Analysis of xx-top500-244-base.sdk
Contents
Original Sudoku
level: medium
position: ....7.8.......84..3.........5.....311......7.....4......86..2...2.3........1..... initial
Autosolve
position: 41.2738..2.7.184.338.4..1278547.2.311.283..74.73.41.827386.421..2138.74..4.1273.8 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # C1: 6,9 => SOL * DIS # C1: 5 => CTR => C1: 6,9 * PRF # H2: 6,9 => SOL * DIS # H2: 5 => CTR => H2: 6,9 * DIS # C1: 6 => CTR => C1: 5,9 * DIS # F3: 5,9 => CTR => F3: 6 * DIS # F3: 5,9 => CTR => F3: 6 * DIS # H2: 6 => CTR => H2: 5,9 * DIS # F5: 6,9 => CTR => F5: 5 * PRF # F5: 5 => SOL * PRF # G5: 6,9 => SOL * DIS # G5: 5 => CTR => G5: 6,9 * DIS # G6: 6,9 => CTR => G6: 5 * PRF # G6: 5 => SOL * PRF # A9: 6,9 => SOL * DIS # F5: 6,9 => CTR => F5: 5 * PRF # F5: 5 => SOL * DIS # E3: 5 => CTR => E3: 6,9 * DIS # F5: 6 => CTR => F5: 5,9 * DIS # G6: 6 => CTR => G6: 5,9 * PRF # G5: 6,9 => SOL * DIS # G5: 5 => CTR => G5: 6,9 * DIS # G6: 6,9 => CTR => G6: 5 * PRF # G6: 5 => SOL * PRF # A9: 6,9 => SOL * PRF # H9: 5 => SOL * PRF # C1: 6,9 => SOL * DIS # C1: 5 => CTR => C1: 6,9 * DIS # E3: 6 => CTR => E3: 5,9 * DIS # I8: 5,9 => CTR => I8: 6 * DIS # F3: 5,9 => CTR => F3: 6 * DIS # I8: 5,9 => CTR => I8: 6 * DIS # I1: 6 => CTR => I1: 5,9 * CNT 33 HDP CHAINS / 55 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # C1: 6,9 => SOL * STA C1: 6,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....7.8.......84..3.........5.....311......7.....4......86..2...2.3........1..... | initial |
| 41.2738..2.7.184.338.4..1278547.2.311.283..74.73.41.827386.421..2138.74..4.1273.8 | autosolve |
| 419273865267518493385496127854762931192835674673941582738654219521389746946127358 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (12) B2: 6,9 C3: 5,9 D2: 5,9 B5: 6,9 A6: 6,9 E4: 6,9 D6: 5,9 G4: 6,9 C9: 6,9 E7: 5,9 F8: 5,9 I7: 5,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C1,C3: 5.. / C1 = 5 => 0 pairs (X) / C3 = 5 => 0 pairs (_) F5,D6: 5.. / F5 = 5 => 0 pairs (*) / D6 = 5 => 0 pairs (X) G5,G6: 5.. / G5 = 5 => 0 pairs (X) / G6 = 5 => 0 pairs (_) A8,A9: 5.. / A8 = 5 => 0 pairs (*) / A9 = 5 => 0 pairs (X) E7,F8: 5.. / E7 = 5 => 16 pairs (_) / F8 = 5 => 0 pairs (X) D2,H2: 5.. / D2 = 5 => 0 pairs (*) / H2 = 5 => 0 pairs (X) F5,G5: 5.. / F5 = 5 => 0 pairs (*) / G5 = 5 => 0 pairs (X) D6,G6: 5.. / D6 = 5 => 0 pairs (X) / G6 = 5 => 0 pairs (_) E7,I7: 5.. / E7 = 5 => 16 pairs (_) / I7 = 5 => 0 pairs (X) A9,H9: 5.. / A9 = 5 => 15 pairs (_) / H9 = 5 => 0 pairs (*) D2,D6: 5.. / D2 = 5 => 0 pairs (*) / D6 = 5 => 0 pairs (X) E3,E7: 5.. / E3 = 5 => 0 pairs (X) / E7 = 5 => 16 pairs (_) C1,B2: 6.. / C1 = 6 => 0 pairs (X) / B2 = 6 => 17 pairs (_) E3,F3: 6.. / E3 = 6 => 0 pairs (X) / F3 = 6 => 14 pairs (_) B5,A6: 6.. / B5 = 6 => 0 pairs (X) / A6 = 6 => 17 pairs (_) E4,F5: 6.. / E4 = 6 => 14 pairs (_) / F5 = 6 => 0 pairs (X) I8,H9: 6.. / I8 = 6 => 15 pairs (_) / H9 = 6 => 0 pairs (X) B2,H2: 6.. / B2 = 6 => 17 pairs (_) / H2 = 6 => 0 pairs (X) E4,G4: 6.. / E4 = 6 => 14 pairs (_) / G4 = 6 => 0 pairs (X) A6,G6: 6.. / A6 = 6 => 17 pairs (_) / G6 = 6 => 0 pairs (X) A8,I8: 6.. / A8 = 6 => 0 pairs (X) / I8 = 6 => 15 pairs (_) B2,B5: 6.. / B2 = 6 => 17 pairs (_) / B5 = 6 => 0 pairs (X) C1,C9: 6.. / C1 = 6 => 0 pairs (X) / C9 = 6 => 17 pairs (_) E3,E4: 6.. / E3 = 6 => 0 pairs (X) / E4 = 6 => 14 pairs (_) F3,F5: 6.. / F3 = 6 => 14 pairs (_) / F5 = 6 => 0 pairs (X) I1,I8: 6.. / I1 = 6 => 0 pairs (X) / I8 = 6 => 15 pairs (_) B5,A6: 9.. / B5 = 9 => 17 pairs (_) / A6 = 9 => 0 pairs (X) E7,F8: 9.. / E7 = 9 => 0 pairs (X) / F8 = 9 => 16 pairs (_) E4,G4: 9.. / E4 = 9 => 0 pairs (X) / G4 = 9 => 14 pairs (_) E7,I7: 9.. / E7 = 9 => 0 pairs (X) / I7 = 9 => 16 pairs (_) B2,B5: 9.. / B2 = 9 => 0 pairs (X) / B5 = 9 => 17 pairs (_) D2,D6: 9.. / D2 = 9 => 0 pairs (X) / D6 = 9 => 0 pairs (_) * DURATION: 0:00:56.150772 START: 11:08:13.008855 END: 11:09:09.159627 2017-05-04 * CP COUNT: (32) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B2,B5,C3,C9,D2,D6,E4,E7,F8,G4,I7) * 41.2738..2.7.184.338.4..1278547.2.311.283..74.73.41.827386.421..2138.74..4.1273.8 * PAIR B2: 6,9 BLK 1 C1: 6,9,5 # reduction candidate for 6,9 C1: 6,9 => SOLVED * 419273865267518493385496127854762931192835674673941582738654219521389746946127358 C1: 5 => CTR * 4152738..267.184533894..1278547.2.3119283..746735419827386.421..21389746.4.1273.8 * PAIR B2: 6,9 ROW 2 H2: 6,9,5 # reduction candidate for 6,9 H2: 6,9 => SOLVED * 419273865267518493385496127854762931192835674673941582738654219521389746946127358 H2: 5 => CTR * 41.2738..2679184533894..1278547.2.3119283..746735419827386.421..21389746.4.1273.8 * PAIR C3: 5,9 BLK 1 C1: 5,9,6 # reduction candidate for 5,9 C1: 6 => CTR * 4162738..2975184633854..1278547.2.31162835974.73.41.827386.421..2138.74..4.1273.8 C1: 5,9 # 17 pairs * PAIR C3: 5,9 ROW 3 E3: 5,9,6 # reduction candidate for 5,9 E3: 5,9 # 14 pairs F3: 5,9,6 # reduction candidate for 5,9 F3: 5,9 => CTR * 41.2738..2.7.184.338.46.1278547926311.2836574673541982738654219.21389746946127358 F3: 6 # 14 pairs * PAIR D2: 5,9 BLK 2 E3: 5,9,6 # reduction candidate for 5,9 E3: 5,9 # 14 pairs F3: 5,9,6 # reduction candidate for 5,9 F3: 5,9 => CTR * 41.2738..2.7.184.338.46.1278547926311.2836574673541982738654219.21389746946127358 F3: 6 # 14 pairs * PAIR D2: 5,9 ROW 2 H2: 5,9,6 # reduction candidate for 5,9 H2: 6 => CTR * 41.2738..2.75184633854..1278547.2.31162835974.73.41.827386.421..2138.74..4.1273.8 H2: 5,9 # 17 pairs * PAIR B5: 6,9 ROW 5 F5: 6,9,5 # reduction candidate for 6,9 F5: 6,9 => CTR * 41.2738..2.79184533894..1278547.2.311928365746735419827386.421..21389746.4.1273.8 F5: 5 => SOLVED * 419273865267518493385496127854762931192835674673941582738654219521389746946127358 G5: 6,9,5 # reduction candidate for 6,9 G5: 6,9 => SOLVED * 419273865267518493385496127854762931192835674673941582738654219521389746946127358 G5: 5 => CTR * 41.2738..2.79184533894..1278547.2.311928365746735419827386.421..21389746.4.1273.8 * PAIR A6: 6,9 ROW 6 G6: 6,9,5 # reduction candidate for 6,9 G6: 6,9 => CTR * 41.2738..2.79184533894..1278547.2.311928365746735419827386.421..21389746.4.1273.8 G6: 5 => SOLVED * 419273865267518493385496127854762931192835674673941582738654219521389746946127358 * PAIR A6: 6,9 COL A A8: 6,9,5 # reduction candidate for 6,9 A8: 6,9 # 15 pairs A9: 6,9,5 # reduction candidate for 6,9 A9: 6,9 => SOLVED * 419273865267518493385496127854762931192835674673941582738654219521389746946127358 A9: 5 # 15 pairs * PAIR E4: 6,9 BLK 5 F5: 6,9,5 # reduction candidate for 6,9 F5: 6,9 => CTR * 41.2738..2.79184533894..1278547.2.311928365746735419827386.421..21389746.4.1273.8 F5: 5 => SOLVED * 419273865267518493385496127854762931192835674673941582738654219521389746946127358 * PAIR E4: 6,9 COL E E3: 6,9,5 # reduction candidate for 6,9 E3: 5 => CTR * 4152738..26791845338945612785476293119283..74.73541682738694215.2138574.54.1273.8 E3: 6,9 # 16 pairs * PAIR D6: 5,9 BLK 5 F5: 5,9,6 # reduction candidate for 5,9 F5: 6 => CTR * 41.27386.26791845338946512785479263119283657467354198273865421..2138.746.461273.8 F5: 5,9 # 14 pairs * PAIR D6: 5,9 ROW 6 G6: 5,9,6 # reduction candidate for 5,9 G6: 6 => CTR * 41.2738..2.79184533894..1278547629311.283.574.735416827386.421..2138.74..4.1273.8 G6: 5,9 # 17 pairs * PAIR G4: 6,9 BLK 6 G5: 6,9,5 # reduction candidate for 6,9 G5: 6,9 => SOLVED * 419273865267518493385496127854762931192835674673941582738654219521389746946127358 G5: 5 => CTR * 41.2738..2.79184533894..1278547.2.311928365746735419827386.421..21389746.4.1273.8 G6: 6,9,5 # reduction candidate for 6,9 G6: 6,9 => CTR * 41.2738..2.79184533894..1278547.2.311928365746735419827386.421..21389746.4.1273.8 G6: 5 => SOLVED * 419273865267518493385496127854762931192835674673941582738654219521389746946127358 * PAIR C9: 6,9 BLK 7 A8: 6,9,5 # reduction candidate for 6,9 A8: 6,9 # 15 pairs A9: 6,9,5 # reduction candidate for 6,9 A9: 6,9 => SOLVED * 419273865267518493385496127854762931192835674673941582738654219521389746946127358 A9: 5 # 15 pairs * PAIR C9: 6,9 ROW 9 H9: 6,9,5 # reduction candidate for 6,9 H9: 5 => SOLVED * 419273865267518493385496127854762931192835674673941582738654219521389746946127358 H9: 6,9 # 15 pairs * PAIR C9: 6,9 COL C C1: 6,9,5 # reduction candidate for 6,9 C1: 6,9 => SOLVED * 419273865267518493385496127854762931192835674673941582738654219521389746946127358 C1: 5 => CTR * 4152738..267.184533894..1278547.2.3119283..746735419827386.421..21389746.4.1273.8 * PAIR E7: 5,9 COL E E3: 5,9,6 # reduction candidate for 5,9 E3: 6 => CTR * 41.2738..2.7.184.338.46.1278547926311.2836574673541982738654219.21389746946127358 E3: 5,9 # 14 pairs * PAIR F8: 5,9 ROW 8 A8: 5,9,6 # reduction candidate for 5,9 A8: 5,9 # 15 pairs I8: 5,9,6 # reduction candidate for 5,9 I8: 5,9 => CTR * 41.2738.6267.184.338.4..1278547.2.3119283..74673.41.827386.421..2138.74..461273.8 I8: 6 # 15 pairs * PAIR F8: 5,9 COL F F3: 5,9,6 # reduction candidate for 5,9 F3: 5,9 => CTR * 41.2738..2.7.184.338.46.1278547926311.2836574673541982738654219.21389746946127358 F3: 6 # 14 pairs F5: 5,9,6 # reduction candidate for 5,9 F5: 5,9 # 14 pairs * PAIR I7: 5,9 BLK 9 I8: 5,9,6 # reduction candidate for 5,9 I8: 5,9 => CTR * 41.2738.6267.184.338.4..1278547.2.3119283..74673.41.827386.421..2138.74..461273.8 I8: 6 # 15 pairs H9: 5,9,6 # reduction candidate for 5,9 H9: 5,9 # 15 pairs * PAIR I7: 5,9 COL I I1: 5,9,6 # reduction candidate for 5,9 I1: 6 => CTR * 41.2738.6267.184.338.4..1278547.2.3119283..74673.41.827386.421..2138.74..461273.8 I1: 5,9 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-244-base-pr-000.dot * REASONING * PRF # C1: 6,9 => SOL * DIS # C1: 5 => CTR => C1: 6,9 * PRF # H2: 6,9 => SOL * DIS # H2: 5 => CTR => H2: 6,9 * DIS # C1: 6 => CTR => C1: 5,9 * DIS # F3: 5,9 => CTR => F3: 6 * DIS # F3: 5,9 => CTR => F3: 6 * DIS # H2: 6 => CTR => H2: 5,9 * DIS # F5: 6,9 => CTR => F5: 5 * PRF # F5: 5 => SOL * PRF # G5: 6,9 => SOL * DIS # G5: 5 => CTR => G5: 6,9 * DIS # G6: 6,9 => CTR => G6: 5 * PRF # G6: 5 => SOL * PRF # A9: 6,9 => SOL * DIS # F5: 6,9 => CTR => F5: 5 * PRF # F5: 5 => SOL * DIS # E3: 5 => CTR => E3: 6,9 * DIS # F5: 6 => CTR => F5: 5,9 * DIS # G6: 6 => CTR => G6: 5,9 * PRF # G5: 6,9 => SOL * DIS # G5: 5 => CTR => G5: 6,9 * DIS # G6: 6,9 => CTR => G6: 5 * PRF # G6: 5 => SOL * PRF # A9: 6,9 => SOL * PRF # H9: 5 => SOL * PRF # C1: 6,9 => SOL * DIS # C1: 5 => CTR => C1: 6,9 * DIS # E3: 6 => CTR => E3: 5,9 * DIS # I8: 5,9 => CTR => I8: 6 * DIS # F3: 5,9 => CTR => F3: 6 * DIS # I8: 5,9 => CTR => I8: 6 * DIS # I1: 6 => CTR => I1: 5,9 * CNT 33 HDP CHAINS / 55 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B2,B5,C3,C9,D2,D6,E4,E7,F8,G4,I7) * 41.2738..2.7.184.338.4..1278547.2.311.283..74.73.41.827386.421..2138.74..4.1273.8 * PAIR B2: 6,9 BLK 1 C1: 6,9,5 # reduction candidate for 6,9 C1: 6,9 => SOLVED * 419273865267518493385496127854762931192835674673941582738654219521389746946127358 * DURATION: 0:00:01.994907 START: 11:10:05.173660 END: 11:10:07.168567 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-244-base-pr-001.dot * REASONING * PRF # C1: 6,9 => SOL * STA C1: 6,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 244 solution: 419273865267518493385496127854762931192835674673941582738654219521389746946127358 info: 2069 FNBWX S8.f 46217 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 419273865267518493385496127854762931192835674673941582738654219521389746946127358 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:
* PRF # C1: 6,9 => SOL * DIS # C1: 5 => CTR => C1: 6,9 * PRF # H2: 6,9 => SOL * DIS # H2: 5 => CTR => H2: 6,9 * INC # C1: 5,9 => UNS * DIS # C1: 6 => CTR => C1: 5,9 * INC # E3: 5,9 => UNS * DIS # F3: 5,9 => CTR => F3: 6 * INC # F3: 6 => UNS * INC # E3: 5,9 => UNS * DIS # F3: 5,9 => CTR => F3: 6 * INC # F3: 6 => UNS * INC # H2: 5,9 => UNS * DIS # H2: 6 => CTR => H2: 5,9 * DIS # F5: 6,9 => CTR => F5: 5 * PRF # F5: 5 => SOL * PRF # G5: 6,9 => SOL * DIS # G5: 5 => CTR => G5: 6,9 * DIS # G6: 6,9 => CTR => G6: 5 * PRF # G6: 5 => SOL * INC # A8: 6,9 => UNS * PRF # A9: 6,9 => SOL * INC # A9: 5 => UNS * DIS # F5: 6,9 => CTR => F5: 5 * PRF # F5: 5 => SOL * INC # E3: 6,9 => UNS * DIS # E3: 5 => CTR => E3: 6,9 * INC # F5: 5,9 => UNS * DIS # F5: 6 => CTR => F5: 5,9 * INC # G6: 5,9 => UNS * DIS # G6: 6 => CTR => G6: 5,9 * PRF # G5: 6,9 => SOL * DIS # G5: 5 => CTR => G5: 6,9 * DIS # G6: 6,9 => CTR => G6: 5 * PRF # G6: 5 => SOL * INC # A8: 6,9 => UNS * PRF # A9: 6,9 => SOL * INC # A9: 5 => UNS * INC # H9: 6,9 => UNS * PRF # H9: 5 => SOL * PRF # C1: 6,9 => SOL * DIS # C1: 5 => CTR => C1: 6,9 * INC # E3: 5,9 => UNS * DIS # E3: 6 => CTR => E3: 5,9 * INC # A8: 5,9 => UNS * DIS # I8: 5,9 => CTR => I8: 6 * INC # I8: 6 => UNS * DIS # F3: 5,9 => CTR => F3: 6 * INC # F3: 6 => UNS * INC # F5: 5,9 => UNS * DIS # I8: 5,9 => CTR => I8: 6 * INC # I8: 6 => UNS * INC # H9: 5,9 => UNS * INC # I1: 5,9 => UNS * DIS # I1: 6 => CTR => I1: 5,9 * CNT 55 HDP CHAINS / 55 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # C1: 6,9 => SOL * STA C1: 6,9 * CNT 1 HDP CHAINS / 1 HYP OPENED