairs (_) I3,I7: 1.. / I3 = 1 => 13 pairs (_) / I7 = 1 => 13 pairs (_) C2,I2: 2.. / C2 = 2 => 0 pairs (*) / I2 = 2 => 0 pairs (X) F6,I6: 2.. / F6 = 2 => 0 pairs (X) / I6 = 2 => 0 pairs (_) C7,F7: 2.. / C7 = 2 => 0 pairs (X) / F7 = 2 => 0 pairs (_) A3,A8: 2.. / A3 = 2 => 0 pairs (X) / A8 = 2 => 0 pairs (_) D4,D8: 2.. / D4 = 2 => 0 pairs (*) / D8 = 2 => 0 pairs (X) G3,G4: 2.. / G3 = 2 => 0 pairs (*) / G4 = 2 => 0 pairs (X) C2,H2: 3.. / C2 = 3 => 0 pairs (X) / H2 = 3 => 0 pairs (_) E6,H6: 3.. / E6 = 3 => 0 pairs (*) / H6 = 3 => 0 pairs (X) C7,E7: 3.. / C7 = 3 => 0 pairs (*) / E7 = 3 => 0 pairs (X) A3,A9: 3.. / A3 = 3 => 0 pairs (*) / A9 = 3 => 0 pairs (X) D5,D9: 3.. / D5 = 3 => 0 pairs (X) / D9 = 3 => 0 pairs (_) G3,G5: 3.. / G3 = 3 => 0 pairs (X) / G5 = 3 => 0 pairs (_) E2,F2: 4.. / E2 = 4 => 13 pairs (_) / F2 = 4 => 13 pairs (_) G4,I4: 4.. / G4 = 4 => 0 pairs (X) / I4 = 4 => 13 pairs (_) D4,F4: 5.. / D4 = 5 => 0 pairs (X) / F4 = 5 => 13 pairs (_) A1,A6: 5.. / A1 = 5 => 16 pairs (_) / A6 = 5 => 14 pairs (_) B1,C1: 6.. / B1 = 6 => 13 pairs (_) / C1 = 6 => 13 pairs (_) E5,E6: 6.. / E5 = 6 => 0 pairs (*) / E6 = 6 => 0 pairs (X) H8,I9: 6.. / H8 = 6 => 12 pairs (_) / I9 = 6 => 0 pairs (*) G4,H6: 7.. / G4 = 7 => 0 pairs (*) / H6 = 7 => 0 pairs (X) F6,H6: 7.. / F6 = 7 => 0 pairs (*) / H6 = 7 => 0 pairs (X) H6,H7: 7.. / H6 = 7 => 0 pairs (X) / H7 = 7 => 0 pairs (_) H8,I9: 8.. / H8 = 8 => 0 pairs (*) / I9 = 8 => 0 pairs (X) A1,A6: 9.. / A1 = 9 => 14 pairs (_) / A6 = 9 => 16 pairs (_) * DURATION: 0:00:47.981021 START: 14:20:18.523685 END: 14:21:06.504706 2017-05-04 * CP COUNT: (29) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A6,A8,A9,D5,E4,E6,F5,F6,H8,I4,I6,I9) * ....23..71.....6......56...638....1.427.........4..8..8..6.............3.......2. * PAIR A1: 5,9 BLK 1 B1: 5,9,4,6,8 # reduction candidate for 5,9 B1: 5,9 # 21 pairs C1: 5,9,4,6 # reduction candidate for 5,9 C1: 5,9 # 21 pairs B2: 5,9,7,8 # reduction candidate for 5,9 B2: 5,9 # 16 pairs C2: 5,9,2,3 # reduction candidate for 5,9 C2: 5,9 => CTR * ....23..71.....632....56...638...214427...3.....4328768..6.............3.......2. C2: 2,3 # 14 pairs * PAIR A1: 5,9 ROW 1 G1: 5,9,1,4 # reduction candidate for 5,9 G1: 5,9 # 16 pairs H1: 5,9,4,8 # reduction candidate for 5,9 H1: 5,9 # 17 pairs * PAIR A6: 5,9 BLK 4 B6: 5,9,1 # reduction candidate for 5,9 B6: 5,9 # 14 pairs C6: 5,9,1 # reduction candidate for 5,9 C6: 5,9 # 14 pairs * PAIR E4: 7,9 BLK 5 D4: 7,9,2,5 # reduction candidate for 7,9 D4: 7,9 => CTR * ....23..71.....6......56...638..5.1.427.........4.28768.263............3.......2. D4: 2,5 # 14 pairs F4: 7,9,2,5 # reduction candidate for 7,9 F4: 7,9 => CTR * ....23..71.....6......56...6385...1.427.........4.28768.263............3.......2. F4: 2,5 # 14 pairs * PAIR E4: 7,9 COL E E2: 7,9,4,8 # reduction candidate for 7,9 E2: 7,9 => CTR * ....23..71....46......56...638....1.4273........46.8328..6...7.........3.......2. E2: 4,8 # 14 pairs E7: 7,9,1,3,4 # reduction candidate for 7,9 E7: 7,9 => CTR * ....23..71.....63.3...56...6382.5.14427...3.....4378628.36.2.7.2......837..3...26 E7: 1,3,4 # 13 pairs E8: 7,9,1,4,8 # reduction candidate for 7,9 E8: 7,9 # 15 pairs E9: 7,9,1,3,4,8 # reduction candidate for 7,9 E9: 7,9 # 15 pairs * PAIR D5: 3,8 BLK 5 E5: 3,8,1,6 # reduction candidate for 3,8 E5: 3,8 => CTR * ....23..71.....6......56...638....1.427..1......46.8328..6...7.........3.......2. E5: 1,6 # 14 pairs * PAIR D5: 3,8 COL D D9: 3,8,5,7,9 # reduction candidate for 3,8 D9: 5,7,9 => CTR * ....23..71.....6......56...638....1.4273........46.8328..6...7.........3.......2. D9: 3,8 # 20 pairs * PAIR F5: 1,8 BLK 5 E5: 1,8,3,6 # reduction candidate for 1,8 E5: 1,8 => CTR * ....23..71.....6......56...638....1.427.........46.8328..6...7.........3.......2. E5: 3,6 => SOLVED * 586923147192784635374156298638295714427861359915437862853642971261579483749318526 * PAIR F5: 1,8 COL F F8: 1,8,2,4,5,7,9 # reduction candidate for 1,8 F8: 1,8 # 14 pairs F9: 1,8,4,5,7,9 # reduction candidate for 1,8 F9: 1,8 # 14 pairs * PAIR E6: 3,6 BLK 5 E5: 3,6,1,8 # reduction candidate for 3,6 E5: 3,6 => SOLVED * 586923147192784635374156298638295714427861359915437862853642971261579483749318526 E5: 1,8 => CTR * ....23..71.....6......56...638....1.427.........46.8328..6...7.........3.......2. * PAIR E6: 3,6 ROW 6 H6: 3,6,7 # reduction candidate for 3,6 H6: 3,6 => SOLVED * 586923147192784635374156298638295714427861359915437862853642971261579483749318526 H6: 7 => CTR * ....23..71.....6......56...638....1.427.........43.8768.36.2...........3.......2. * PAIR F6: 2,7 BLK 5 D4: 2,7,5,9 # reduction candidate for 2,7 D4: 2,7 # 13 pairs F4: 2,7,5,9 # reduction candidate for 2,7 F4: 2,7 => CTR * ....23..71.....6..2...56...63859.214427.........4.28768.263.......2....3.......2. F4: 5,9 # 14 pairs * PAIR F6: 2,7 COL F F7: 2,7,1,4,5,9 # reduction candidate for 2,7 F7: 2,7 # 15 pairs F8: 2,7,1,4,5,8,9 # reduction candidate for 2,7 F8: 2,7 => CTR * ....23..71.....6......56...6382.5.14427.........4.78.28.263..7.7....2..33......2. F8: 1,4,5,8,9 # 13 pairs * PAIR I4: 2,4 BLK 6 G4: 2,4,7 # reduction candidate for 2,4 G4: 2,4 => CTR * ....23..71.....6......56...638....1.427.........4328768..6.............3.......2. G4: 7 => SOLVED * 586923147192784635374156298638295714427861359915437862853642971261579483749318526 * PAIR I4: 2,4 COL I I3: 2,4,1,8,9 # reduction candidate for 2,4 I3: 2,4 => CTR * ....23..71.2...63.....56...638....1.427...3.....4328768.36....12......637..3...28 I3: 1,8,9 # 13 pairs * PAIR A8: 2,7 ROW 8 D8: 2,7,5,8,9 # reduction candidate for 2,7 D8: 2,7 # 14 pairs F8: 2,7,1,4,5,8,9 # reduction candidate for 2,7 F8: 2,7 => CTR * ....23..71.....6......56...6382.5.14427.........4.78.28.263..7.7....2..33......2. F8: 1,4,5,8,9 # 13 pairs * PAIR A8: 2,7 COL A A3: 2,7,3 # reduction candidate for 2,7 A3: 2,7 => CTR * ....23..71.....6......56...638....1.4273........46.8328..63..7.........33......2. A3: 3 => SOLVED * 586923147192784635374156298638295714427861359915437862853642971261579483749318526 * PAIR A9: 3,7 ROW 9 D9: 3,7,5,8,9 # reduction candidate for 3,7 D9: 3,7 # 16 pairs E9: 3,7,1,4,8,9 # reduction candidate for 3,7 E9: 3,7 => CTR * ....23..71.....6......56...638....1.4273........46.8328..6...7.........3.......2. E9: 1,4,8,9 # 13 pairs * PAIR A9: 3,7 COL A A3: 3,7,2 # reduction candidate for 3,7 A3: 3,7 => SOLVED * 586923147192784635374156298638295714427861359915437862853642971261579483749318526 A3: 2 => CTR * ....23..71.....6..2...56...638...214427.........4.28768.263............3.......2. * INCONCLUSIVE * SAVE PR GRAPH xx-top500-339-base-pr-000.dot * REASONING * DIS # C2: 5,9 => CTR => C2: 2,3 * DIS # D4: 7,9 => CTR => D4: 2,5 * DIS # F4: 7,9 => CTR => F4: 2,5 * DIS # E2: 7,9 => CTR => E2: 4,8 * DIS # E7: 7,9 => CTR => E7: 1,3,4 * DIS # E5: 3,8 => CTR => E5: 1,6 * DIS # D9: 5,7,9 => CTR => D9: 3,8 * DIS # E5: 1,8 => CTR => E5: 3,6 * PRF # E5: 3,6 => SOL * PRF # E5: 3,6 => SOL * DIS # E5: 1,8 => CTR => E5: 3,6 * PRF # H6: 3,6 => SOL * DIS # H6: 7 => CTR => H6: 3,6 * DIS # F4: 2,7 => CTR => F4: 5,9 * DIS # F8: 2,7 => CTR => F8: 1,4,5,8,9 * DIS # G4: 2,4 => CTR => G4: 7 * PRF # G4: 7 => SOL * DIS # I3: 2,4 => CTR => I3: 1,8,9 * DIS # F8: 2,7 => CTR => F8: 1,4,5,8,9 * DIS # A3: 2,7 => CTR => A3: 3 * PRF # A3: 3 => SOL * DIS # E9: 3,7 => CTR => E9: 1,4,8,9 * PRF # A3: 3,7 => SOL * DIS # A3: 2 => CTR => A3: 3,7 * CNT 24 HDP CHAINS / 51 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A6,A8,A9,D5,E4,E6,F5,F6,H8,I4,I6,I9) * ....23..71.....6......56...638....1.427.........4..8..8..6.............3.......2. * PAIR A1: 5,9 BLK 1 B1: 5,9,4,6,8 # reduction candidate for 5,9 B1: 5,9 # 21 pairs C1: 5,9,4,6 # reduction candidate for 5,9 C1: 5,9 # 21 pairs B2: 5,9,7,8 # reduction candidate for 5,9 B2: 5,9 # 16 pairs C2: 5,9,2,3 # reduction candidate for 5,9 C2: 5,9 => CTR * ....23..71.....632....56...638...214427...3.....4328768..6.............3.......2. * PAIR A1: 5,9 ROW 1 G1: 5,9,1,4 # reduction candidate for 5,9 G1: 5,9 # 17 pairs H1: 5,9,4,8 # reduction candidate for 5,9 H1: 5,9 # 18 pairs * PAIR RESTART * PAIR A1: 5,9 BLK 1 B1: 5,9,4,6,8 # reduction candidate for 5,9 B1: 5,9 # 21 pairs C1: 5,9,4,6 # reduction candidate for 5,9 C1: 5,9 # 21 pairs B2: 5,9,7,8 # reduction candidate for 5,9 B2: 5,9 # 16 pairs * PAIR A1: 5,9 ROW 1 G1: 5,9,1,4 # reduction candidate for 5,9 G1: 5,9 # 17 pairs H1: 5,9,4,8 # reduction candidate for 5,9 H1: 5,9 # 18 pairs * PAIR A6: 5,9 BLK 4 B6: 5,9,1 # reduction candidate for 5,9 B6: 5,9 # 15 pairs C6: 5,9,1 # reduction candidate for 5,9 C6: 5,9 # 15 pairs * PAIR E4: 7,9 BLK 5 D4: 7,9,2,5 # reduction candidate for 7,9 D4: 7,9 => CTR * ....23..71.....6......56...638..5.1.427.........4.28768.263............3.......2. F4: 7,9,2,5 # reduction candidate for 7,9 F4: 7,9 => CTR * ....23..71.....6......56...6385...1.427.........4.28768.263............3.......2. F4: 2,5 => SOLVED * 586923147192784635374156298638295714427861359915437862853642971261579483749318526 * DURATION: 0:00:12.837036 START: 14:21:50.075538 END: 14:22:02.912574 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-339-base-pr-001.dot * REASONING * DIS # C2: 5,9 => CTR => C2: 2,3 * DIS C2: 2,3 # D4: 7,9 => CTR => D4: 2,5 * DIS C2: 2,3 + D4: 2,5 # F4: 7,9 => CTR => F4: 2,5 * PRF C2: 2,3 + D4: 2,5 + F4: 2,5 => SOL * STA C2: 2,3 + D4: 2,5 + F4: 2,5 * CNT 4 HDP CHAINS / 15 HYP OPENED
Header Info
Top 500 Minimum 17 339 solution: 586923147192784635374156298638295714427861359915437862853642971261579483749318526 info: 3173 FNBTHWY S8.f 3546 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 586923147192784635374156298638295714427861359915437862853642971261579483749318526 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 # B1: 5,9 => UNS * INC # C1: 5,9 => UNS * INC # B2: 5,9 => UNS * DIS # C2: 5,9 => CTR => C2: 2,3 * INC # C2: 2,3 => UNS * INC # G1: 5,9 => UNS * INC # H1: 5,9 => UNS * INC # B6: 5,9 => UNS * INC # C6: 5,9 => UNS * DIS # D4: 7,9 => CTR => D4: 2,5 * INC # D4: 2,5 => UNS * DIS # F4: 7,9 => CTR => F4: 2,5 * INC # F4: 2,5 => UNS * DIS # E2: 7,9 => CTR => E2: 4,8 * INC # E2: 4,8 => UNS * DIS # E7: 7,9 => CTR => E7: 1,3,4 * INC # E7: 1,3,4 => UNS * INC # E8: 7,9 => UNS * INC # E9: 7,9 => UNS * DIS # E5: 3,8 => CTR => E5: 1,6 * INC # E5: 1,6 => UNS * INC # D9: 3,8 => UNS * DIS # D9: 5,7,9 => CTR => D9: 3,8 * DIS # E5: 1,8 => CTR => E5: 3,6 * PRF # E5: 3,6 => SOL * INC # F8: 1,8 => UNS * INC # F9: 1,8 => UNS * PRF # E5: 3,6 => SOL * DIS # E5: 1,8 => CTR => E5: 3,6 * PRF # H6: 3,6 => SOL * DIS # H6: 7 => CTR => H6: 3,6 * INC # D4: 2,7 => UNS * DIS # F4: 2,7 => CTR => F4: 5,9 * INC # F4: 5,9 => UNS * INC # F7: 2,7 => UNS * DIS # F8: 2,7 => CTR => F8: 1,4,5,8,9 * INC # F8: 1,4,5,8,9 => UNS * DIS # G4: 2,4 => CTR => G4: 7 * PRF # G4: 7 => SOL * DIS # I3: 2,4 => CTR => I3: 1,8,9 * INC # I3: 1,8,9 => UNS * INC # D8: 2,7 => UNS * DIS # F8: 2,7 => CTR => F8: 1,4,5,8,9 * INC # F8: 1,4,5,8,9 => UNS * DIS # A3: 2,7 => CTR => A3: 3 * PRF # A3: 3 => SOL * INC # D9: 3,7 => UNS * DIS # E9: 3,7 => CTR => E9: 1,4,8,9 * INC # E9: 1,4,8,9 => UNS * PRF # A3: 3,7 => SOL * DIS # A3: 2 => CTR => A3: 3,7 * CNT 51 HDP CHAINS / 51 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B1: 5,9 => UNS * INC # C1: 5,9 => UNS * INC # B2: 5,9 => UNS * DIS # C2: 5,9 => CTR => C2: 2,3 * INC C2: 2,3 # G1: 5,9 => UNS * INC C2: 2,3 # H1: 5,9 => UNS * INC C2: 2,3 # B1: 5,9 => UNS * INC C2: 2,3 # C1: 5,9 => UNS * INC C2: 2,3 # B2: 5,9 => UNS * INC C2: 2,3 # G1: 5,9 => UNS * INC C2: 2,3 # H1: 5,9 => UNS * INC C2: 2,3 # B6: 5,9 => UNS * INC C2: 2,3 # C6: 5,9 => UNS * DIS C2: 2,3 # D4: 7,9 => CTR => D4: 2,5 * DIS C2: 2,3 + D4: 2,5 # F4: 7,9 => CTR => F4: 2,5 * PRF C2: 2,3 + D4: 2,5 + F4: 2,5 => SOL * STA C2: 2,3 + D4: 2,5 + F4: 2,5 * CNT 16 HDP CHAINS / 15 HYP OPENED