Analysis of xx-top500-489-base.sdk
Contents
Original Sudoku
level: medium
position: 4.....8......6..7.......3..9..4....6...3.7..........1....29...4..7...5...1....... initial
Autosolve
position: 4.....86.....6417.7.....34.97.41.2361..327958......4176..291784..7...5.1.1....6.3 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C2: 3,5 => CTR => C2: 2,8,9 * DIS # D3: 5,8 => CTR => D3: 1,9 * DIS # B3: 5,8 => CTR => B3: 2,6,9 * PRF # F1: 3 => SOL * PRF # B3: 2,9 => SOL * DIS # C3: 2,9 => CTR => C3: 1,5,6,8 * DIS # C6: 5,8 => CTR => C6: 2,3 * DIS # B6: 3,5 => CTR => B6: 2,8 * DIS # C6: 3,5 => CTR => C6: 2,8 * DIS # C6: 5,8 => CTR => C6: 2,3 * DIS # B6: 3,5 => CTR => B6: 2,8 * DIS # C2: 3,5 => CTR => C2: 2,8,9 * DIS # C6: 3,5 => CTR => C6: 2,8 * PRF # D9: 7 => SOL * CNT 14 HDP CHAINS / 37 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C2: 3,5 => CTR => C2: 2,8,9 * DIS C2: 2,8,9 # B2: 2,8,9 => CTR => B2: 3,5 * DIS C2: 2,8,9 + B2: 3,5 # F1: 2,9 => CTR => F1: 3 * PRF C2: 2,8,9 + B2: 3,5 + F1: 3 => SOL * STA C2: 2,8,9 + B2: 3,5 + F1: 3 * CNT 4 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 4.....8......6..7.......3..9..4....6...3.7..........1....29...4..7...5...1....... | initial |
| 4.....86.....6417.7.....34.97.41.2361..327958......4176..291784..7...5.1.1....6.3 | autosolve |
| 421573869538964172796182345975418236164327958382659417653291784247836591819745623 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (25) A2: 3,5 E1: 3,7 E3: 5,8 F3: 2,9 C4: 5,8 B5: 4,6 C5: 4,6 A6: 3,5 F4: 5,8 D6: 6,9 E6: 5,8 F6: 6,9 B7: 3,5 C7: 3,5 A8: 2,8 B8: 4,9 A9: 2,8 C9: 4,9 D8: 6,8 E8: 3,4 F8: 3,6 E9: 4,7 F9: 5,8 H8: 2,9 H9: 2,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C1,C3: 1.. / C1 = 1 => 25 pairs (_) / C3 = 1 => 0 pairs (X) D1,D3: 1.. / D1 = 1 => 0 pairs (X) / D3 = 1 => 25 pairs (_) C1,D1: 1.. / C1 = 1 => 25 pairs (_) / D1 = 1 => 0 pairs (X) C3,D3: 1.. / C3 = 1 => 0 pairs (X) / D3 = 1 => 25 pairs (_) F1,F3: 2.. / F1 = 2 => 0 pairs (X) / F3 = 2 => 26 pairs (_) B6,C6: 2.. / B6 = 2 => 26 pairs (_) / C6 = 2 => 25 pairs (_) A8,A9: 2.. / A8 = 2 => 0 pairs (*) / A9 = 2 => 0 pairs (X) H8,H9: 2.. / H8 = 2 => 14 pairs (_) / H9 = 2 => 0 pairs (*) A8,H8: 2.. / A8 = 2 => 0 pairs (*) / H8 = 2 => 0 pairs (X) A9,H9: 2.. / A9 = 2 => 14 pairs (_) / H9 = 2 => 0 pairs (*) E1,F1: 3.. / E1 = 3 => 14 pairs (_) / F1 = 3 => 0 pairs (*) B7,C7: 3.. / B7 = 3 => 0 pairs (X) / C7 = 3 => 24 pairs (_) E8,F8: 3.. / E8 = 3 => 0 pairs (*) / F8 = 3 => 0 pairs (X) A2,A6: 3.. / A2 = 3 => 0 pairs (X) / A6 = 3 => 28 pairs (_) E1,E8: 3.. / E1 = 3 => 14 pairs (_) / E8 = 3 => 0 pairs (*) F1,F8: 3.. / F1 = 3 => 0 pairs (*) / F8 = 3 => 0 pairs (X) B5,C5: 4.. / B5 = 4 => 14 pairs (_) / C5 = 4 => 0 pairs (*) B8,C9: 4.. / B8 = 4 => 0 pairs (*) / C9 = 4 => 0 pairs (X) E8,E9: 4.. / E8 = 4 => 14 pairs (_) / E9 = 4 => 0 pairs (*) B8,E8: 4.. / B8 = 4 => 0 pairs (*) / E8 = 4 => 0 pairs (X) C9,E9: 4.. / C9 = 4 => 14 pairs (_) / E9 = 4 => 0 pairs (*) B5,B8: 4.. / B5 = 4 => 14 pairs (_) / B8 = 4 => 0 pairs (*) C5,C9: 4.. / C5 = 4 => 0 pairs (*) / C9 = 4 => 0 pairs (X) F4,E6: 5.. / F4 = 5 => 0 pairs (X) / E6 = 5 => 0 pairs (_) B7,C7: 5.. / B7 = 5 => 24 pairs (_) / C7 = 5 => 0 pairs (X) D9,F9: 5.. / D9 = 5 => 0 pairs (X) / F9 = 5 => 0 pairs (_) C4,F4: 5.. / C4 = 5 => 0 pairs (*) / F4 = 5 => 0 pairs (X) A2,A6: 5.. / A2 = 5 => 28 pairs (_) / A6 = 5 => 0 pairs (X) E3,E6: 5.. / E3 = 5 => 0 pairs (X) / E6 = 5 => 0 pairs (_) F4,F9: 5.. / F4 = 5 => 0 pairs (X) / F9 = 5 => 0 pairs (_) B3,C3: 6.. / B3 = 6 => 14 pairs (_) / C3 = 6 => 0 pairs (*) B5,C5: 6.. / B5 = 6 => 0 pairs (*) / C5 = 6 => 0 pairs (X) D6,F6: 6.. / D6 = 6 => 0 pairs (*) / F6 = 6 => 0 pairs (X) D8,F8: 6.. / D8 = 6 => 14 pairs (_) / F8 = 6 => 0 pairs (*) B3,B5: 6.. / B3 = 6 => 14 pairs (_) / B5 = 6 => 0 pairs (*) C3,C5: 6.. / C3 = 6 => 0 pairs (*) / C5 = 6 => 0 pairs (X) D6,D8: 6.. / D6 = 6 => 0 pairs (*) / D8 = 6 => 0 pairs (X) F6,F8: 6.. / F6 = 6 => 14 pairs (_) / F8 = 6 => 0 pairs (*) D1,E1: 7.. / D1 = 7 => 14 pairs (_) / E1 = 7 => 0 pairs (*) D9,E9: 7.. / D9 = 7 => 0 pairs (*) / E9 = 7 => 0 pairs (X) D1,D9: 7.. / D1 = 7 => 14 pairs (_) / D9 = 7 => 0 pairs (*) E1,E9: 7.. / E1 = 7 => 0 pairs (*) / E9 = 7 => 0 pairs (X) F4,E6: 8.. / F4 = 8 => 0 pairs (*) / E6 = 8 => 0 pairs (X) A8,A9: 8.. / A8 = 8 => 14 pairs (_) / A9 = 8 => 0 pairs (*) C4,F4: 8.. / C4 = 8 => 0 pairs (X) / F4 = 8 => 0 pairs (_) A8,D8: 8.. / A8 = 8 => 14 pairs (_) / D8 = 8 => 0 pairs (*) E3,E6: 8.. / E3 = 8 => 0 pairs (*) / E6 = 8 => 0 pairs (X) F4,F9: 8.. / F4 = 8 => 0 pairs (*) / F9 = 8 => 0 pairs (X) D6,F6: 9.. / D6 = 9 => 14 pairs (_) / F6 = 9 => 0 pairs (*) B8,C9: 9.. / B8 = 9 => 14 pairs (_) / C9 = 9 => 0 pairs (*) H8,H9: 9.. / H8 = 9 => 0 pairs (*) / H9 = 9 => 0 pairs (X) B8,H8: 9.. / B8 = 9 => 14 pairs (_) / H8 = 9 => 0 pairs (*) C9,H9: 9.. / C9 = 9 => 0 pairs (*) / H9 = 9 => 0 pairs (X) * DURATION: 0:01:56.617866 START: 19:21:47.143505 END: 19:23:43.761371 2017-05-04 * CP COUNT: (53) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A6,A8,A9,B5,B7,B8,C4,C5,C7,C9,D6,D8,E1,E3,E6,E8,E9,F3,F4,F6,F8,F9,H8,H9) * 4.....86.....6417.7.....34.97.41.2361..327958......4176..291784..7...5.1.1....6.3 * PAIR A2: 3,5 BLK 1 B2: 3,5,2,8,9 # reduction candidate for 3,5 B2: 3,5 # 32 pairs C2: 3,5,2,8,9 # reduction candidate for 3,5 C2: 3,5 => CTR * 4..73.865...86417.78615.34.978415236164327958..29864176..291784847...5.1.1.5786.3 C2: 2,8,9 # 25 pairs * PAIR E3: 5,8 BLK 2 D2: 5,8,9 # reduction candidate for 5,8 D2: 5,8 # 27 pairs D3: 5,8,1,9 # reduction candidate for 5,8 D3: 5,8 => CTR * 4..17386.....6417.7.1..234.97.41.2361.6327958.....94176..291784..7.365.1.14...6.3 D3: 1,9 # 26 pairs * PAIR E3: 5,8 ROW 3 B3: 5,8,2,6,9 # reduction candidate for 5,8 B3: 5,8 => CTR * 4.1.7386.....6417.7.61823499754182361643279583..65941765.291784247836591819745623 B3: 2,6,9 # 25 pairs C3: 5,8,1,2,6,9 # reduction candidate for 5,8 C3: 5,8 # 12 pairs * PAIR F3: 2,9 BLK 2 F1: 2,9,3 # reduction candidate for 2,9 F1: 3 => SOLVED * 421573869538964172796182345975418236164327958382659417653291784247836591819745623 F1: 2,9 # 14 pairs * PAIR F3: 2,9 ROW 3 B3: 2,9,5,6,8 # reduction candidate for 2,9 B3: 2,9 => SOLVED * 421573869538964172796182345975418236164327958382659417653291784247836591819745623 B3: 5,6,8 # 25 pairs C3: 2,9,1,5,6,8 # reduction candidate for 2,9 C3: 2,9 => CTR * 4.173.86.5..96417276918234597.418236146327958....5.4176..291784.97.43521214875693 C3: 1,5,6,8 # 25 pairs I3: 2,9,5 # reduction candidate for 2,9 I3: 2,9 # 26 pairs * PAIR C4: 5,8 BLK 4 B6: 5,8,2,3 # reduction candidate for 5,8 B6: 5,8 # 30 pairs C6: 5,8,2,3 # reduction candidate for 5,8 C6: 5,8 => CTR * 49....86.53..6417.78615.34.97.415236164327958325.8.417653291784.47.36591.195..6.3 C6: 2,3 # 26 pairs * PAIR C4: 5,8 COL C C2: 5,8,2,3,9 # reduction candidate for 5,8 C2: 5,8 # 31 pairs C3: 5,8,1,2,6,9 # reduction candidate for 5,8 C3: 5,8 # 12 pairs * PAIR A6: 3,5 BLK 4 B6: 3,5,2,8 # reduction candidate for 3,5 B6: 3,5 => CTR * 4.173.86....86417.78615.34.9784152361..327958..29864176..291784897643521214578693 B6: 2,8 # 26 pairs C6: 3,5,2,8 # reduction candidate for 3,5 C6: 3,5 => CTR * 45173.86.38..6417.7..15.34.9784152361..327958.2.9864176..291784897643521214578693 C6: 2,8 # 26 pairs * PAIR E6: 5,8 ROW 6 B6: 5,8,2,3 # reduction candidate for 5,8 B6: 5,8 # 30 pairs C6: 5,8,2,3 # reduction candidate for 5,8 C6: 5,8 => CTR * 49....86.53..6417.78615.34.97.415236164327958325.8.417653291784.47.36591.195..6.3 C6: 2,3 # 26 pairs * PAIR B7: 3,5 COL B B2: 3,5,2,8,9 # reduction candidate for 3,5 B2: 3,5 # 32 pairs B6: 3,5,2,8 # reduction candidate for 3,5 B6: 3,5 => CTR * 4.173.86....86417.78615.34.9784152361..327958..29864176..291784897643521214578693 B6: 2,8 # 26 pairs * PAIR C7: 3,5 COL C C2: 3,5,2,8,9 # reduction candidate for 3,5 C2: 3,5 => CTR * 4..73.865...86417.78615.34.978415236164327958..29864176..291784847...5.1.1.5786.3 C2: 2,8,9 # 25 pairs C6: 3,5,2,8 # reduction candidate for 3,5 C6: 3,5 => CTR * 45173.86.38..6417.7..15.34.9784152361..327958.2.9864176..291784897643521214578693 C6: 2,8 # 26 pairs * PAIR F9: 5,8 BLK 8 D9: 5,8,7 # reduction candidate for 5,8 D9: 7 => SOLVED * 421573869538964172796182345975418236164327958382659417653291784247836591819745623 D9: 5,8 # 14 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-489-base-pr-000.dot * REASONING * DIS # C2: 3,5 => CTR => C2: 2,8,9 * DIS # D3: 5,8 => CTR => D3: 1,9 * DIS # B3: 5,8 => CTR => B3: 2,6,9 * PRF # F1: 3 => SOL * PRF # B3: 2,9 => SOL * DIS # C3: 2,9 => CTR => C3: 1,5,6,8 * DIS # C6: 5,8 => CTR => C6: 2,3 * DIS # B6: 3,5 => CTR => B6: 2,8 * DIS # C6: 3,5 => CTR => C6: 2,8 * DIS # C6: 5,8 => CTR => C6: 2,3 * DIS # B6: 3,5 => CTR => B6: 2,8 * DIS # C2: 3,5 => CTR => C2: 2,8,9 * DIS # C6: 3,5 => CTR => C6: 2,8 * PRF # D9: 7 => SOL * CNT 14 HDP CHAINS / 37 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A6,A8,A9,B5,B7,B8,C4,C5,C7,C9,D6,D8,E1,E3,E6,E8,E9,F3,F4,F6,F8,F9,H8,H9) * 4.....86.....6417.7.....34.97.41.2361..327958......4176..291784..7...5.1.1....6.3 * PAIR A2: 3,5 BLK 1 B2: 3,5,2,8,9 # reduction candidate for 3,5 B2: 3,5 # 32 pairs C2: 3,5,2,8,9 # reduction candidate for 3,5 C2: 3,5 => CTR * 4..73.865...86417.78615.34.978415236164327958..29864176..291784847...5.1.1.5786.3 * RESTART * PAIR A2: 3,5 BLK 1 B2: 3,5,2,8,9 # reduction candidate for 3,5 B2: 2,8,9 => CTR * 4.173.86.3.986417578615.34.9784152361..3279585..9864176..291784897643521214578693 * PAIR F3: 2,9 BLK 2 F1: 2,9,3 # reduction candidate for 2,9 F1: 2,9 => CTR * 4..73.865....6417.7..15.34.97.415236146327958....864176..291784.97.435.1.14.7.693 F1: 3 => SOLVED * 421573869538964172796182345975418236164327958382659417653291784247836591819745623 * DURATION: 0:00:08.794395 START: 19:24:27.610049 END: 19:24:36.404444 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-489-base-pr-001.dot * REASONING * DIS # C2: 3,5 => CTR => C2: 2,8,9 * DIS C2: 2,8,9 # B2: 2,8,9 => CTR => B2: 3,5 * DIS C2: 2,8,9 + B2: 3,5 # F1: 2,9 => CTR => F1: 3 * PRF C2: 2,8,9 + B2: 3,5 + F1: 3 => SOL * STA C2: 2,8,9 + B2: 3,5 + F1: 3 * CNT 4 HDP CHAINS / 5 HYP OPENED
Header Info
Top 500 Minimum 17 489 solution: 421573869538964172796182345975418236164327958382659417653291784247836591819745623 info: 96228 FNBTXYK S8.f 30525 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 421573869538964172796182345975418236164327958382659417653291784247836591819745623 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 # B2: 3,5 => UNS * DIS # C2: 3,5 => CTR => C2: 2,8,9 * INC # C2: 2,8,9 => UNS * INC # D2: 5,8 => UNS * DIS # D3: 5,8 => CTR => D3: 1,9 * INC # D3: 1,9 => UNS * DIS # B3: 5,8 => CTR => B3: 2,6,9 * INC # B3: 2,6,9 => UNS * INC # C3: 5,8 => UNS * INC # F1: 2,9 => UNS * PRF # F1: 3 => SOL * PRF # B3: 2,9 => SOL * INC # B3: 5,6,8 => UNS * DIS # C3: 2,9 => CTR => C3: 1,5,6,8 * INC # C3: 1,5,6,8 => UNS * INC # I3: 2,9 => UNS * INC # B6: 5,8 => UNS * DIS # C6: 5,8 => CTR => C6: 2,3 * INC # C6: 2,3 => UNS * INC # C2: 5,8 => UNS * INC # C3: 5,8 => UNS * DIS # B6: 3,5 => CTR => B6: 2,8 * INC # B6: 2,8 => UNS * DIS # C6: 3,5 => CTR => C6: 2,8 * INC # C6: 2,8 => UNS * INC # B6: 5,8 => UNS * DIS # C6: 5,8 => CTR => C6: 2,3 * INC # C6: 2,3 => UNS * INC # B2: 3,5 => UNS * DIS # B6: 3,5 => CTR => B6: 2,8 * INC # B6: 2,8 => UNS * DIS # C2: 3,5 => CTR => C2: 2,8,9 * INC # C2: 2,8,9 => UNS * DIS # C6: 3,5 => CTR => C6: 2,8 * INC # C6: 2,8 => UNS * INC # D9: 5,8 => UNS * PRF # D9: 7 => SOL * CNT 37 HDP CHAINS / 37 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B2: 3,5 => UNS * DIS # C2: 3,5 => CTR => C2: 2,8,9 * INC C2: 2,8,9 # B2: 3,5 => UNS * DIS C2: 2,8,9 # B2: 2,8,9 => CTR => B2: 3,5 * DIS C2: 2,8,9 + B2: 3,5 # F1: 2,9 => CTR => F1: 3 * PRF C2: 2,8,9 + B2: 3,5 + F1: 3 => SOL * STA C2: 2,8,9 + B2: 3,5 + F1: 3 * CNT 6 HDP CHAINS / 5 HYP OPENED