Analysis of xx-top500-124-base.sdk
Contents
Original Sudoku
level: medium
position: ...4.5.2..1.7......6....8....4....57....6....7............9.1.35..............6.. initial
Autosolve
position: ..7415926.1.786534465.2.8716.413.257.5.26741.721.5436..7659.1435..6417.214..7.6.5 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # A5: 3,8 => SOL * DIS # A5: 9 => CTR => A5: 3,8 * DIS # B8: 3,8 => CTR => B8: 9 * PRF # B8: 9 => SOL * PRF # C9: 8 => SOL * DIS # A5: 8,9 => CTR => A5: 3 * PRF # A5: 3 => SOL * PRF # C5: 8,9 => SOL * DIS # C5: 3 => CTR => C5: 8,9 * PRF # B8: 8,9 => SOL * DIS # B8: 3 => CTR => B8: 8,9 * DIS # A5: 8,9 => CTR => A5: 3 * PRF # A5: 3 => SOL * PRF # C5: 8,9 => SOL * DIS # C5: 3 => CTR => C5: 8,9 * DIS # C9: 9 => CTR => C9: 2,8 * PRF # F9: 2,8 => SOL * DIS # F9: 3 => CTR => F9: 2,8 * DIS # F9: 3,8 => CTR => F9: 2 * PRF # F9: 2 => SOL * PRF # B8: 8,9 => SOL * DIS # B8: 3 => CTR => B8: 8,9 * DIS # C8: 8,9 => CTR => C8: 3 * PRF # C8: 3 => SOL * PRF # C9: 8,9 => SOL * DIS # C9: 2 => CTR => C9: 8,9 * CNT 26 HDP CHAINS / 28 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # A5: 3,8 => SOL * STA A5: 3,8 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...4.5.2..1.7......6....8....4....57....6....7............9.1.35..............6.. | initial |
| ..7415926.1.786534465.2.8716.413.257.5.26741.721.5436..7659.1435..6417.214..7.6.5 | autosolve |
| 837415926912786534465923871684139257359267418721854369276598143593641782148372695 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) A1: 3,8 B1: 3,8 A2: 2,9 C2: 2,9 D3: 3,9 F3: 3,9 B4: 8,9 F4: 8,9 D6: 8,9 I5: 8,9 I6: 8,9 A7: 2,8 F7: 2,8 D9: 3,8 H8: 8,9 H9: 8,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A2,C2: 2.. / A2 = 2 => 0 pairs (X) / C2 = 2 => 0 pairs (_) A7,C9: 2.. / A7 = 2 => 0 pairs (*) / C9 = 2 => 0 pairs (X) F7,F9: 2.. / F7 = 2 => 0 pairs (X) / F9 = 2 => 0 pairs (_) A7,F7: 2.. / A7 = 2 => 0 pairs (*) / F7 = 2 => 0 pairs (X) C9,F9: 2.. / C9 = 2 => 0 pairs (X) / F9 = 2 => 0 pairs (_) A2,A7: 2.. / A2 = 2 => 0 pairs (X) / A7 = 2 => 0 pairs (_) C2,C9: 2.. / C2 = 2 => 0 pairs (*) / C9 = 2 => 0 pairs (X) A1,B1: 3.. / A1 = 3 => 0 pairs (X) / B1 = 3 => 0 pairs (_) D3,F3: 3.. / D3 = 3 => 0 pairs (X) / F3 = 3 => 0 pairs (_) A5,C5: 3.. / A5 = 3 => 0 pairs (*) / C5 = 3 => 0 pairs (X) B8,C8: 3.. / B8 = 3 => 0 pairs (X) / C8 = 3 => 0 pairs (_) D9,F9: 3.. / D9 = 3 => 0 pairs (*) / F9 = 3 => 0 pairs (X) A1,A5: 3.. / A1 = 3 => 0 pairs (X) / A5 = 3 => 0 pairs (_) B1,B8: 3.. / B1 = 3 => 0 pairs (*) / B8 = 3 => 0 pairs (X) C5,C8: 3.. / C5 = 3 => 0 pairs (X) / C8 = 3 => 0 pairs (_) D3,D9: 3.. / D3 = 3 => 0 pairs (X) / D9 = 3 => 0 pairs (_) F3,F9: 3.. / F3 = 3 => 0 pairs (*) / F9 = 3 => 0 pairs (X) A1,B1: 8.. / A1 = 8 => 0 pairs (*) / B1 = 8 => 0 pairs (X) F4,D6: 8.. / F4 = 8 => 0 pairs (X) / D6 = 8 => 0 pairs (_) I5,I6: 8.. / I5 = 8 => 0 pairs (*) / I6 = 8 => 0 pairs (X) H8,H9: 8.. / H8 = 8 => 17 pairs (_) / H9 = 8 => 0 pairs (X) B4,F4: 8.. / B4 = 8 => 0 pairs (*) / F4 = 8 => 0 pairs (X) D6,I6: 8.. / D6 = 8 => 0 pairs (*) / I6 = 8 => 0 pairs (X) A7,F7: 8.. / A7 = 8 => 0 pairs (X) / F7 = 8 => 0 pairs (_) D6,D9: 8.. / D6 = 8 => 0 pairs (*) / D9 = 8 => 0 pairs (X) A2,C2: 9.. / A2 = 9 => 0 pairs (*) / C2 = 9 => 0 pairs (X) D3,F3: 9.. / D3 = 9 => 0 pairs (*) / F3 = 9 => 0 pairs (X) F4,D6: 9.. / F4 = 9 => 0 pairs (*) / D6 = 9 => 0 pairs (X) I5,I6: 9.. / I5 = 9 => 0 pairs (X) / I6 = 9 => 0 pairs (_) H8,H9: 9.. / H8 = 9 => 0 pairs (X) / H9 = 9 => 17 pairs (_) B4,F4: 9.. / B4 = 9 => 0 pairs (X) / F4 = 9 => 0 pairs (_) D6,I6: 9.. / D6 = 9 => 0 pairs (X) / I6 = 9 => 0 pairs (_) C9,H9: 9.. / C9 = 9 => 0 pairs (X) / H9 = 9 => 17 pairs (_) A2,A5: 9.. / A2 = 9 => 0 pairs (*) / A5 = 9 => 0 pairs (X) B4,B8: 9.. / B4 = 9 => 0 pairs (X) / B8 = 9 => 0 pairs (_) D3,D6: 9.. / D3 = 9 => 0 pairs (*) / D6 = 9 => 0 pairs (X) F3,F4: 9.. / F3 = 9 => 0 pairs (X) / F4 = 9 => 0 pairs (_) * DURATION: 0:01:01.900397 START: 07:00:16.218130 END: 07:01:18.118527 2017-05-04 * CP COUNT: (37) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A2,A7,B1,B4,C2,D3,D6,D9,F3,F4,F7,H8,H9,I5,I6) * ..7415926.1.786534465.2.8716.413.257.5.26741.721.5436..7659.1435..6417.214..7.6.5 * PAIR A1: 3,8 COL A A5: 3,8,9 # reduction candidate for 3,8 A5: 3,8 => SOLVED * 837415926912786534465923871684139257359267418721854369276598143593641782148372695 A5: 9 => CTR * 387415926.1.786534465.2.87169413.257.5.26741.721.5436..7659.1435..6417.214..7.6.5 * PAIR B1: 3,8 COL B B8: 3,8,9 # reduction candidate for 3,8 B8: 3,8 => CTR * ..7415926.1.786534465.2.871694138257.5.2674197219543688765921435396417.214..7.6.5 B8: 9 => SOLVED * 837415926912786534465923871684139257359267418721854369276598143593641782148372695 * PAIR C2: 2,9 COL C C9: 2,9,8 # reduction candidate for 2,9 C9: 8 => SOLVED * 837415926912786534465923871684139257359267418721854369276598143593641782148372695 C9: 2,9 # 19 pairs * PAIR B4: 8,9 BLK 4 A5: 8,9,3 # reduction candidate for 8,9 A5: 8,9 => CTR * 387415926.1.786534465.2.87169413825785326741972195436827659.1435..6417.214..7.6.5 A5: 3 => SOLVED * 837415926912786534465923871684139257359267418721854369276598143593641782148372695 C5: 8,9,3 # reduction candidate for 8,9 C5: 8,9 => SOLVED * 837415926912786534465923871684139257359267418721854369276598143593641782148372695 C5: 3 => CTR * 387415926.1.786534465.2.87169413825785326741972195436827659.14353.6417.214..7.6.5 * PAIR B4: 8,9 COL B B8: 8,9,3 # reduction candidate for 8,9 B8: 8,9 => SOLVED * 837415926912786534465923871684139257359267418721854369276598143593641782148372695 B8: 3 => CTR * ..7415926.1.786534465.2.871694138257.5.2674197219543688765921435396417.214..7.6.5 * PAIR I5: 8,9 ROW 5 A5: 8,9,3 # reduction candidate for 8,9 A5: 8,9 => CTR * 387415926.1.786534465.2.87169413825785326741972195436827659.1435..6417.214..7.6.5 A5: 3 => SOLVED * 837415926912786534465923871684139257359267418721854369276598143593641782148372695 C5: 8,9,3 # reduction candidate for 8,9 C5: 8,9 => SOLVED * 837415926912786534465923871684139257359267418721854369276598143593641782148372695 C5: 3 => CTR * 387415926.1.786534465.2.87169413825785326741972195436827659.14353.6417.214..7.6.5 * PAIR A7: 2,8 BLK 7 C9: 2,8,9 # reduction candidate for 2,8 C9: 9 => CTR * ..7415926.12786534465.2.8716.413.257.5.26741.721.5436.2765981435..6417.2149372685 C9: 2,8 # 17 pairs * PAIR F7: 2,8 BLK 8 F9: 2,8,3 # reduction candidate for 2,8 F9: 2,8 => SOLVED * 837415926912786534465923871684139257359267418721854369276598143593641782148372695 F9: 3 => CTR * ..7415926219786534465329871694138257.5.26741972195436887659214353.6417.2142873695 * PAIR D9: 3,8 BLK 8 F9: 3,8,2 # reduction candidate for 3,8 F9: 3,8 => CTR * ..7415926219786534465.2.8716.413.2579532674187218543698765921435..6417.2142.7.695 F9: 2 => SOLVED * 837415926912786534465923871684139257359267418721854369276598143593641782148372695 * PAIR H8: 8,9 ROW 8 B8: 8,9,3 # reduction candidate for 8,9 B8: 8,9 => SOLVED * 837415926912786534465923871684139257359267418721854369276598143593641782148372695 B8: 3 => CTR * ..7415926.1.786534465.2.871694138257.5.2674197219543688765921435396417.214..7.6.5 C8: 8,9,3 # reduction candidate for 8,9 C8: 8,9 => CTR * 387415926.1.786534465.2.87169413825785326741972195436827659.14353.6417.214..7.6.5 C8: 3 => SOLVED * 837415926912786534465923871684139257359267418721854369276598143593641782148372695 * PAIR H9: 8,9 ROW 9 C9: 8,9,2 # reduction candidate for 8,9 C9: 8,9 => SOLVED * 837415926912786534465923871684139257359267418721854369276598143593641782148372695 C9: 2 => CTR * ..7415926219786534465.2.8716.413.25795326741872185436987659.1435..6417.2142.7.695 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-124-base-pr-000.dot * REASONING * PRF # A5: 3,8 => SOL * DIS # A5: 9 => CTR => A5: 3,8 * DIS # B8: 3,8 => CTR => B8: 9 * PRF # B8: 9 => SOL * PRF # C9: 8 => SOL * DIS # A5: 8,9 => CTR => A5: 3 * PRF # A5: 3 => SOL * PRF # C5: 8,9 => SOL * DIS # C5: 3 => CTR => C5: 8,9 * PRF # B8: 8,9 => SOL * DIS # B8: 3 => CTR => B8: 8,9 * DIS # A5: 8,9 => CTR => A5: 3 * PRF # A5: 3 => SOL * PRF # C5: 8,9 => SOL * DIS # C5: 3 => CTR => C5: 8,9 * DIS # C9: 9 => CTR => C9: 2,8 * PRF # F9: 2,8 => SOL * DIS # F9: 3 => CTR => F9: 2,8 * DIS # F9: 3,8 => CTR => F9: 2 * PRF # F9: 2 => SOL * PRF # B8: 8,9 => SOL * DIS # B8: 3 => CTR => B8: 8,9 * DIS # C8: 8,9 => CTR => C8: 3 * PRF # C8: 3 => SOL * PRF # C9: 8,9 => SOL * DIS # C9: 2 => CTR => C9: 8,9 * CNT 26 HDP CHAINS / 28 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A2,A7,B1,B4,C2,D3,D6,D9,F3,F4,F7,H8,H9,I5,I6) * ..7415926.1.786534465.2.8716.413.257.5.26741.721.5436..7659.1435..6417.214..7.6.5 * PAIR A1: 3,8 COL A A5: 3,8,9 # reduction candidate for 3,8 A5: 3,8 => SOLVED * 837415926912786534465923871684139257359267418721854369276598143593641782148372695 * DURATION: 0:00:01.868742 START: 07:01:50.115721 END: 07:01:51.984463 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-124-base-pr-001.dot * REASONING * PRF # A5: 3,8 => SOL * STA A5: 3,8 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 124 solution: 837415926912786534465923871684139257359267418721854369276598143593641782148372695 info: 1808 FNBWY S8.f 9308 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 837415926912786534465923871684139257359267418721854369276598143593641782148372695 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:
* PRF # A5: 3,8 => SOL * DIS # A5: 9 => CTR => A5: 3,8 * DIS # B8: 3,8 => CTR => B8: 9 * PRF # B8: 9 => SOL * INC # C9: 2,9 => UNS * PRF # C9: 8 => SOL * DIS # A5: 8,9 => CTR => A5: 3 * PRF # A5: 3 => SOL * PRF # C5: 8,9 => SOL * DIS # C5: 3 => CTR => C5: 8,9 * PRF # B8: 8,9 => SOL * DIS # B8: 3 => CTR => B8: 8,9 * DIS # A5: 8,9 => CTR => A5: 3 * PRF # A5: 3 => SOL * PRF # C5: 8,9 => SOL * DIS # C5: 3 => CTR => C5: 8,9 * INC # C9: 2,8 => UNS * DIS # C9: 9 => CTR => C9: 2,8 * PRF # F9: 2,8 => SOL * DIS # F9: 3 => CTR => F9: 2,8 * DIS # F9: 3,8 => CTR => F9: 2 * PRF # F9: 2 => SOL * PRF # B8: 8,9 => SOL * DIS # B8: 3 => CTR => B8: 8,9 * DIS # C8: 8,9 => CTR => C8: 3 * PRF # C8: 3 => SOL * PRF # C9: 8,9 => SOL * DIS # C9: 2 => CTR => C9: 8,9 * CNT 28 HDP CHAINS / 28 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # A5: 3,8 => SOL * STA A5: 3,8 * CNT 1 HDP CHAINS / 1 HYP OPENED