Analysis of xx-top500-500-base.sdk
Contents
Original Sudoku
level: medium
position: .2..7.5...9.3...........1..4...5...........36.......9..6.9.2...1..4.....5........ initial
Autosolve
position: 321.745.9.95321......59.1234...59...95.....3621.....95.6.9.2.5.1..4.5...5........ autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A3: 7 => CTR => A3: 6,8 * DIS # H2: 6,8 => CTR => H2: 4,7 * DIS # D4: 6,8 => CTR => D4: 2,7 * PRF # D4: 2,7 => SOL * PRF # D6: 6,8 => SOL * DIS # D6: 7 => CTR => D6: 6,8 * DIS # D9: 6,8 => CTR => D9: 1,7 * DIS # A3: 7 => CTR => A3: 6,8 * PRF # F6: 6,8 => SOL * DIS # F9: 6,8 => CTR => F9: 3,7 * DIS # H2: 6,8 => CTR => H2: 4,7 * DIS # B4: 7,8 => CTR => B4: 3 * PRF # B4: 3 => SOL * DIS # C4: 7,8 => CTR => C4: 3,6 * PRF # C6: 7,8 => SOL * DIS # C6: 6 => CTR => C6: 7,8 * DIS # C3: 7,8 => CTR => C3: 4 * PRF # C3: 4 => SOL * DIS # C7: 7,8 => CTR => C7: 3,4 * DIS # D4: 7,8 => CTR => D4: 2,6 * DIS # F6: 7,8 => CTR => F6: 3,6 * DIS # F9: 7,8 => CTR => F9: 3,6 * PRF # F9: 3,6 => SOL * DIS # C7: 7,8 => CTR => C7: 3,4 * PRF # G7: 7,8 => SOL * DIS # G7: 3 => CTR => G7: 7,8 * DIS # I7: 7,8 => CTR => I7: 1,4 * DIS # A3: 7,8 => CTR => A3: 6 * PRF # A3: 6 => SOL * CNT 29 HDP CHAINS / 52 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A3: 7 => CTR => A3: 6,8 * DIS A3: 6,8 # H2: 6,8 => CTR => H2: 4,7 * DIS A3: 6,8 + H2: 4,7 # G2: 7 => CTR => G2: 6,8 * DIS A3: 6,8 + H2: 4,7 + G2: 6,8 # D4: 6,8 => CTR => D4: 2,7 * PRF A3: 6,8 + H2: 4,7 + G2: 6,8 + D4: 2,7 => SOL * STA A3: 6,8 + H2: 4,7 + G2: 6,8 + D4: 2,7 * CNT 5 HDP CHAINS / 7 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .2..7.5...9.3...........1..4...5...........36.......9..6.9.2...1..4.....5........ | initial |
| 321.745.9.95321......59.1234...59...95.....3621.....95.6.9.2.5.1..4.5...5........ | autosolve |
| 321674589895321647674598123436259718958147236217836495763912854189465372542783961 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (12) A2: 6,8 D1: 6,8 F3: 6,8 H1: 6,8 C5: 7,8 D5: 1,2 E5: 1,4 F5: 7,8 G5: 2,4 A7: 7,8 C8: 2,9 C9: 2,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D5,E5: 1.. / D5 = 1 => 0 pairs (*) / E5 = 1 => 0 pairs (X) H4,I4: 1.. / H4 = 1 => 12 pairs (_) / I4 = 1 => 0 pairs (X) E7,I7: 1.. / E7 = 1 => 0 pairs (*) / I7 = 1 => 0 pairs (X) D5,D9: 1.. / D5 = 1 => 0 pairs (*) / D9 = 1 => 0 pairs (X) H4,H9: 1.. / H4 = 1 => 12 pairs (_) / H9 = 1 => 0 pairs (X) D4,D5: 2.. / D4 = 2 => 0 pairs (*) / D5 = 2 => 0 pairs (X) C8,C9: 2.. / C8 = 2 => 11 pairs (_) / C9 = 2 => 10 pairs (_) D5,G5: 2.. / D5 = 2 => 0 pairs (X) / G5 = 2 => 0 pairs (_) B4,C4: 3.. / B4 = 3 => 0 pairs (*) / C4 = 3 => 0 pairs (X) E6,F6: 3.. / E6 = 3 => 0 pairs (*) / F6 = 3 => 0 pairs (X) C4,C7: 3.. / C4 = 3 => 0 pairs (X) / C7 = 3 => 0 pairs (_) F6,F9: 3.. / F6 = 3 => 12 pairs (_) / F9 = 3 => 0 pairs (*) B3,C3: 4.. / B3 = 4 => 0 pairs (X) / C3 = 4 => 0 pairs (_) H2,I2: 4.. / H2 = 4 => 13 pairs (_) / I2 = 4 => 0 pairs (X) E5,E6: 4.. / E5 = 4 => 0 pairs (*) / E6 = 4 => 0 pairs (X) G5,G6: 4.. / G5 = 4 => 0 pairs (X) / G6 = 4 => 0 pairs (_) C7,B9: 4.. / C7 = 4 => 0 pairs (X) / B9 = 4 => 0 pairs (_) E5,G5: 4.. / E5 = 4 => 0 pairs (*) / G5 = 4 => 0 pairs (X) E6,G6: 4.. / E6 = 4 => 0 pairs (X) / G6 = 4 => 0 pairs (_) C7,I7: 4.. / C7 = 4 => 0 pairs (X) / I7 = 4 => 0 pairs (_) B3,B9: 4.. / B3 = 4 => 0 pairs (X) / B9 = 4 => 0 pairs (_) C3,C7: 4.. / C3 = 4 => 0 pairs (*) / C7 = 4 => 0 pairs (X) H2,H9: 4.. / H2 = 4 => 13 pairs (_) / H9 = 4 => 0 pairs (X) A2,A3: 6.. / A2 = 6 => 0 pairs (X) / A3 = 6 => 0 pairs (_) D1,F3: 6.. / D1 = 6 => 0 pairs (*) / F3 = 6 => 0 pairs (X) C4,C6: 6.. / C4 = 6 => 0 pairs (*) / C6 = 6 => 0 pairs (X) D1,H1: 6.. / D1 = 6 => 0 pairs (*) / H1 = 6 => 0 pairs (X) A3,F3: 6.. / A3 = 6 => 0 pairs (*) / F3 = 6 => 0 pairs (X) C4,D4: 6.. / C4 = 6 => 0 pairs (*) / D4 = 6 => 0 pairs (X) D9,F9: 7.. / D9 = 7 => 0 pairs (*) / F9 = 7 => 0 pairs (X) C5,F5: 7.. / C5 = 7 => 0 pairs (X) / F5 = 7 => 0 pairs (_) A3,A7: 7.. / A3 = 7 => 0 pairs (X) / A7 = 7 => 16 pairs (_) D1,F3: 8.. / D1 = 8 => 0 pairs (X) / F3 = 8 => 0 pairs (_) D1,H1: 8.. / D1 = 8 => 0 pairs (X) / H1 = 8 => 0 pairs (_) C5,F5: 8.. / C5 = 8 => 0 pairs (*) / F5 = 8 => 0 pairs (X) C8,C9: 9.. / C8 = 9 => 10 pairs (_) / C9 = 9 => 11 pairs (_) G8,G9: 9.. / G8 = 9 => 11 pairs (_) / G9 = 9 => 10 pairs (_) C8,G8: 9.. / C8 = 9 => 10 pairs (_) / G8 = 9 => 11 pairs (_) C9,G9: 9.. / C9 = 9 => 11 pairs (_) / G9 = 9 => 10 pairs (_) * DURATION: 0:01:17.700129 START: 19:47:17.179046 END: 19:48:34.879175 2017-05-04 * CP COUNT: (39) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A7,C5,C8,C9,D1,D5,E5,F3,F5,G5,H1) * 321.745.9.95321......59.1234...59...95.....3621.....95.6.9.2.5.1..4.5...5........ * PAIR A2: 6,8 BLK 1 A3: 6,8,7 # reduction candidate for 6,8 A3: 7 => CTR * 321874569695321...7..5961234.3659...95.21.43621674389586.932.5.1..4.5...5........ A3: 6,8 # 16 pairs * PAIR A2: 6,8 ROW 2 G2: 6,8,7 # reduction candidate for 6,8 G2: 6,8 # 15 pairs H2: 6,8,4,7 # reduction candidate for 6,8 H2: 6,8 => CTR * 321.745.9.953217.4.4.59.1234.3659.1795.21.436216.438957649.23511..4.5.7.5..1.7.4. H2: 4,7 # 13 pairs * PAIR D1: 6,8 COL D D4: 6,8,2,7 # reduction candidate for 6,8 D4: 6,8 => CTR * 3218745696953217...48596123483659217957218436216743895.649.2.511..4.5...5..1.7... D4: 2,7 => SOLVED * 321674589895321647674598123436259718958147236217836495763912854189465372542783961 D6: 6,8,7 # reduction candidate for 6,8 D6: 6,8 => SOLVED * 321674589895321647674598123436259718958147236217836495763912854189465372542783961 D6: 7 => CTR * 3218745696953217..8745961234.3659...957218436216743895.6.9823511..4.5...5..1.7... D9: 6,8,1,7 # reduction candidate for 6,8 D9: 6,8 => CTR * 321874569695321.....4596123436259...957148236218763495.639.2.541..4.56..54...7... D9: 1,7 # 13 pairs * PAIR F3: 6,8 ROW 3 A3: 6,8,7 # reduction candidate for 6,8 A3: 7 => CTR * 321874569695321...7..5961234.3659...95.21.43621674389586.932.5.1..4.5...5........ A3: 6,8 # 16 pairs * PAIR F3: 6,8 COL F F6: 6,8,3,7 # reduction candidate for 6,8 F6: 6,8 => SOLVED * 321674589895321647674598123436259718958147236217836495763912854189465372542783961 F6: 3,7 # 13 pairs F9: 6,8,3,7 # reduction candidate for 6,8 F9: 6,8 => CTR * 321.745.9.95321647674598123436259...9581472362178634957639128541..4.5...54.7..... F9: 3,7 # 13 pairs * PAIR H1: 6,8 BLK 3 G2: 6,8,7 # reduction candidate for 6,8 G2: 6,8 # 15 pairs H2: 6,8,4,7 # reduction candidate for 6,8 H2: 6,8 => CTR * 321.745.9.953217.4.4.59.1234.3659.1795.21.436216.438957649.23511..4.5.7.5..1.7.4. H2: 4,7 # 13 pairs * PAIR H1: 6,8 COL H H8: 6,8,7 # reduction candidate for 6,8 H8: 6,8 # 16 pairs H9: 6,8,1,4 # reduction candidate for 6,8 H9: 6,8 # 20 pairs * PAIR C5: 7,8 BLK 4 B4: 7,8,3 # reduction candidate for 7,8 B4: 7,8 => CTR * 3218745696953217...48596123483659217957218436216743895.649.2.511..4.5...5..1.7... B4: 3 => SOLVED * 321674589895321647674598123436259718958147236217836495763912854189465372542783961 C4: 7,8,3,6 # reduction candidate for 7,8 C4: 7,8 => CTR * 321.745.9.95321......59.12343.659...95.21.436216.43.95.63982.5.1..4.5...5........ C4: 3,6 # 13 pairs C6: 7,8,6 # reduction candidate for 7,8 C6: 7,8 => SOLVED * 321674589895321647674598123436259718958147236217836495763912854189465372542783961 C6: 6 => CTR * 3218745696953217...48596123483659217957218436216743895.649.2.511..4.5...5..1.7... * PAIR C5: 7,8 COL C C3: 7,8,4 # reduction candidate for 7,8 C3: 7,8 => CTR * 321874569695321....4.5961234.3659.1.957218436216743895.649.2.5117.4.5.82532187... C3: 4 => SOLVED * 321674589895321647674598123436259718958147236217836495763912854189465372542783961 C7: 7,8,3,4 # reduction candidate for 7,8 C7: 7,8 => CTR * 321.745.9.95321.....459.1234.3659...95.21.436216.43.95.6.9.2.5.1..4.5...5........ C7: 3,4 # 13 pairs * PAIR F5: 7,8 BLK 5 D4: 7,8,2,6 # reduction candidate for 7,8 D4: 7,8 => CTR * 321.745.9.95321......59.1234.6.59...95.21.43621..43.95.63982.5.1..4.5...5........ D4: 2,6 # 13 pairs D6: 7,8,6 # reduction candidate for 7,8 D6: 7,8 # 15 pairs F6: 7,8,3,6 # reduction candidate for 7,8 F6: 7,8 => CTR * 321874569695321......5961234.6259...95.14.23621.63.495.639.2.541..4.53..54.7.3... F6: 3,6 # 13 pairs * PAIR F5: 7,8 COL F F9: 7,8,3,6 # reduction candidate for 7,8 F9: 7,8 => CTR * 3218745696953217..8..596123483659...95.21.436216743895.6.9823511..4.5...5..1.7... F9: 3,6 => SOLVED * 321674589895321647674598123436259718958147236217836495763912854189465372542783961 * PAIR A7: 7,8 BLK 7 C7: 7,8,3,4 # reduction candidate for 7,8 C7: 7,8 => CTR * 321.745.9.95321.....459.1234.3659...95.21.436216.43.95.6.9.2.5.1..4.5...5........ C7: 3,4 # 13 pairs B8: 7,8,3 # reduction candidate for 7,8 B8: 7,8 # 15 pairs * PAIR A7: 7,8 ROW 7 G7: 7,8,3 # reduction candidate for 7,8 G7: 7,8 => SOLVED * 321674589895321647674598123436259718958147236217836495763912854189465372542783961 G7: 3 => CTR * 321874569695321...8..5961234.3659.1.95.21.436216.43.95.6.9823511..4.5...5..1.7... I7: 7,8,1,4 # reduction candidate for 7,8 I7: 7,8 => CTR * 321.745.9.95321....4.59.1234.3659...95.....3621.....95.6491235.1..4.5...5........ I7: 1,4 # 13 pairs * PAIR A7: 7,8 COL A A3: 7,8,6 # reduction candidate for 7,8 A3: 7,8 => CTR * 3218745696953217..8..596123483659...95.21.436216743895.6.9823511..4.5...5..1.7... A3: 6 => SOLVED * 321674589895321647674598123436259718958147236217836495763912854189465372542783961 * PAIR C8: 2,9 ROW 8 G8: 2,9,3,6,7,8 # reduction candidate for 2,9 G8: 2,9 # 14 pairs G8: 3,6,7,8 # 10 pairs * PAIR C9: 2,9 ROW 9 G9: 2,9,3,6,8 # reduction candidate for 2,9 G9: 3,6,8 # 13 pairs G9: 2,9 # 13 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-500-base-pr-000.dot * REASONING * DIS # A3: 7 => CTR => A3: 6,8 * DIS # H2: 6,8 => CTR => H2: 4,7 * DIS # D4: 6,8 => CTR => D4: 2,7 * PRF # D4: 2,7 => SOL * PRF # D6: 6,8 => SOL * DIS # D6: 7 => CTR => D6: 6,8 * DIS # D9: 6,8 => CTR => D9: 1,7 * DIS # A3: 7 => CTR => A3: 6,8 * PRF # F6: 6,8 => SOL * DIS # F9: 6,8 => CTR => F9: 3,7 * DIS # H2: 6,8 => CTR => H2: 4,7 * DIS # B4: 7,8 => CTR => B4: 3 * PRF # B4: 3 => SOL * DIS # C4: 7,8 => CTR => C4: 3,6 * PRF # C6: 7,8 => SOL * DIS # C6: 6 => CTR => C6: 7,8 * DIS # C3: 7,8 => CTR => C3: 4 * PRF # C3: 4 => SOL * DIS # C7: 7,8 => CTR => C7: 3,4 * DIS # D4: 7,8 => CTR => D4: 2,6 * DIS # F6: 7,8 => CTR => F6: 3,6 * DIS # F9: 7,8 => CTR => F9: 3,6 * PRF # F9: 3,6 => SOL * DIS # C7: 7,8 => CTR => C7: 3,4 * PRF # G7: 7,8 => SOL * DIS # G7: 3 => CTR => G7: 7,8 * DIS # I7: 7,8 => CTR => I7: 1,4 * DIS # A3: 7,8 => CTR => A3: 6 * PRF # A3: 6 => SOL * CNT 29 HDP CHAINS / 52 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A7,C5,C8,C9,D1,D5,E5,F3,F5,G5,H1) * 321.745.9.95321......59.1234...59...95.....3621.....95.6.9.2.5.1..4.5...5........ * PAIR A2: 6,8 BLK 1 A3: 6,8,7 # reduction candidate for 6,8 A3: 7 => CTR * 321874569695321...7..5961234.3659...95.21.43621674389586.932.5.1..4.5...5........ * PAIR A2: 6,8 ROW 2 G2: 6,8,7 # reduction candidate for 6,8 G2: 6,8 # 19 pairs H2: 6,8,4,7 # reduction candidate for 6,8 H2: 6,8 => CTR * 321.745.9.953217.4.4759.123473659.1.9582174362168...957649.2.5.1..4.5...5......4. * RESTART * PAIR A2: 6,8 ROW 2 G2: 6,8,7 # reduction candidate for 6,8 G2: 7 => CTR * 3218745696953217488745961234..2598..95.14.23621....49576891235413.4.5...54....... * PAIR RESTART * PAIR D1: 6,8 COL D D4: 6,8,2,7 # reduction candidate for 6,8 D4: 6,8 => CTR * 321.745.9.95321......5961234...59.1.95721843621.7438957649.2.511..4.5...5..1.7... D4: 2,7 => SOLVED * 321674589895321647674598123436259718958147236217836495763912854189465372542783961 * DURATION: 0:00:08.363006 START: 19:49:30.980222 END: 19:49:39.343228 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-500-base-pr-001.dot * REASONING * DIS # A3: 7 => CTR => A3: 6,8 * DIS A3: 6,8 # H2: 6,8 => CTR => H2: 4,7 * DIS A3: 6,8 + H2: 4,7 # G2: 7 => CTR => G2: 6,8 * DIS A3: 6,8 + H2: 4,7 + G2: 6,8 # D4: 6,8 => CTR => D4: 2,7 * PRF A3: 6,8 + H2: 4,7 + G2: 6,8 + D4: 2,7 => SOL * STA A3: 6,8 + H2: 4,7 + G2: 6,8 + D4: 2,7 * CNT 5 HDP CHAINS / 7 HYP OPENED
Header Info
Top 500 Minimum 17 500 solution: 321674589895321647674598123436259718958147236217836495763912854189465372542783961 info: 97182 FNBTHYK S8.f 16638 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 321674589895321647674598123436259718958147236217836495763912854189465372542783961 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 # A3: 6,8 => UNS * DIS # A3: 7 => CTR => A3: 6,8 * INC # G2: 6,8 => UNS * DIS # H2: 6,8 => CTR => H2: 4,7 * INC # H2: 4,7 => UNS * DIS # D4: 6,8 => CTR => D4: 2,7 * PRF # D4: 2,7 => SOL * PRF # D6: 6,8 => SOL * DIS # D6: 7 => CTR => D6: 6,8 * DIS # D9: 6,8 => CTR => D9: 1,7 * INC # D9: 1,7 => UNS * INC # A3: 6,8 => UNS * DIS # A3: 7 => CTR => A3: 6,8 * PRF # F6: 6,8 => SOL * INC # F6: 3,7 => UNS * DIS # F9: 6,8 => CTR => F9: 3,7 * INC # F9: 3,7 => UNS * INC # G2: 6,8 => UNS * DIS # H2: 6,8 => CTR => H2: 4,7 * INC # H2: 4,7 => UNS * INC # H8: 6,8 => UNS * INC # H9: 6,8 => UNS * DIS # B4: 7,8 => CTR => B4: 3 * PRF # B4: 3 => SOL * DIS # C4: 7,8 => CTR => C4: 3,6 * INC # C4: 3,6 => UNS * PRF # C6: 7,8 => SOL * DIS # C6: 6 => CTR => C6: 7,8 * DIS # C3: 7,8 => CTR => C3: 4 * PRF # C3: 4 => SOL * DIS # C7: 7,8 => CTR => C7: 3,4 * INC # C7: 3,4 => UNS * DIS # D4: 7,8 => CTR => D4: 2,6 * INC # D4: 2,6 => UNS * INC # D6: 7,8 => UNS * DIS # F6: 7,8 => CTR => F6: 3,6 * INC # F6: 3,6 => UNS * DIS # F9: 7,8 => CTR => F9: 3,6 * PRF # F9: 3,6 => SOL * DIS # C7: 7,8 => CTR => C7: 3,4 * INC # C7: 3,4 => UNS * INC # B8: 7,8 => UNS * PRF # G7: 7,8 => SOL * DIS # G7: 3 => CTR => G7: 7,8 * DIS # I7: 7,8 => CTR => I7: 1,4 * INC # I7: 1,4 => UNS * DIS # A3: 7,8 => CTR => A3: 6 * PRF # A3: 6 => SOL * INC # G8: 2,9 => UNS * INC # G8: 3,6,7,8 => UNS * INC # G9: 2,9 => UNS * INC # G9: 3,6,8 => UNS * CNT 52 HDP CHAINS / 52 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A3: 6,8 => UNS * DIS # A3: 7 => CTR => A3: 6,8 * INC A3: 6,8 # G2: 6,8 => UNS * DIS A3: 6,8 # H2: 6,8 => CTR => H2: 4,7 * INC A3: 6,8 + H2: 4,7 # G2: 6,8 => UNS * DIS A3: 6,8 + H2: 4,7 # G2: 7 => CTR => G2: 6,8 * DIS A3: 6,8 + H2: 4,7 + G2: 6,8 # D4: 6,8 => CTR => D4: 2,7 * PRF A3: 6,8 + H2: 4,7 + G2: 6,8 + D4: 2,7 => SOL * STA A3: 6,8 + H2: 4,7 + G2: 6,8 + D4: 2,7 * CNT 8 HDP CHAINS / 7 HYP OPENED