Analysis of xx-top500-479-base.sdk
Contents
Original Sudoku
level: medium
position: ...2.7..4.3.5.....6.....9..15..4.....2.....7.......3..8...6.......7...5.......... initial
Autosolve
position: ...2.7..4.3.5.6...6.....9..157.4.....2.....7.....7.3..8...6.......7...5.......... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C1: 5,9 => CTR => C1: 1,8 * DIS # A9: 5,9 => CTR => A9: 2,3,4,7 * PRF # A9: 2,3,4,7 => SOL * PRF # A5: 4,9 => SOL * DIS # B6: 4,9 => CTR => B6: 6,8 * DIS # C6: 4,9 => CTR => C6: 6,8 * DIS # H6: 1,2,6,8 => CTR => H6: 4,9 * DIS # A2: 4,9 => CTR => A2: 2,7 * DIS # A8: 4,9 => CTR => A8: 2,3 * DIS # A9: 4,9 => CTR => A9: 2,3,5,7 * CNT 10 HDP CHAINS / 19 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C1: 5,9 => CTR => C1: 1,8 * DIS C1: 1,8 # A9: 5,9 => CTR => A9: 2,3,4,7 * PRF C1: 1,8 + A9: 2,3,4,7 => SOL * STA C1: 1,8 + A9: 2,3,4,7 * CNT 3 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...2.7..4.3.5.....6.....9..15..4.....2.....7.......3..8...6.......7...5.......... | initial |
| ...2.7..4.3.5.6...6.....9..157.4.....2.....7.....7.3..8...6.......7...5.......... | autosolve |
| 598217634234596718671834925157342869423689571986175342815463297349728156762951483 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (2) A1: 5,9 A6: 4,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F4,F6: 2.. / F4 = 2 => 4 pairs (_) / F6 = 2 => 0 pairs (X) E8,E9: 2.. / E8 = 2 => 0 pairs (*) / E9 = 2 => 0 pairs (X) A5,C5: 3.. / A5 = 3 => 2 pairs (_) / C5 = 3 => 0 pairs (*) D4,F4: 3.. / D4 = 3 => 2 pairs (_) / F4 = 3 => 0 pairs (X) E1,H1: 3.. / E1 = 3 => 0 pairs (X) / H1 = 3 => 0 pairs (_) A2,C2: 4.. / A2 = 4 => 0 pairs (X) / C2 = 4 => 2 pairs (_) D3,F3: 4.. / D3 = 4 => 2 pairs (_) / F3 = 4 => 2 pairs (_) G5,H6: 4.. / G5 = 4 => 0 pairs (X) / H6 = 4 => 0 pairs (_) G1,I3: 5.. / G1 = 5 => 0 pairs (X) / I3 = 5 => 0 pairs (_) C3,I3: 5.. / C3 = 5 => 0 pairs (X) / I3 = 5 => 0 pairs (_) F6,I6: 5.. / F6 = 5 => 0 pairs (*) / I6 = 5 => 0 pairs (X) C7,F7: 5.. / C7 = 5 => 0 pairs (*) / F7 = 5 => 0 pairs (X) A1,A9: 5.. / A1 = 5 => 0 pairs (*) / A9 = 5 => 0 pairs (X) E5,E9: 5.. / E5 = 5 => 0 pairs (X) / E9 = 5 => 0 pairs (_) G1,G5: 5.. / G1 = 5 => 0 pairs (X) / G5 = 5 => 0 pairs (_) G1,H1: 6.. / G1 = 6 => 0 pairs (*) / H1 = 6 => 0 pairs (X) A2,B3: 7.. / A2 = 7 => 0 pairs (X) / B3 = 7 => 0 pairs (_) B3,I3: 7.. / B3 = 7 => 0 pairs (*) / I3 = 7 => 0 pairs (X) A2,A9: 7.. / A2 = 7 => 0 pairs (X) / A9 = 7 => 0 pairs (_) E1,E2: 9.. / E1 = 9 => 0 pairs (X) / E2 = 9 => 2 pairs (_) * DURATION: 0:00:30.298146 START: 19:03:07.960831 END: 19:03:38.258977 2017-05-04 * CP COUNT: (20) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A6) * ...2.7..4.3.5.6...6.....9..157.4.....2.....7.....7.3..8...6.......7...5.......... * PAIR A1: 5,9 BLK 1 C1: 5,9,1,8 # reduction candidate for 5,9 C1: 5,9 => CTR * 5.92.7.3423459671867..3.925157342...4236895719..1753428.5.6329739.72..5676295..83 C1: 1,8 # 3 pairs * PAIR A1: 5,9 COL A A9: 5,9,2,3,4,7 # reduction candidate for 5,9 A9: 5,9 => CTR * ...2.7..4734596...6.2...9..157.4.....2.....7.....7.3..8...6.......7...5.......... A9: 2,3,4,7 => SOLVED * 598217634234596718671834925157342869423689571986175342815463297349728156762951483 * PAIR A6: 4,9 BLK 4 A5: 4,9,3 # reduction candidate for 4,9 A5: 4,9 => SOLVED * 598217634234596718671834925157342869423689571986175342815463297349728156762951483 A5: 3 # 2 pairs C5: 4,9,3,6,8 # reduction candidate for 4,9 C5: 4,9 # 7 pairs B6: 4,9,6,8 # reduction candidate for 4,9 B6: 4,9 => CTR * 9.123756473.5.6...6.5...9..157.4....32....47.....7.3..8...65......7...5.5........ B6: 6,8 # 3 pairs C6: 4,9,6,8 # reduction candidate for 4,9 C6: 4,9 => CTR * 9..23756473.5.6...6.5...9..157.4....32....47.....7.3..8...65......7...5.5........ C6: 6,8 # 3 pairs * PAIR A6: 4,9 ROW 6 H6: 4,9,1,2,6,8 # reduction candidate for 4,9 H6: 1,2,6,8 => CTR * 9..23756473.5.6...6.5...9..157.4.....2....47.....7.3..8...65......7...5.5........ H6: 4,9 # 8 pairs * PAIR A6: 4,9 COL A A2: 4,9,2,7 # reduction candidate for 4,9 A2: 4,9 => CTR * 5..2.7..4.3.5.6...67....9.5157.4.....2....57.....753428.5.6....2..7...5.7........ A2: 2,7 # 6 pairs A8: 4,9,2,3 # reduction candidate for 4,9 A8: 4,9 => CTR * 5..2.7..4.34596...6.....9.5157.4....32.....7.....7.3..8...6.......7...5.......... A8: 2,3 # 3 pairs A9: 4,9,2,3,5,7 # reduction candidate for 4,9 A9: 4,9 => CTR * 5..2.7..4734596...6.2...9..157.4.....2.....7.....7.3..8...6.......7...5.......... A9: 2,3,5,7 # 2 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-479-base-pr-000.dot * REASONING * DIS # C1: 5,9 => CTR => C1: 1,8 * DIS # A9: 5,9 => CTR => A9: 2,3,4,7 * PRF # A9: 2,3,4,7 => SOL * PRF # A5: 4,9 => SOL * DIS # B6: 4,9 => CTR => B6: 6,8 * DIS # C6: 4,9 => CTR => C6: 6,8 * DIS # H6: 1,2,6,8 => CTR => H6: 4,9 * DIS # A2: 4,9 => CTR => A2: 2,7 * DIS # A8: 4,9 => CTR => A8: 2,3 * DIS # A9: 4,9 => CTR => A9: 2,3,5,7 * CNT 10 HDP CHAINS / 19 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A6) * ...2.7..4.3.5.6...6.....9..157.4.....2.....7.....7.3..8...6.......7...5.......... * PAIR A1: 5,9 BLK 1 C1: 5,9,1,8 # reduction candidate for 5,9 C1: 5,9 => CTR * 5.92.7.3423459671867..3.925157342...4236895719..1753428.5.6329739.72..5676295..83 * PAIR A1: 5,9 COL A A9: 5,9,2,3,4,7 # reduction candidate for 5,9 A9: 5,9 => CTR * ...2.7..4734596...6.2...9..157.4.....2.....7.....7.3..8...6.......7...5.......... A9: 2,3,4,7 => SOLVED * 598217634234596718671834925157342869423689571986175342815463297349728156762951483 * DURATION: 0:00:04.731159 START: 19:03:51.270777 END: 19:03:56.001936 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-479-base-pr-001.dot * REASONING * DIS # C1: 5,9 => CTR => C1: 1,8 * DIS C1: 1,8 # A9: 5,9 => CTR => A9: 2,3,4,7 * PRF C1: 1,8 + A9: 2,3,4,7 => SOL * STA C1: 1,8 + A9: 2,3,4,7 * CNT 3 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 479 solution: 598217634234596718671834925157342869423689571986175342815463297349728156762951483 info: 95777 FNBWXYK S8.f 7910 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 598217634234596718671834925157342869423689571986175342815463297349728156762951483 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:
* DIS # C1: 5,9 => CTR => C1: 1,8 * INC # C1: 1,8 => UNS * DIS # A9: 5,9 => CTR => A9: 2,3,4,7 * PRF # A9: 2,3,4,7 => SOL * PRF # A5: 4,9 => SOL * INC # A5: 3 => UNS * INC # C5: 4,9 => UNS * DIS # B6: 4,9 => CTR => B6: 6,8 * INC # B6: 6,8 => UNS * DIS # C6: 4,9 => CTR => C6: 6,8 * INC # C6: 6,8 => UNS * INC # H6: 4,9 => UNS * DIS # H6: 1,2,6,8 => CTR => H6: 4,9 * DIS # A2: 4,9 => CTR => A2: 2,7 * INC # A2: 2,7 => UNS * DIS # A8: 4,9 => CTR => A8: 2,3 * INC # A8: 2,3 => UNS * DIS # A9: 4,9 => CTR => A9: 2,3,5,7 * INC # A9: 2,3,5,7 => UNS * CNT 19 HDP CHAINS / 19 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # C1: 5,9 => CTR => C1: 1,8 * DIS C1: 1,8 # A9: 5,9 => CTR => A9: 2,3,4,7 * PRF C1: 1,8 + A9: 2,3,4,7 => SOL * STA C1: 1,8 + A9: 2,3,4,7 * CNT 3 HDP CHAINS / 2 HYP OPENED