Analysis of xx-top500-332-base.sdk
Contents
Original Sudoku
level: medium
position: ......1.7.9..2............4...4.15...2...3.6....7.........9..3.4..8.....1........ initial
Autosolve
position: ......1.7.9..2............4...4.15...2.9.3.6....7.2.......9..3.4..8.....1........ autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C1: 3,4 => CTR => C1: 2,5,6,8 * PRF # E9: 7 => SOL * DIS # A2: 5,8 => CTR => A2: 3,6,7 * DIS # C2: 5,8 => CTR => C2: 1,3,4,6,7 * DIS # F2: 5,8 => CTR => F2: 4,6,7 * DIS # H9: 5,8 => CTR => H9: 2,4,7,9 * DIS # E6: 5 => CTR => E6: 6,8 * DIS # A4: 6,8 => CTR => A4: 3,7,9 * DIS # A5: 5,8 => CTR => A5: 7 * PRF # A5: 7 => SOL * DIS # C5: 5,8 => CTR => C5: 1,4,7 * PRF # H6: 1,8 => SOL * DIS # H6: 4,9 => CTR => H6: 1,8 * DIS # I6: 1,8 => CTR => I6: 3,9 * PRF # C5: 1,8 => SOL * DIS # C5: 4,5,7 => CTR => C5: 1,8 * DIS # I7: 2,5,6 => CTR => I7: 1,8 * CNT 17 HDP CHAINS / 36 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C1: 3,4 => CTR => C1: 2,5,6,8 * PRF C1: 2,5,6,8 # B1: 5,6,8 => SOL * STA C1: 2,5,6,8 + B1: 5,6,8 * CNT 2 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ......1.7.9..2............4...4.15...2...3.6....7.........9..3.4..8.....1........ | initial |
| ......1.7.9..2............4...4.15...2.9.3.6....7.2.......9..3.4..8.....1........ | autosolve |
| 358649127694127385217538694963481572721953468845762913576294831432816759189375246 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (5) E1: 3,4 H2: 5,8 E4: 6,8 E5: 5,8 I5: 1,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D7,E8: 1.. / D7 = 1 => 0 pairs (X) / E8 = 1 => 0 pairs (_) C2,D2: 1.. / C2 = 1 => 0 pairs (X) / D2 = 1 => 0 pairs (_) C5,I5: 1.. / C5 = 1 => 0 pairs (*) / I5 = 1 => 0 pairs (X) D7,I7: 1.. / D7 = 1 => 0 pairs (X) / I7 = 1 => 0 pairs (_) B3,B6: 1.. / B3 = 1 => 0 pairs (*) / B6 = 1 => 0 pairs (X) E3,E8: 1.. / E3 = 1 => 0 pairs (X) / E8 = 1 => 0 pairs (_) H6,H8: 1.. / H6 = 1 => 0 pairs (*) / H8 = 1 => 0 pairs (X) H4,I4: 2.. / H4 = 2 => 0 pairs (X) / I4 = 2 => 5 pairs (_) D7,D9: 2.. / D7 = 2 => 0 pairs (*) / D9 = 2 => 0 pairs (X) C2,F2: 4.. / C2 = 4 => 0 pairs (*) / F2 = 4 => 0 pairs (X) C5,G5: 4.. / C5 = 4 => 0 pairs (X) / G5 = 4 => 0 pairs (_) F7,G7: 4.. / F7 = 4 => 0 pairs (*) / G7 = 4 => 0 pairs (X) B1,B6: 4.. / B1 = 4 => 0 pairs (X) / B6 = 4 => 0 pairs (_) E1,E9: 4.. / E1 = 4 => 0 pairs (*) / E9 = 4 => 0 pairs (X) H6,H9: 4.. / H6 = 4 => 0 pairs (X) / H9 = 4 => 0 pairs (_) E5,E6: 5.. / E5 = 5 => 6 pairs (_) / E6 = 5 => 0 pairs (X) E4,E6: 6.. / E4 = 6 => 5 pairs (_) / E6 = 6 => 4 pairs (_) H4,G5: 7.. / H4 = 7 => 6 pairs (_) / G5 = 7 => 0 pairs (X) F1,F3: 9.. / F1 = 9 => 5 pairs (_) / F3 = 9 => 5 pairs (_) A4,A6: 9.. / A4 = 9 => 5 pairs (_) / A6 = 9 => 0 pairs (X) C8,C9: 9.. / C8 = 9 => 5 pairs (_) / C9 = 9 => 5 pairs (_) F1,H1: 9.. / F1 = 9 => 5 pairs (_) / H1 = 9 => 5 pairs (_) * DURATION: 0:00:32.705368 START: 14:08:28.372893 END: 14:09:01.078261 2017-05-04 * CP COUNT: (22) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (E1,E4,E5,H2,I5) * ......1.7.9..2............4...4.15...2.9.3.6....7.2.......9..3.4..8.....1........ * PAIR E1: 3,4 ROW 1 B1: 3,4,5,6,8 # reduction candidate for 3,4 B1: 3,4 # 7 pairs C1: 3,4,2,5,6,8 # reduction candidate for 3,4 C1: 3,4 => CTR * ..3.4.1.7.9412.....1......4...4.1572.219.3468.4.7.2.1.....94.3143.81....1......4. C1: 2,5,6,8 # 5 pairs * PAIR E1: 3,4 COL E E9: 3,4,7 # reduction candidate for 3,4 E9: 7 => SOLVED * 358649127694127385217538694963481572721953468845762913576294831432816759189375246 E9: 3,4 # 8 pairs * PAIR H2: 5,8 BLK 3 H1: 5,8,2,9 # reduction candidate for 5,8 H1: 5,8 # 11 pairs I2: 5,8,3,6 # reduction candidate for 5,8 I2: 5,8 # 14 pairs H3: 5,8,2,9 # reduction candidate for 5,8 H3: 5,8 # 11 pairs * PAIR H2: 5,8 ROW 2 A2: 5,8,3,6,7 # reduction candidate for 5,8 A2: 5,8 => CTR * 3..5491275941276832176389549..4.1572721953468.457.2319.5.294.314..81..9.1.937.24. A2: 3,6,7 # 5 pairs C2: 5,8,1,3,4,6,7 # reduction candidate for 5,8 C2: 5,8 => CTR * ......1.7.9.124...........4...4.15...2.9.3.6....7.2.......9.4314..81....1...4.... C2: 1,3,4,6,7 # 5 pairs F2: 5,8,4,6,7 # reduction candidate for 5,8 F2: 5,8 => CTR * ....4.1.779412.....1......4...4.1572.2.9.346..4.7.2.......94.314..81....1......4. F2: 4,6,7 # 7 pairs * PAIR H2: 5,8 COL H H9: 5,8,2,4,7,9 # reduction candidate for 5,8 H9: 5,8 => CTR * .4..3.1.7.9..24.......17..4...4.1572.249.3861.1.7.2.4....19.43.4..87..1.1........ H9: 2,4,7,9 # 5 pairs * PAIR E4: 6,8 BLK 5 E6: 6,8,5 # reduction candidate for 6,8 E6: 5 => CTR * ......1.7.91.24.......17..4...4615...2.983.61.1.752......19.43.4..8...1.1..24.... E6: 6,8 # 6 pairs * PAIR E4: 6,8 ROW 4 A4: 6,8,3,7,9 # reduction candidate for 6,8 A4: 6,8 => CTR * .4..3.1.7.91.24.......17..4...4.15...249.376191.7.2.4....19.43.4..87..1.1..24..7. A4: 3,7,9 # 5 pairs B4: 6,8,3,7 # reduction candidate for 6,8 B4: 6,8 # 7 pairs C4: 6,8,3,7 # reduction candidate for 6,8 C4: 6,8 # 7 pairs * PAIR E5: 5,8 BLK 5 E6: 5,8,6 # reduction candidate for 5,8 E6: 5,8 # 5 pairs E6: 6 # 4 pairs * PAIR E5: 5,8 ROW 5 A5: 5,8,7 # reduction candidate for 5,8 A5: 5,8 => CTR * ......1.7.91.24.......17..4...4.15...2.9.3.61.1.7.2......19.43.4..8...1.1..24.... A5: 7 => SOLVED * 358649127694127385217538694963481572721953468845762913576294831432816759189375246 C5: 5,8,1,4,7 # reduction candidate for 5,8 C5: 5,8 => CTR * ......1.7.9..2............4...4.15...2.9.3461...7.2......194.3.4..8...1.1..2...4. C5: 1,4,7 # 5 pairs * PAIR I5: 1,8 BLK 6 H6: 1,8,4,9 # reduction candidate for 1,8 H6: 1,8 => SOLVED * 358649127694127385217538694963481572721953468845762913576294831432816759189375246 H6: 4,9 => CTR * .4..3.1.7.91.24.......17..4...4.15...2.9.3.61.1.7.2......19.43.4..87..1.1..24.... I6: 1,8,3,9 # reduction candidate for 1,8 I6: 1,8 => CTR * ......1.7.91.24.......17..4...4.15...2.9.3.61.1.7.2..8...19.43.4..8...1.1..24.... I6: 3,9 # 6 pairs * PAIR I5: 1,8 ROW 5 C5: 1,8,4,5,7 # reduction candidate for 1,8 C5: 1,8 => SOLVED * 358649127694127385217538694963481572721953468845762913576294831432816759189375246 C5: 4,5,7 => CTR * ......1.7.91.24.......17..4...4.15...2.9.3.61.1.7.2......19.43.4..8...1.1..24.... * PAIR I5: 1,8 COL I I7: 1,8,2,5,6 # reduction candidate for 1,8 I7: 2,5,6 => CTR * ......1.7.91.24.......17..4...4.15...2.9.3.61.1.7.2......19.43.4..8...1.1..24.... I7: 1,8 # 7 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-332-base-pr-000.dot * REASONING * DIS # C1: 3,4 => CTR => C1: 2,5,6,8 * PRF # E9: 7 => SOL * DIS # A2: 5,8 => CTR => A2: 3,6,7 * DIS # C2: 5,8 => CTR => C2: 1,3,4,6,7 * DIS # F2: 5,8 => CTR => F2: 4,6,7 * DIS # H9: 5,8 => CTR => H9: 2,4,7,9 * DIS # E6: 5 => CTR => E6: 6,8 * DIS # A4: 6,8 => CTR => A4: 3,7,9 * DIS # A5: 5,8 => CTR => A5: 7 * PRF # A5: 7 => SOL * DIS # C5: 5,8 => CTR => C5: 1,4,7 * PRF # H6: 1,8 => SOL * DIS # H6: 4,9 => CTR => H6: 1,8 * DIS # I6: 1,8 => CTR => I6: 3,9 * PRF # C5: 1,8 => SOL * DIS # C5: 4,5,7 => CTR => C5: 1,8 * DIS # I7: 2,5,6 => CTR => I7: 1,8 * CNT 17 HDP CHAINS / 36 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (E1,E4,E5,H2,I5) * ......1.7.9..2............4...4.15...2.9.3.6....7.2.......9..3.4..8.....1........ * PAIR E1: 3,4 ROW 1 B1: 3,4,5,6,8 # reduction candidate for 3,4 B1: 3,4 # 7 pairs C1: 3,4,2,5,6,8 # reduction candidate for 3,4 C1: 3,4 => CTR * ..3.4.1.7.9412.....1......4...4.1572.219.3468.4.7.2.1.....94.3143.81....1......4. * RESTART * PAIR E1: 3,4 ROW 1 B1: 3,4,5,6,8 # reduction candidate for 3,4 B1: 5,6,8 => SOLVED * 358649127694127385217538694963481572721953468845762913576294831432816759189375246 * DURATION: 0:00:04.659957 START: 14:09:25.803208 END: 14:09:30.463165 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-332-base-pr-001.dot * REASONING * DIS # C1: 3,4 => CTR => C1: 2,5,6,8 * PRF C1: 2,5,6,8 # B1: 5,6,8 => SOL * STA C1: 2,5,6,8 + B1: 5,6,8 * CNT 2 HDP CHAINS / 4 HYP OPENED
Header Info
Top 500 Minimum 17 332 solution: 358649127694127385217538694963481572721953468845762913576294831432816759189375246 info: 3039 FNBHWY S8.f 899 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 358649127694127385217538694963481572721953468845762913576294831432816759189375246 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 # B1: 3,4 => UNS * DIS # C1: 3,4 => CTR => C1: 2,5,6,8 * INC # C1: 2,5,6,8 => UNS * INC # E9: 3,4 => UNS * PRF # E9: 7 => SOL * INC # H1: 5,8 => UNS * INC # I2: 5,8 => UNS * INC # H3: 5,8 => UNS * DIS # A2: 5,8 => CTR => A2: 3,6,7 * INC # A2: 3,6,7 => UNS * DIS # C2: 5,8 => CTR => C2: 1,3,4,6,7 * INC # C2: 1,3,4,6,7 => UNS * DIS # F2: 5,8 => CTR => F2: 4,6,7 * INC # F2: 4,6,7 => UNS * DIS # H9: 5,8 => CTR => H9: 2,4,7,9 * INC # H9: 2,4,7,9 => UNS * INC # E6: 6,8 => UNS * DIS # E6: 5 => CTR => E6: 6,8 * DIS # A4: 6,8 => CTR => A4: 3,7,9 * INC # A4: 3,7,9 => UNS * INC # B4: 6,8 => UNS * INC # C4: 6,8 => UNS * INC # E6: 5,8 => UNS * INC # E6: 6 => UNS * DIS # A5: 5,8 => CTR => A5: 7 * PRF # A5: 7 => SOL * DIS # C5: 5,8 => CTR => C5: 1,4,7 * INC # C5: 1,4,7 => UNS * PRF # H6: 1,8 => SOL * DIS # H6: 4,9 => CTR => H6: 1,8 * DIS # I6: 1,8 => CTR => I6: 3,9 * INC # I6: 3,9 => UNS * PRF # C5: 1,8 => SOL * DIS # C5: 4,5,7 => CTR => C5: 1,8 * INC # I7: 1,8 => UNS * DIS # I7: 2,5,6 => CTR => I7: 1,8 * CNT 36 HDP CHAINS / 36 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B1: 3,4 => UNS * DIS # C1: 3,4 => CTR => C1: 2,5,6,8 * INC C1: 2,5,6,8 # B1: 3,4 => UNS * PRF C1: 2,5,6,8 # B1: 5,6,8 => SOL * STA C1: 2,5,6,8 + B1: 5,6,8 * CNT 4 HDP CHAINS / 4 HYP OPENED