Analysis of xx-top500-362-base.sdk
Contents
Original Sudoku
level: medium
position: 2...1.5...7.3........4.......4...17......9..38............456....3.......9....... initial
Autosolve
position: 23..1759447539.81.9.145.3.73.45..179.5.1.94838197342.....94563..43.719...9...374. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # C9: 2 => SOL * DIS # F3: 2 => CTR => F3: 6,8 * DIS # F3: 2 => CTR => F3: 6,8 * PRF # D9: 6,8 => SOL * DIS # F3: 2,6 => CTR => F3: 8 * PRF # F3: 8 => SOL * DIS # F3: 2,6 => CTR => F3: 8 * PRF # F3: 8 => SOL * DIS # C5: 7 => CTR => C5: 2,6 * DIS # E4: 2,6 => CTR => E4: 8 * PRF # E4: 8 => SOL * PRF # C5: 6,7 => SOL * DIS # C5: 2 => CTR => C5: 6,7 * PRF # E4: 6,8 => SOL * DIS # E4: 2 => CTR => E4: 6,8 * DIS # F3: 2 => CTR => F3: 6,8 * DIS # E4: 2,6 => CTR => E4: 8 * PRF # E4: 8 => SOL * DIS # C5: 7 => CTR => C5: 2,6 * DIS # C7: 2,8 => CTR => C7: 7 * DIS # I7: 1 => CTR => I7: 2,8 * PRF # D9: 6,8 => SOL * PRF # C9: 2 => SOL * PRF # E4: 6,8 => SOL * DIS # E4: 2 => CTR => E4: 6,8 * DIS # I8: 2,5 => CTR => I8: 8 * CNT 26 HDP CHAINS / 41 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # C9: 2 => SOL * STA C9: 2 * CNT 1 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 2...1.5...7.3........4.......4...17......9..38............456....3.......9....... | initial |
| 23..1759447539.81.9.145.3.73.45..179.5.1.94838197342.....94563..43.719...9...374. | autosolve |
| 238617594475392816961458327324586179756129483819734265187945632643271958592863741 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (19) C1: 6,8 B3: 6,8 D1: 6,8 F2: 2,6 I2: 2,6 H3: 2,6 B4: 2,6 A5: 6,7 F4: 6,8 E5: 2,6 H6: 5,6 I6: 5,6 A7: 1,7 B7: 2,8 A8: 5,6 A9: 1,5 E9: 6,8 H8: 2,5 I9: 1,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A7,A9: 1.. / A7 = 1 => 18 pairs (_) / A9 = 1 => 0 pairs (X) I7,I9: 1.. / I7 = 1 => 0 pairs (X) / I9 = 1 => 18 pairs (_) A7,I7: 1.. / A7 = 1 => 18 pairs (_) / I7 = 1 => 0 pairs (X) A9,I9: 1.. / A9 = 1 => 0 pairs (X) / I9 = 1 => 18 pairs (_) F2,F3: 2.. / F2 = 2 => 14 pairs (_) / F3 = 2 => 0 pairs (X) I2,H3: 2.. / I2 = 2 => 0 pairs (X) / H3 = 2 => 14 pairs (_) B4,C5: 2.. / B4 = 2 => 0 pairs (*) / C5 = 2 => 0 pairs (X) E4,E5: 2.. / E4 = 2 => 0 pairs (X) / E5 = 2 => 0 pairs (_) D8,D9: 2.. / D8 = 2 => 0 pairs (*) / D9 = 2 => 0 pairs (X) F2,I2: 2.. / F2 = 2 => 14 pairs (_) / I2 = 2 => 0 pairs (X) F3,H3: 2.. / F3 = 2 => 0 pairs (X) / H3 = 2 => 14 pairs (_) B4,E4: 2.. / B4 = 2 => 0 pairs (*) / E4 = 2 => 0 pairs (X) C5,E5: 2.. / C5 = 2 => 0 pairs (X) / E5 = 2 => 0 pairs (_) C9,D9: 2.. / C9 = 2 => 0 pairs (*) / D9 = 2 => 0 pairs (X) B4,B7: 2.. / B4 = 2 => 0 pairs (*) / B7 = 2 => 0 pairs (X) H3,H8: 2.. / H3 = 2 => 14 pairs (_) / H8 = 2 => 0 pairs (X) H6,I6: 5.. / H6 = 5 => 0 pairs (X) / I6 = 5 => 14 pairs (_) A8,A9: 5.. / A8 = 5 => 0 pairs (X) / A9 = 5 => 18 pairs (_) A9,I9: 5.. / A9 = 5 => 18 pairs (_) / I9 = 5 => 0 pairs (X) H6,H8: 5.. / H6 = 5 => 0 pairs (X) / H8 = 5 => 14 pairs (_) C1,B3: 6.. / C1 = 6 => 0 pairs (X) / B3 = 6 => 0 pairs (_) I2,H3: 6.. / I2 = 6 => 14 pairs (_) / H3 = 6 => 0 pairs (X) H6,I6: 6.. / H6 = 6 => 14 pairs (_) / I6 = 6 => 0 pairs (X) A8,C9: 6.. / A8 = 6 => 18 pairs (_) / C9 = 6 => 0 pairs (X) C1,D1: 6.. / C1 = 6 => 0 pairs (X) / D1 = 6 => 0 pairs (_) F2,I2: 6.. / F2 = 6 => 0 pairs (X) / I2 = 6 => 14 pairs (_) A8,D8: 6.. / A8 = 6 => 18 pairs (_) / D8 = 6 => 0 pairs (X) A5,A8: 6.. / A5 = 6 => 0 pairs (X) / A8 = 6 => 18 pairs (_) B3,B4: 6.. / B3 = 6 => 0 pairs (*) / B4 = 6 => 0 pairs (X) H3,H6: 6.. / H3 = 6 => 0 pairs (X) / H6 = 6 => 14 pairs (_) I2,I6: 6.. / I2 = 6 => 14 pairs (_) / I6 = 6 => 0 pairs (X) A5,C5: 7.. / A5 = 7 => 18 pairs (_) / C5 = 7 => 0 pairs (X) A7,C7: 7.. / A7 = 7 => 0 pairs (X) / C7 = 7 => 18 pairs (_) A5,A7: 7.. / A5 = 7 => 18 pairs (_) / A7 = 7 => 0 pairs (X) C5,C7: 7.. / C5 = 7 => 0 pairs (X) / C7 = 7 => 18 pairs (_) C1,B3: 8.. / C1 = 8 => 0 pairs (*) / B3 = 8 => 0 pairs (X) D1,F3: 8.. / D1 = 8 => 0 pairs (X) / F3 = 8 => 0 pairs (_) E4,F4: 8.. / E4 = 8 => 0 pairs (*) / F4 = 8 => 0 pairs (X) I7,I8: 8.. / I7 = 8 => 0 pairs (X) / I8 = 8 => 22 pairs (_) C1,D1: 8.. / C1 = 8 => 0 pairs (*) / D1 = 8 => 0 pairs (X) B3,F3: 8.. / B3 = 8 => 0 pairs (X) / F3 = 8 => 0 pairs (_) D8,I8: 8.. / D8 = 8 => 0 pairs (X) / I8 = 8 => 22 pairs (_) B3,B7: 8.. / B3 = 8 => 0 pairs (X) / B7 = 8 => 0 pairs (_) E4,E9: 8.. / E4 = 8 => 0 pairs (*) / E9 = 8 => 0 pairs (X) F3,F4: 8.. / F3 = 8 => 0 pairs (*) / F4 = 8 => 0 pairs (X) * DURATION: 0:01:20.934628 START: 15:10:09.246599 END: 15:11:30.181227 2017-05-04 * CP COUNT: (45) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A7,A8,A9,B3,B4,B7,C1,D1,E5,E9,F2,F4,H3,H6,H8,I2,I6,I9) * 23..1759447539.81.9.145.3.73.45..179.5.1.94838197342.....94563..43.719...9...374. * PAIR C1: 6,8 COL C C9: 6,8,2 # reduction candidate for 6,8 C9: 2 => SOLVED * 238617594475392816961458327324586179756129483819734265187945632643271958592863741 C9: 6,8 # 24 pairs * PAIR B3: 6,8 ROW 3 F3: 6,8,2 # reduction candidate for 6,8 F3: 2 => CTR * 23.8175944753968129814523673645281797521694838197342561279456386432719...9...374. F3: 6,8 # 14 pairs * PAIR D1: 6,8 BLK 2 F3: 6,8,2 # reduction candidate for 6,8 F3: 2 => CTR * 23.8175944753968129814523673645281797521694838197342561279456386432719...9...374. F3: 6,8 # 14 pairs * PAIR D1: 6,8 COL D D8: 6,8,2 # reduction candidate for 6,8 D8: 6,8 # 24 pairs D9: 6,8,2 # reduction candidate for 6,8 D9: 6,8 => SOLVED * 238617594475392816961458327324586179756129483819734265187945632643271958592863741 D9: 2 # 24 pairs * PAIR F2: 2,6 BLK 2 F3: 2,6,8 # reduction candidate for 2,6 F3: 2,6 => CTR * 23.81759447539.81.98145.3.73645281797521694838197342..1279456386432719...9...374. F3: 8 => SOLVED * 238617594475392816961458327324586179756129483819734265187945632643271958592863741 * PAIR H3: 2,6 ROW 3 F3: 2,6,8 # reduction candidate for 2,6 F3: 2,6 => CTR * 23.81759447539.81.98145.3.73645281797521694838197342..1279456386432719...9...374. F3: 8 => SOLVED * 238617594475392816961458327324586179756129483819734265187945632643271958592863741 * PAIR B4: 2,6 BLK 4 C5: 2,6,7 # reduction candidate for 2,6 C5: 7 => CTR * 23..1759447539.81.9.145.3.73245..1796571294838197342..782945631543671928196..374. C5: 2,6 # 18 pairs * PAIR B4: 2,6 ROW 4 E4: 2,6,8 # reduction candidate for 2,6 E4: 2,6 => CTR * 23.81759447539.81.98145.3.73645281797521.94838197342.....94563..43.719...9..8374. E4: 8 => SOLVED * 238617594475392816961458327324586179756129483819734265187945632643271958592863741 * PAIR A5: 6,7 BLK 4 C5: 6,7,2 # reduction candidate for 6,7 C5: 6,7 => SOLVED * 238617594475392816961458327324586179756129483819734265187945632643271958592863741 C5: 2 => CTR * 23..1759447539.81.9.145.3.73.45..1797521694838197342..1279456386438719...9...374. * PAIR F4: 6,8 BLK 5 E4: 6,8,2 # reduction candidate for 6,8 E4: 6,8 => SOLVED * 238617594475392816961458327324586179756129483819734265187945632643271958592863741 E4: 2 => CTR * 23..1759447539.81.9.145.3.73.4528179.521694838197342...279456386438719...9...374. * PAIR F4: 6,8 COL F F3: 6,8,2 # reduction candidate for 6,8 F3: 2 => CTR * 23.8175944753968129814523673645281797521694838197342561279456386432719...9...374. F3: 6,8 # 14 pairs * PAIR E5: 2,6 BLK 5 E4: 2,6,8 # reduction candidate for 2,6 E4: 2,6 => CTR * 23.81759447539.81.98145.3.73645281797521.94838197342.....94563..43.719...9..8374. E4: 8 => SOLVED * 238617594475392816961458327324586179756129483819734265187945632643271958592863741 * PAIR E5: 2,6 ROW 5 C5: 2,6,7 # reduction candidate for 2,6 C5: 7 => CTR * 23..1759447539.81.9.145.3.73245..1796571294838197342..782945631543671928196..374. C5: 2,6 # 18 pairs * PAIR B7: 2,8 BLK 7 C7: 2,8,7 # reduction candidate for 2,8 C7: 2,8 => CTR * 23..1759447539.8129.14523673.45..179.571294838197342..7..945631.43.719.819...3745 C7: 7 # 18 pairs C9: 2,8,6 # reduction candidate for 2,8 C9: 2,8 # 18 pairs * PAIR B7: 2,8 ROW 7 I7: 2,8,1 # reduction candidate for 2,8 I7: 1 => CTR * 23..1759447539.8129.145236736452817975.1.94838197342.....945631.43.719.819...3745 I7: 2,8 # 18 pairs * PAIR E9: 6,8 BLK 8 D8: 6,8,2 # reduction candidate for 6,8 D8: 6,8 # 24 pairs D9: 6,8,2 # reduction candidate for 6,8 D9: 6,8 => SOLVED * 238617594475392816961458327324586179756129483819734265187945632643271958592863741 D9: 2 # 24 pairs * PAIR E9: 6,8 ROW 9 C9: 6,8,2 # reduction candidate for 6,8 C9: 2 => SOLVED * 238617594475392816961458327324586179756129483819734265187945632643271958592863741 C9: 6,8 # 24 pairs * PAIR E9: 6,8 COL E E4: 6,8,2 # reduction candidate for 6,8 E4: 6,8 => SOLVED * 238617594475392816961458327324586179756129483819734265187945632643271958592863741 E4: 2 => CTR * 23..1759447539.81.9.145.3.73.4528179.521694838197342...279456386438719...9...374. * PAIR H8: 2,5 BLK 9 I8: 2,5,8 # reduction candidate for 2,5 I8: 2,5 => CTR * 23..1759447539.81.9.145.3.73.45..179.5.1.94838197342.....945638.438719...98263741 I8: 8 # 22 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-362-base-pr-000.dot * REASONING * PRF # C9: 2 => SOL * DIS # F3: 2 => CTR => F3: 6,8 * DIS # F3: 2 => CTR => F3: 6,8 * PRF # D9: 6,8 => SOL * DIS # F3: 2,6 => CTR => F3: 8 * PRF # F3: 8 => SOL * DIS # F3: 2,6 => CTR => F3: 8 * PRF # F3: 8 => SOL * DIS # C5: 7 => CTR => C5: 2,6 * DIS # E4: 2,6 => CTR => E4: 8 * PRF # E4: 8 => SOL * PRF # C5: 6,7 => SOL * DIS # C5: 2 => CTR => C5: 6,7 * PRF # E4: 6,8 => SOL * DIS # E4: 2 => CTR => E4: 6,8 * DIS # F3: 2 => CTR => F3: 6,8 * DIS # E4: 2,6 => CTR => E4: 8 * PRF # E4: 8 => SOL * DIS # C5: 7 => CTR => C5: 2,6 * DIS # C7: 2,8 => CTR => C7: 7 * DIS # I7: 1 => CTR => I7: 2,8 * PRF # D9: 6,8 => SOL * PRF # C9: 2 => SOL * PRF # E4: 6,8 => SOL * DIS # E4: 2 => CTR => E4: 6,8 * DIS # I8: 2,5 => CTR => I8: 8 * CNT 26 HDP CHAINS / 41 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A7,A8,A9,B3,B4,B7,C1,D1,E5,E9,F2,F4,H3,H6,H8,I2,I6,I9) * 23..1759447539.81.9.145.3.73.45..179.5.1.94838197342.....94563..43.719...9...374. * PAIR C1: 6,8 COL C C9: 6,8,2 # reduction candidate for 6,8 C9: 2 => SOLVED * 238617594475392816961458327324586179756129483819734265187945632643271958592863741 * DURATION: 0:00:02.951832 START: 15:12:14.572491 END: 15:12:17.524323 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-362-base-pr-001.dot * REASONING * PRF # C9: 2 => SOL * STA C9: 2 * CNT 1 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 362 solution: 238617594475392816961458327324586179756129483819734265187945632643271958592863741 info: 4947 FNBHWX S8.f 45357 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 238617594475392816961458327324586179756129483819734265187945632643271958592863741 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 # C9: 6,8 => UNS * PRF # C9: 2 => SOL * INC # F3: 6,8 => UNS * DIS # F3: 2 => CTR => F3: 6,8 * INC # F3: 6,8 => UNS * DIS # F3: 2 => CTR => F3: 6,8 * INC # D8: 6,8 => UNS * PRF # D9: 6,8 => SOL * INC # D9: 2 => UNS * DIS # F3: 2,6 => CTR => F3: 8 * PRF # F3: 8 => SOL * DIS # F3: 2,6 => CTR => F3: 8 * PRF # F3: 8 => SOL * INC # C5: 2,6 => UNS * DIS # C5: 7 => CTR => C5: 2,6 * DIS # E4: 2,6 => CTR => E4: 8 * PRF # E4: 8 => SOL * PRF # C5: 6,7 => SOL * DIS # C5: 2 => CTR => C5: 6,7 * PRF # E4: 6,8 => SOL * DIS # E4: 2 => CTR => E4: 6,8 * INC # F3: 6,8 => UNS * DIS # F3: 2 => CTR => F3: 6,8 * DIS # E4: 2,6 => CTR => E4: 8 * PRF # E4: 8 => SOL * INC # C5: 2,6 => UNS * DIS # C5: 7 => CTR => C5: 2,6 * DIS # C7: 2,8 => CTR => C7: 7 * INC # C7: 7 => UNS * INC # C9: 2,8 => UNS * INC # I7: 2,8 => UNS * DIS # I7: 1 => CTR => I7: 2,8 * INC # D8: 6,8 => UNS * PRF # D9: 6,8 => SOL * INC # D9: 2 => UNS * INC # C9: 6,8 => UNS * PRF # C9: 2 => SOL * PRF # E4: 6,8 => SOL * DIS # E4: 2 => CTR => E4: 6,8 * DIS # I8: 2,5 => CTR => I8: 8 * INC # I8: 8 => UNS * CNT 41 HDP CHAINS / 41 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C9: 6,8 => UNS * PRF # C9: 2 => SOL * STA C9: 2 * CNT 2 HDP CHAINS / 2 HYP OPENED