Analysis of xx-top500-093-base.sdk
Contents
Original Sudoku
level: medium
position: 5..2...3.6.1..5............1....64...3..7..8...........7.83..........6.1......... initial
Autosolve
position: 5..26713.6213.58.77.3.18.6.1.7.86423.3.17..8686...371..76831.5.3..7..6.1.1.6..378 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B1: 4,9 => CTR => B1: 8 * DIS # B8: 4,9 => CTR => B8: 5,8 * DIS # E9: 4,9 => CTR => E9: 2,5 * PRF # D6: 4,9 => SOL * DIS # D6: 5 => CTR => D6: 4,9 * DIS # B1: 4,9 => CTR => B1: 8 * DIS # I7: 4,9 => CTR => I7: 2 * PRF # I7: 2 => SOL * PRF # C6: 5,9 => SOL * PRF # B8: 5,9 => SOL * DIS # B8: 4,8 => CTR => B8: 5,9 * DIS # D6: 5,9 => CTR => D6: 4 * PRF # D6: 4 => SOL * PRF # C5: 2,4 => SOL * PRF # C6: 5,9 => SOL * DIS # D6: 5,9 => CTR => D6: 4 * PRF # D6: 4 => SOL * DIS # B8: 4,9 => CTR => B8: 5,8 * DIS # C8: 4,9 => CTR => C8: 2,5,8 * DIS # I7: 4,9 => CTR => I7: 2 * PRF # I7: 2 => SOL * PRF # I7: 2,9 => SOL * DIS # I7: 4 => CTR => I7: 2,9 * DIS # I7: 4,9 => CTR => I7: 2 * PRF # I7: 2 => SOL * DIS # B8: 4,9 => CTR => B8: 5,8 * DIS # C8: 4,9 => CTR => C8: 2,5,8 * CNT 27 HDP CHAINS / 49 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B1: 4,9 => CTR => B1: 8 * DIS B1: 8 # B8: 4,9 => CTR => B8: 5 * PRF B1: 8 + B8: 5 => SOL * STA B1: 8 + B8: 5 * CNT 3 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 5..2...3.6.1..5............1....64...3..7..8...........7.83..........6.1......... | initial |
| 5..26713.6213.58.77.3.18.6.1.7.86423.3.17..8686...371..76831.5.3..7..6.1.1.6..378 | autosolve |
| 589267134621345897743918265197586423234179586865423719476831952358792641912654378 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) B3: 4,9 E2: 4,9 D3: 4,9 I1: 4,9 H2: 4,9 G3: 2,5 I3: 2,5 B4: 5,9 D4: 5,9 G5: 5,9 I6: 5,9 A7: 4,9 G7: 2,9 H8: 4,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G3,I3: 2.. / G3 = 2 => 0 pairs (*) / I3 = 2 => 0 pairs (X) F5,E6: 2.. / F5 = 2 => 22 pairs (_) / E6 = 2 => 15 pairs (_) G7,I7: 2.. / G7 = 2 => 0 pairs (X) / I7 = 2 => 0 pairs (_) C6,E6: 2.. / C6 = 2 => 22 pairs (_) / E6 = 2 => 15 pairs (_) A5,A9: 2.. / A5 = 2 => 19 pairs (_) / A9 = 2 => 16 pairs (_) G3,G7: 2.. / G3 = 2 => 0 pairs (*) / G7 = 2 => 0 pairs (X) I3,I7: 2.. / I3 = 2 => 0 pairs (X) / I7 = 2 => 0 pairs (_) E2,D3: 4.. / E2 = 4 => 0 pairs (*) / D3 = 4 => 0 pairs (X) I1,H2: 4.. / I1 = 4 => 0 pairs (*) / H2 = 4 => 0 pairs (X) I7,H8: 4.. / I7 = 4 => 0 pairs (X) / H8 = 4 => 0 pairs (_) E2,H2: 4.. / E2 = 4 => 0 pairs (*) / H2 = 4 => 0 pairs (X) B3,D3: 4.. / B3 = 4 => 0 pairs (*) / D3 = 4 => 0 pairs (X) A7,I7: 4.. / A7 = 4 => 0 pairs (*) / I7 = 4 => 0 pairs (X) D3,D6: 4.. / D3 = 4 => 0 pairs (X) / D6 = 4 => 0 pairs (_) H2,H8: 4.. / H2 = 4 => 0 pairs (X) / H8 = 4 => 0 pairs (_) I1,I7: 4.. / I1 = 4 => 0 pairs (*) / I7 = 4 => 0 pairs (X) G3,I3: 5.. / G3 = 5 => 0 pairs (X) / I3 = 5 => 0 pairs (_) D4,D6: 5.. / D4 = 5 => 0 pairs (*) / D6 = 5 => 0 pairs (X) G5,I6: 5.. / G5 = 5 => 0 pairs (*) / I6 = 5 => 0 pairs (X) E8,E9: 5.. / E8 = 5 => 0 pairs (X) / E9 = 5 => 18 pairs (_) B4,D4: 5.. / B4 = 5 => 0 pairs (X) / D4 = 5 => 0 pairs (_) C5,G5: 5.. / C5 = 5 => 0 pairs (X) / G5 = 5 => 0 pairs (_) C9,E9: 5.. / C9 = 5 => 0 pairs (X) / E9 = 5 => 18 pairs (_) B4,B8: 5.. / B4 = 5 => 0 pairs (X) / B8 = 5 => 0 pairs (_) G3,G5: 5.. / G3 = 5 => 0 pairs (X) / G5 = 5 => 0 pairs (_) I3,I6: 5.. / I3 = 5 => 0 pairs (*) / I6 = 5 => 0 pairs (X) B1,C1: 8.. / B1 = 8 => 16 pairs (_) / C1 = 8 => 0 pairs (X) B8,C8: 8.. / B8 = 8 => 0 pairs (X) / C8 = 8 => 16 pairs (_) B1,B8: 8.. / B1 = 8 => 16 pairs (_) / B8 = 8 => 0 pairs (X) C1,C8: 8.. / C1 = 8 => 0 pairs (X) / C8 = 8 => 16 pairs (_) E2,D3: 9.. / E2 = 9 => 0 pairs (X) / D3 = 9 => 0 pairs (_) I1,H2: 9.. / I1 = 9 => 0 pairs (X) / H2 = 9 => 0 pairs (_) G5,I6: 9.. / G5 = 9 => 0 pairs (X) / I6 = 9 => 0 pairs (_) E2,H2: 9.. / E2 = 9 => 0 pairs (X) / H2 = 9 => 0 pairs (_) B3,D3: 9.. / B3 = 9 => 0 pairs (X) / D3 = 9 => 0 pairs (_) B4,D4: 9.. / B4 = 9 => 0 pairs (*) / D4 = 9 => 0 pairs (X) G5,G7: 9.. / G5 = 9 => 0 pairs (X) / G7 = 9 => 0 pairs (_) H2,H8: 9.. / H2 = 9 => 0 pairs (*) / H8 = 9 => 0 pairs (X) * DURATION: 0:01:12.310903 START: 05:57:23.249301 END: 05:58:35.560204 2017-05-04 * CP COUNT: (38) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B3,B4,D3,D4,E2,G3,G5,G7,H2,H8,I1,I3,I6) * 5..26713.6213.58.77.3.18.6.1.7.86423.3.17..8686...371..76831.5.3..7..6.1.1.6..378 * PAIR B3: 4,9 BLK 1 B1: 4,9,8 # reduction candidate for 4,9 B1: 4,9 => CTR * 5.826713.6213.58.77.3.18.6.157986423.3.17.58686.5.3719.7683195238.7..641.1.6..378 B1: 8 # 16 pairs C1: 4,9,8 # reduction candidate for 4,9 C1: 4,9 # 16 pairs * PAIR B3: 4,9 COL B B8: 4,9,5,8 # reduction candidate for 4,9 B8: 4,9 => CTR * 58.26713.6213.58.77.3.18.6.157986423.3.17.58686.5.3719.768319523.8752641.156.9378 B8: 5,8 # 16 pairs * PAIR E2: 4,9 COL E E6: 4,9,2 # reduction candidate for 4,9 E6: 4,9 # 22 pairs E8: 4,9,2,5 # reduction candidate for 4,9 E8: 4,9 # 20 pairs E9: 4,9,2,5 # reduction candidate for 4,9 E9: 4,9 => CTR * 5..26713.6213.58.77.3.18.6.157986423.3.17.58686.523719.768319523..75.641.156..378 E9: 2,5 # 15 pairs * PAIR D3: 4,9 COL D D6: 4,9,5 # reduction candidate for 4,9 D6: 4,9 => SOLVED * 589267134621345897743918265197586423234179586865423719476831952358792641912654378 D6: 5 => CTR * 5..26713.6213.58.77.3418.6.1.7986423.3.17..8686.5.3719.768319523..7..641.1.6..378 * PAIR I1: 4,9 ROW 1 B1: 4,9,8 # reduction candidate for 4,9 B1: 4,9 => CTR * 5.826713.6213.58.77.3.18.6.157986423.3.17.58686.5.3719.7683195238.7..641.1.6..378 B1: 8 # 16 pairs C1: 4,9,8 # reduction candidate for 4,9 C1: 4,9 # 16 pairs * PAIR I1: 4,9 COL I I7: 4,9,2 # reduction candidate for 4,9 I7: 4,9 => CTR * 5892671346213.58.7743918562197586423.3517.98686.493715.7683125.35872.6.1.14659378 I7: 2 => SOLVED * 589267134621345897743918265197586423234179586865423719476831952358792641912654378 * PAIR B4: 5,9 BLK 4 C5: 5,9,2,4 # reduction candidate for 5,9 C5: 5,9 # 18 pairs C6: 5,9,2,4 # reduction candidate for 5,9 C6: 5,9 => SOLVED * 589267134621345897743918265197586423234179586865423719476831952358792641912654378 C6: 2,4 # 15 pairs * PAIR B4: 5,9 COL B B8: 5,9,4,8 # reduction candidate for 5,9 B8: 5,9 => SOLVED * 589267134621345897743918265197586423234179586865423719476831952358792641912654378 B8: 4,8 => CTR * 5..26713.6213.58.77.3.18.6.157986423.3.17.58686.5.3719.768319523..7..641.1.6..378 * PAIR D4: 5,9 BLK 5 D6: 5,9,4 # reduction candidate for 5,9 D6: 5,9 => CTR * 5..26713.621395847793418.6.157986423.3.17.58686.5.3719.76831.5.3..7..6.1.1.6..378 D6: 4 => SOLVED * 589267134621345897743918265197586423234179586865423719476831952358792641912654378 * PAIR G5: 5,9 ROW 5 C5: 5,9,2,4 # reduction candidate for 5,9 C5: 2,4 => SOLVED * 589267134621345897743918265197586423234179586865423719476831952358792641912654378 C5: 5,9 # 18 pairs * PAIR I6: 5,9 ROW 6 C6: 5,9,2,4 # reduction candidate for 5,9 C6: 5,9 => SOLVED * 589267134621345897743918265197586423234179586865423719476831952358792641912654378 C6: 2,4 # 15 pairs D6: 5,9,4 # reduction candidate for 5,9 D6: 5,9 => CTR * 5..26713.621395847793418.6.157986423.3.17.58686.5.3719.76831.5.3..7..6.1.1.6..378 D6: 4 => SOLVED * 589267134621345897743918265197586423234179586865423719476831952358792641912654378 * PAIR A7: 4,9 BLK 7 B8: 4,9,5,8 # reduction candidate for 4,9 B8: 4,9 => CTR * 58.26713.6213.58.77.3.18.6.157986423.3.17.58686.5.3719.768319523.8752641.156.9378 B8: 5,8 # 16 pairs C8: 4,9,2,5,8 # reduction candidate for 4,9 C8: 4,9 => CTR * 5.826713.6213.58.77.3.18.6.157986423.3.174586864523719.7683195238975264121564.378 C8: 2,5,8 # 14 pairs A9: 4,9,2 # reduction candidate for 4,9 A9: 4,9 # 19 pairs C9: 4,9,2,5 # reduction candidate for 4,9 C9: 4,9 # 20 pairs * PAIR A7: 4,9 ROW 7 I7: 4,9,2 # reduction candidate for 4,9 I7: 4,9 => CTR * 5892671346213.58.7743918562197586423.3517.98686.493715.7683125.35872.6.1.14659378 I7: 2 => SOLVED * 589267134621345897743918265197586423234179586865423719476831952358792641912654378 * PAIR A7: 4,9 COL A A5: 4,9,2 # reduction candidate for 4,9 A5: 2 # 19 pairs A5: 4,9 # 16 pairs * PAIR G7: 2,9 BLK 9 I7: 2,9,4 # reduction candidate for 2,9 I7: 2,9 => SOLVED * 589267134621345897743918265197586423234179586865423719476831952358792641912654378 I7: 4 => CTR * 5..267139621395847793418.621.7.86423.3.17..8686...3715.768312543..7..691.1.6..378 * PAIR H8: 4,9 BLK 9 I7: 4,9,2 # reduction candidate for 4,9 I7: 4,9 => CTR * 5892671346213.58.7743918562197586423.3517.98686.493715.7683125.35872.6.1.14659378 I7: 2 => SOLVED * 589267134621345897743918265197586423234179586865423719476831952358792641912654378 * PAIR H8: 4,9 ROW 8 B8: 4,9,5,8 # reduction candidate for 4,9 B8: 4,9 => CTR * 58.26713.6213.58.77.3.18.6.157986423.3.17.58686.5.3719.768319523.8752641.156.9378 B8: 5,8 # 16 pairs C8: 4,9,2,5,8 # reduction candidate for 4,9 C8: 4,9 => CTR * 5.826713.6213.58.77.3.18.6.157986423.3.174586864523719.7683195238975264121564.378 C8: 2,5,8 # 14 pairs E8: 4,9,2,5 # reduction candidate for 4,9 E8: 4,9 # 20 pairs F8: 4,9,2 # reduction candidate for 4,9 F8: 4,9 # 18 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-093-base-pr-000.dot * REASONING * DIS # B1: 4,9 => CTR => B1: 8 * DIS # B8: 4,9 => CTR => B8: 5,8 * DIS # E9: 4,9 => CTR => E9: 2,5 * PRF # D6: 4,9 => SOL * DIS # D6: 5 => CTR => D6: 4,9 * DIS # B1: 4,9 => CTR => B1: 8 * DIS # I7: 4,9 => CTR => I7: 2 * PRF # I7: 2 => SOL * PRF # C6: 5,9 => SOL * PRF # B8: 5,9 => SOL * DIS # B8: 4,8 => CTR => B8: 5,9 * DIS # D6: 5,9 => CTR => D6: 4 * PRF # D6: 4 => SOL * PRF # C5: 2,4 => SOL * PRF # C6: 5,9 => SOL * DIS # D6: 5,9 => CTR => D6: 4 * PRF # D6: 4 => SOL * DIS # B8: 4,9 => CTR => B8: 5,8 * DIS # C8: 4,9 => CTR => C8: 2,5,8 * DIS # I7: 4,9 => CTR => I7: 2 * PRF # I7: 2 => SOL * PRF # I7: 2,9 => SOL * DIS # I7: 4 => CTR => I7: 2,9 * DIS # I7: 4,9 => CTR => I7: 2 * PRF # I7: 2 => SOL * DIS # B8: 4,9 => CTR => B8: 5,8 * DIS # C8: 4,9 => CTR => C8: 2,5,8 * CNT 27 HDP CHAINS / 49 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B3,B4,D3,D4,E2,G3,G5,G7,H2,H8,I1,I3,I6) * 5..26713.6213.58.77.3.18.6.1.7.86423.3.17..8686...371..76831.5.3..7..6.1.1.6..378 * PAIR B3: 4,9 BLK 1 B1: 4,9,8 # reduction candidate for 4,9 B1: 4,9 => CTR * 5.826713.6213.58.77.3.18.6.157986423.3.17.58686.5.3719.7683195238.7..641.1.6..378 * RESTART * PAIR B3: 4,9 COL B B8: 4,9,5 # reduction candidate for 4,9 B8: 4,9 => CTR * 58.26713.6213.58.77.3.18.6.157986423.3.17.58686.5.3719.768319523.8752641.156.9378 B8: 5 => SOLVED * 589267134621345897743918265197586423234179586865423719476831952358792641912654378 * DURATION: 0:00:04.476814 START: 05:59:29.834850 END: 05:59:34.311664 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-093-base-pr-001.dot * REASONING * DIS # B1: 4,9 => CTR => B1: 8 * DIS B1: 8 # B8: 4,9 => CTR => B8: 5 * PRF B1: 8 + B8: 5 => SOL * STA B1: 8 + B8: 5 * CNT 3 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 093 solution: 589267134621345897743918265197586423234179586865423719476831952358792641912654378 info: 1570 FNBTWXY S8.f 32754 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 589267134621345897743918265197586423234179586865423719476831952358792641912654378 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 # B1: 4,9 => CTR => B1: 8 * INC # B1: 8 => UNS * INC # C1: 4,9 => UNS * DIS # B8: 4,9 => CTR => B8: 5,8 * INC # B8: 5,8 => UNS * INC # E6: 4,9 => UNS * INC # E8: 4,9 => UNS * DIS # E9: 4,9 => CTR => E9: 2,5 * INC # E9: 2,5 => UNS * PRF # D6: 4,9 => SOL * DIS # D6: 5 => CTR => D6: 4,9 * DIS # B1: 4,9 => CTR => B1: 8 * INC # B1: 8 => UNS * INC # C1: 4,9 => UNS * DIS # I7: 4,9 => CTR => I7: 2 * PRF # I7: 2 => SOL * INC # C5: 5,9 => UNS * PRF # C6: 5,9 => SOL * INC # C6: 2,4 => UNS * PRF # B8: 5,9 => SOL * DIS # B8: 4,8 => CTR => B8: 5,9 * DIS # D6: 5,9 => CTR => D6: 4 * PRF # D6: 4 => SOL * INC # C5: 5,9 => UNS * PRF # C5: 2,4 => SOL * PRF # C6: 5,9 => SOL * INC # C6: 2,4 => UNS * DIS # D6: 5,9 => CTR => D6: 4 * PRF # D6: 4 => SOL * DIS # B8: 4,9 => CTR => B8: 5,8 * INC # B8: 5,8 => UNS * DIS # C8: 4,9 => CTR => C8: 2,5,8 * INC # C8: 2,5,8 => UNS * INC # A9: 4,9 => UNS * INC # C9: 4,9 => UNS * DIS # I7: 4,9 => CTR => I7: 2 * PRF # I7: 2 => SOL * INC # A5: 4,9 => UNS * INC # A5: 2 => UNS * PRF # I7: 2,9 => SOL * DIS # I7: 4 => CTR => I7: 2,9 * DIS # I7: 4,9 => CTR => I7: 2 * PRF # I7: 2 => SOL * DIS # B8: 4,9 => CTR => B8: 5,8 * INC # B8: 5,8 => UNS * DIS # C8: 4,9 => CTR => C8: 2,5,8 * INC # C8: 2,5,8 => UNS * INC # E8: 4,9 => UNS * INC # F8: 4,9 => UNS * CNT 49 HDP CHAINS / 49 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B1: 4,9 => CTR => B1: 8 * DIS B1: 8 # B8: 4,9 => CTR => B8: 5 * PRF B1: 8 + B8: 5 => SOL * STA B1: 8 + B8: 5 * CNT 3 HDP CHAINS / 2 HYP OPENED