Analysis of xx-top500-002-base.sdk
Contents
Original Sudoku
level: medium
position: 6..35....2......8.........15..4..3.....2.1.7...........17..........9.5...8....... initial
Autosolve
position: 6.13587..25.71..837389...5157.48.31.8..2.1.751..57.8...178.52.....1975.8.856..1.7 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # B6: 4,9 => SOL * PRF # G2: 6 => SOL * PRF # C5: 4,9 => SOL * PRF # G2: 4,6 => SOL * DIS # G2: 9 => CTR => G2: 4,6 * PRF # G2: 4,6 => SOL * DIS # G2: 9 => CTR => G2: 4,6 * PRF # F6: 6,9 => SOL * DIS # F6: 9 => CTR => F6: 3,6 * PRF # C5: 4,9 => SOL * PRF # C5: 4,9 => SOL * PRF # G2: 6 => SOL * PRF # B6: 4,9 => SOL * DIS # C6: 2,6 => CTR => C6: 3,4,9 * CNT 14 HDP CHAINS / 46 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # B6: 4,9 => SOL * STA B6: 4,9 * CNT 1 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 6..35....2......8.........15..4..3.....2.1.7...........17..........9.5...8....... | initial |
| 6.13587..25.71..837389...5157.48.31.8..2.1.751..57.8...178.52.....1975.8.856..1.7 | autosolve |
| 641358792259714683738962451572489316864231975193576824317845269426197538985623147 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (12) B1: 4,9 C2: 4,9 F2: 4,6 G3: 4,6 F4: 6,9 E5: 3,6 G5: 4,9 A8: 3,4 B8: 2,6 C8: 2,6 E7: 3,4 H8: 3,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E3,F3: 2.. / E3 = 2 => 17 pairs (_) / F3 = 2 => 14 pairs (_) H1,I1: 2.. / H1 = 2 => 13 pairs (_) / I1 = 2 => 13 pairs (_) B8,C8: 2.. / B8 = 2 => 11 pairs (_) / C8 = 2 => 15 pairs (_) E9,F9: 2.. / E9 = 2 => 14 pairs (_) / F9 = 2 => 17 pairs (_) C4,I4: 2.. / C4 = 2 => 11 pairs (_) / I4 = 2 => 15 pairs (_) B6,B8: 2.. / B6 = 2 => 15 pairs (_) / B8 = 2 => 11 pairs (_) E3,E9: 2.. / E3 = 2 => 17 pairs (_) / E9 = 2 => 14 pairs (_) F3,F9: 2.. / F3 = 2 => 14 pairs (_) / F9 = 2 => 17 pairs (_) H1,H6: 2.. / H1 = 2 => 13 pairs (_) / H6 = 2 => 13 pairs (_) C5,C6: 3.. / C5 = 3 => 17 pairs (_) / C6 = 3 => 0 pairs (*) E5,F6: 3.. / E5 = 3 => 0 pairs (*) / F6 = 3 => 0 pairs (X) C5,E5: 3.. / C5 = 3 => 17 pairs (_) / E5 = 3 => 0 pairs (*) C6,F6: 3.. / C6 = 3 => 0 pairs (*) / F6 = 3 => 0 pairs (X) A8,H8: 3.. / A8 = 3 => 15 pairs (_) / H8 = 3 => 13 pairs (_) F6,F9: 3.. / F6 = 3 => 17 pairs (_) / F9 = 3 => 0 pairs (*) B1,C2: 4.. / B1 = 4 => 0 pairs (*) / C2 = 4 => 0 pairs (X) A8,H8: 4.. / A8 = 4 => 13 pairs (_) / H8 = 4 => 15 pairs (_) G2,G3: 6.. / G2 = 6 => 0 pairs (*) / G3 = 6 => 0 pairs (X) B8,C8: 6.. / B8 = 6 => 15 pairs (_) / C8 = 6 => 11 pairs (_) H7,I7: 6.. / H7 = 6 => 13 pairs (_) / I7 = 6 => 15 pairs (_) F2,G2: 6.. / F2 = 6 => 17 pairs (_) / G2 = 6 => 0 pairs (*) E3,E5: 6.. / E3 = 6 => 0 pairs (*) / E5 = 6 => 0 pairs (X) H6,H7: 6.. / H6 = 6 => 15 pairs (_) / H7 = 6 => 13 pairs (_) B1,C2: 9.. / B1 = 9 => 0 pairs (X) / C2 = 9 => 0 pairs (_) F4,F6: 9.. / F4 = 9 => 14 pairs (_) / F6 = 9 => 0 pairs (X) A7,A9: 9.. / A7 = 9 => 15 pairs (_) / A9 = 9 => 17 pairs (_) C2,G2: 9.. / C2 = 9 => 0 pairs (*) / G2 = 9 => 0 pairs (X) A9,H9: 9.. / A9 = 9 => 17 pairs (_) / H9 = 9 => 15 pairs (_) G2,G5: 9.. / G2 = 9 => 0 pairs (X) / G5 = 9 => 0 pairs (_) * DURATION: 0:00:50.306953 START: 02:39:07.794148 END: 02:39:58.101101 2017-05-04 * CP COUNT: (29) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,B1,B8,C2,C8,E5,E7,F2,F4,G3,G5,H8) * 6.13587..25.71..837389...5157.48.31.8..2.1.751..57.8...178.52.....1975.8.856..1.7 * PAIR B1: 4,9 ROW 1 H1: 4,9,2 # reduction candidate for 4,9 H1: 4,9 # 13 pairs I1: 4,9,2 # reduction candidate for 4,9 I1: 4,9 # 13 pairs * PAIR B1: 4,9 COL B B5: 4,9,6 # reduction candidate for 4,9 B5: 4,9 # 15 pairs B6: 4,9,2,6 # reduction candidate for 4,9 B6: 4,9 => SOLVED * 641358792259714683738962451572489316864231975193576824317845269426197538985623147 B6: 2,6 # 15 pairs * PAIR C2: 4,9 ROW 2 G2: 4,9,6 # reduction candidate for 4,9 G2: 6 => SOLVED * 641358792259714683738962451572489316864231975193576824317845269426197538985623147 G2: 4,9 # 17 pairs * PAIR C2: 4,9 COL C C5: 4,9,3,6 # reduction candidate for 4,9 C5: 4,9 => SOLVED * 641358792259714683738962451572489316864231975193576824317845269426197538985623147 C5: 3,6 # 15 pairs C6: 4,9,2,3,6 # reduction candidate for 4,9 C6: 4,9 # 17 pairs * PAIR F2: 4,6 BLK 2 E3: 4,6,2 # reduction candidate for 4,6 E3: 4,6 # 14 pairs F3: 4,6,2 # reduction candidate for 4,6 F3: 4,6 # 17 pairs * PAIR F2: 4,6 ROW 2 G2: 4,6,9 # reduction candidate for 4,6 G2: 4,6 => SOLVED * 641358792259714683738962451572489316864231975193576824317845269426197538985623147 G2: 9 => CTR * 6913587..25.7169837389..65157.48931.8..2614751..5738...178.52.....1975.8.856..1.7 * PAIR G3: 4,6 BLK 3 G2: 4,6,9 # reduction candidate for 4,6 G2: 4,6 => SOLVED * 641358792259714683738962451572489316864231975193576824317845269426197538985623147 G2: 9 => CTR * 6913587..25.7169837389..65157.48931.8..2614751..5738...178.52.....1975.8.856..1.7 * PAIR G3: 4,6 ROW 3 E3: 4,6,2 # reduction candidate for 4,6 E3: 4,6 # 14 pairs F3: 4,6,2 # reduction candidate for 4,6 F3: 4,6 # 17 pairs * PAIR F4: 6,9 BLK 5 F6: 6,9,3 # reduction candidate for 6,9 F6: 6,9 => SOLVED * 641358792259714683738962451572489316864231975193576824317845269426197538985623147 F6: 3 # 17 pairs * PAIR F4: 6,9 ROW 4 C4: 6,9,2 # reduction candidate for 6,9 C4: 6,9 # 15 pairs I4: 6,9,2 # reduction candidate for 6,9 I4: 6,9 # 11 pairs * PAIR E5: 3,6 BLK 5 F6: 3,6,9 # reduction candidate for 3,6 F6: 9 => CTR * 6.13587..25.71..8373896245157.48631.8..2319751.35798.4.178452.6...1975.8.856231.7 F6: 3,6 # 14 pairs * PAIR E5: 3,6 ROW 5 C5: 3,6,4,9 # reduction candidate for 3,6 C5: 4,9 => SOLVED * 641358792259714683738962451572489316864231975193576824317845269426197538985623147 C5: 3,6 # 15 pairs * PAIR G5: 4,9 BLK 6 H6: 4,9,2,6 # reduction candidate for 4,9 H6: 4,9 # 17 pairs I6: 4,9,2,6 # reduction candidate for 4,9 I6: 4,9 # 15 pairs * PAIR G5: 4,9 ROW 5 B5: 4,9,6 # reduction candidate for 4,9 B5: 4,9 # 15 pairs C5: 4,9,3,6 # reduction candidate for 4,9 C5: 4,9 => SOLVED * 641358792259714683738962451572489316864231975193576824317845269426197538985623147 C5: 3,6 # 15 pairs * PAIR G5: 4,9 COL G G2: 4,9,6 # reduction candidate for 4,9 G2: 6 => SOLVED * 641358792259714683738962451572489316864231975193576824317845269426197538985623147 G2: 4,9 # 17 pairs * PAIR A8: 3,4 BLK 7 A7: 3,4,9 # reduction candidate for 3,4 A7: 3,4 # 17 pairs A9: 3,4,9 # reduction candidate for 3,4 A9: 3,4 # 15 pairs * PAIR B8: 2,6 COL B B6: 2,6,4,9 # reduction candidate for 2,6 B6: 4,9 => SOLVED * 641358792259714683738962451572489316864231975193576824317845269426197538985623147 B6: 2,6 # 15 pairs * PAIR C8: 2,6 COL C C4: 2,6,9 # reduction candidate for 2,6 C4: 2,6 # 13 pairs C6: 2,6,3,4,9 # reduction candidate for 2,6 C6: 2,6 => CTR * 6.13587..2547169837389..65157948.31.8.3261.751..5738...178.52.....1975.8.856..1.7 C6: 3,4,9 # 12 pairs * PAIR E7: 3,4 BLK 8 E9: 3,4,2 # reduction candidate for 3,4 E9: 3,4 # 17 pairs F9: 3,4,2 # reduction candidate for 3,4 F9: 3,4 # 14 pairs * PAIR E7: 3,4 ROW 7 A7: 3,4,9 # reduction candidate for 3,4 A7: 3,4 # 17 pairs H7: 3,4,6,9 # reduction candidate for 3,4 H7: 3,4 # 17 pairs * PAIR H8: 3,4 BLK 9 H7: 3,4,6,9 # reduction candidate for 3,4 H7: 3,4 # 17 pairs H9: 3,4,9 # reduction candidate for 3,4 H9: 3,4 # 17 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-002-base-pr-000.dot * REASONING * PRF # B6: 4,9 => SOL * PRF # G2: 6 => SOL * PRF # C5: 4,9 => SOL * PRF # G2: 4,6 => SOL * DIS # G2: 9 => CTR => G2: 4,6 * PRF # G2: 4,6 => SOL * DIS # G2: 9 => CTR => G2: 4,6 * PRF # F6: 6,9 => SOL * DIS # F6: 9 => CTR => F6: 3,6 * PRF # C5: 4,9 => SOL * PRF # C5: 4,9 => SOL * PRF # G2: 6 => SOL * PRF # B6: 4,9 => SOL * DIS # C6: 2,6 => CTR => C6: 3,4,9 * CNT 14 HDP CHAINS / 46 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,B1,B8,C2,C8,E5,E7,F2,F4,G3,G5,H8) * 6.13587..25.71..837389...5157.48.31.8..2.1.751..57.8...178.52.....1975.8.856..1.7 * PAIR B1: 4,9 ROW 1 H1: 4,9,2 # reduction candidate for 4,9 H1: 4,9 # 13 pairs I1: 4,9,2 # reduction candidate for 4,9 I1: 4,9 # 13 pairs * PAIR B1: 4,9 COL B B5: 4,9,6 # reduction candidate for 4,9 B5: 4,9 # 15 pairs B6: 4,9,2,6 # reduction candidate for 4,9 B6: 4,9 => SOLVED * 641358792259714683738962451572489316864231975193576824317845269426197538985623147 * DURATION: 0:00:04.851093 START: 02:40:45.152470 END: 02:40:50.003563 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-002-base-pr-001.dot * REASONING * PRF # B6: 4,9 => SOL * STA B6: 4,9 * CNT 1 HDP CHAINS / 4 HYP OPENED
Header Info
Top 500 Minimum 17 002 solution: 641358792259714683738962451572489316864231975193576824317845269426197538985623147 info: 1305 FNBTWXY S8.f 35060 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 641358792259714683738962451572489316864231975193576824317845269426197538985623147 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 # H1: 4,9 => UNS * INC # I1: 4,9 => UNS * INC # B5: 4,9 => UNS * PRF # B6: 4,9 => SOL * INC # B6: 2,6 => UNS * INC # G2: 4,9 => UNS * PRF # G2: 6 => SOL * PRF # C5: 4,9 => SOL * INC # C5: 3,6 => UNS * INC # C6: 4,9 => UNS * INC # E3: 4,6 => UNS * INC # F3: 4,6 => UNS * PRF # G2: 4,6 => SOL * DIS # G2: 9 => CTR => G2: 4,6 * PRF # G2: 4,6 => SOL * DIS # G2: 9 => CTR => G2: 4,6 * INC # E3: 4,6 => UNS * INC # F3: 4,6 => UNS * PRF # F6: 6,9 => SOL * INC # F6: 3 => UNS * INC # C4: 6,9 => UNS * INC # I4: 6,9 => UNS * INC # F6: 3,6 => UNS * DIS # F6: 9 => CTR => F6: 3,6 * INC # C5: 3,6 => UNS * PRF # C5: 4,9 => SOL * INC # H6: 4,9 => UNS * INC # I6: 4,9 => UNS * INC # B5: 4,9 => UNS * PRF # C5: 4,9 => SOL * INC # C5: 3,6 => UNS * INC # G2: 4,9 => UNS * PRF # G2: 6 => SOL * INC # A7: 3,4 => UNS * INC # A9: 3,4 => UNS * INC # B6: 2,6 => UNS * PRF # B6: 4,9 => SOL * INC # C4: 2,6 => UNS * DIS # C6: 2,6 => CTR => C6: 3,4,9 * INC # C6: 3,4,9 => UNS * INC # E9: 3,4 => UNS * INC # F9: 3,4 => UNS * INC # A7: 3,4 => UNS * INC # H7: 3,4 => UNS * INC # H7: 3,4 => UNS * INC # H9: 3,4 => UNS * CNT 46 HDP CHAINS / 46 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # H1: 4,9 => UNS * INC # I1: 4,9 => UNS * INC # B5: 4,9 => UNS * PRF # B6: 4,9 => SOL * STA B6: 4,9 * CNT 4 HDP CHAINS / 4 HYP OPENED