Analysis of xx-top500-464-base.sdk
Contents
Original Sudoku
level: medium
position: ...5..48.2.....5..1.........3.7.5......9................9.6...1.....1.6..8..2.... initial
Autosolve
position: ...513482243698517158274....3.7.51...1.9........1.....529.678.1374851269681.29... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A6: 7,9 => CTR => A6: 4,8 * PRF # C5: 6,7 => SOL * DIS # C6: 6,7 => CTR => C6: 2,5 * DIS # G3: 3,9 => CTR => G3: 6 * PRF # G3: 6 => SOL * DIS # H6: 3,9 => CTR => H6: 2,4,5,7 * PRF # G3: 3,6 => SOL * DIS # G3: 9 => CTR => G3: 3,6 * DIS # I5: 3,6 => CTR => I5: 4,5,8 * DIS # I6: 3,6 => CTR => I6: 4,5,8 * DIS # C5: 2,6 => CTR => C5: 5,7 * DIS # C6: 2,6 => CTR => C6: 5,7 * DIS # G6: 3,7 => CTR => G6: 6,9 * DIS # A4: 4,8 => CTR => A4: 9 * PRF # A4: 9 => SOL * DIS # I4: 4,8 => CTR => I4: 6 * PRF # I4: 6 => SOL * DIS # C5: 2,6 => CTR => C5: 5,7 * DIS # C6: 2,6 => CTR => C6: 5,7 * DIS # H9: 3,4 => CTR => H9: 5,7 * DIS # H9: 3,4 => CTR => H9: 5,7 * DIS # H5: 3,4 => CTR => H5: 2,5,7 * DIS # H6: 3,4 => CTR => H6: 2,5,7,9 * DIS # G6: 3,7 => CTR => G6: 6,9 * CNT 24 HDP CHAINS / 47 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A6: 7,9 => CTR => A6: 4,8 * PRF A6: 4,8 # C5: 6,7 => SOL * STA A6: 4,8 + C5: 6,7 * CNT 2 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...5..48.2.....5..1.........3.7.5......9................9.6...1.....1.6..8..2.... | initial |
| ...513482243698517158274....3.7.51...1.9........1.....529.678.1374851269681.29... | autosolve |
| 796513482243698517158274693932785146817946325465132978529467831374851269681329754 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) A1: 7,9 B1: 6,9 C1: 6,7 H3: 3,9 I3: 3,6 C4: 2,6 B6: 6,9 E4: 4,8 F5: 2,6 F6: 2,6 D7: 3,4 D9: 3,4 H7: 3,4 G9: 3,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F5,F6: 2.. / F5 = 2 => 0 pairs (X) / F6 = 2 => 16 pairs (_) C4,H4: 2.. / C4 = 2 => 0 pairs (*) / H4 = 2 => 0 pairs (X) E5,E6: 3.. / E5 = 3 => 16 pairs (_) / E6 = 3 => 15 pairs (_) D7,D9: 3.. / D7 = 3 => 13 pairs (_) / D9 = 3 => 0 pairs (*) D7,H7: 3.. / D7 = 3 => 13 pairs (_) / H7 = 3 => 0 pairs (*) D7,D9: 4.. / D7 = 4 => 0 pairs (*) / D9 = 4 => 0 pairs (X) D7,H7: 4.. / D7 = 4 => 0 pairs (*) / H7 = 4 => 0 pairs (X) C5,C6: 5.. / C5 = 5 => 14 pairs (_) / C6 = 5 => 14 pairs (_) H9,I9: 5.. / H9 = 5 => 15 pairs (_) / I9 = 5 => 15 pairs (_) B1,C1: 6.. / B1 = 6 => 0 pairs (X) / C1 = 6 => 0 pairs (_) G3,I3: 6.. / G3 = 6 => 0 pairs (*) / I3 = 6 => 0 pairs (X) F5,F6: 6.. / F5 = 6 => 16 pairs (_) / F6 = 6 => 0 pairs (X) C4,I4: 6.. / C4 = 6 => 0 pairs (X) / I4 = 6 => 0 pairs (_) B1,B6: 6.. / B1 = 6 => 0 pairs (X) / B6 = 6 => 0 pairs (_) A1,C1: 7.. / A1 = 7 => 0 pairs (*) / C1 = 7 => 0 pairs (X) G9,H9: 7.. / G9 = 7 => 14 pairs (_) / H9 = 7 => 13 pairs (_) A1,B1: 9.. / A1 = 9 => 0 pairs (X) / B1 = 9 => 0 pairs (_) G3,H3: 9.. / G3 = 9 => 0 pairs (X) / H3 = 9 => 0 pairs (_) A4,H4: 9.. / A4 = 9 => 0 pairs (*) / H4 = 9 => 0 pairs (X) B1,B6: 9.. / B1 = 9 => 0 pairs (*) / B6 = 9 => 0 pairs (X) G3,G6: 9.. / G3 = 9 => 0 pairs (X) / G6 = 9 => 0 pairs (_) * DURATION: 0:00:40.439683 START: 18:34:48.165664 END: 18:35:28.605347 2017-05-04 * CP COUNT: (21) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B1,B6,C1,C4,D7,D9,E4,F5,F6,G9,H3,H7,I3) * ...513482243698517158274....3.7.51...1.9........1.....529.678.1374851269681.29... * PAIR A1: 7,9 COL A A6: 7,9,4,8 # reduction candidate for 7,9 A6: 7,9 => CTR * ...513482243698517158274..3.3.7.519..1.9........1.....529.678.1374851269681.29... A6: 4,8 # 15 pairs * PAIR C1: 6,7 COL C C5: 6,7,2,5 # reduction candidate for 6,7 C5: 6,7 => SOLVED * 796513482243698517158274693932785146817946325465132978529467831374851269681329754 C5: 2,5 # 15 pairs C6: 6,7,2,5 # reduction candidate for 6,7 C6: 6,7 => CTR * ...513482243698517158274693932785146.159.6.2886714293.529.678.1374851269681.29... C6: 2,5 # 15 pairs * PAIR H3: 3,9 BLK 3 G3: 3,9,6 # reduction candidate for 3,9 G3: 3,9 => CTR * ...513482243698517158274..6.367.512..1.9......9.1.....529.678.1374851269681.29... G3: 6 => SOLVED * 796513482243698517158274693932785146817946325465132978529467831374851269681329754 * PAIR H3: 3,9 COL H H6: 3,9,2,4,5,7 # reduction candidate for 3,9 H6: 3,9 => CTR * ...513482243698517158274...93.7.512..1.9......6.1.....529.678.1374851269681.29... H6: 2,4,5,7 # 14 pairs * PAIR I3: 3,6 BLK 3 G3: 3,6,9 # reduction candidate for 3,6 G3: 3,6 => SOLVED * 796513482243698517158274693932785146817946325465132978529467831374851269681329754 G3: 9 => CTR * ...513482243698517158274936.367.512..1.9......9.1.....529367841374851269681429... * PAIR I3: 3,6 COL I I5: 3,6,4,5,8 # reduction candidate for 3,6 I5: 3,6 => CTR * ...513482243698517158274....367.512..1.9......9.1.....529.678.1374851269681.29... I5: 4,5,8 # 14 pairs I6: 3,6,4,5,8 # reduction candidate for 3,6 I6: 3,6 => CTR * ...513482243698517158274....367.512..1.9......9.1.....529.678.1374851269681.29... I6: 4,5,8 # 14 pairs * PAIR C4: 2,6 BLK 4 C5: 2,6,5,7 # reduction candidate for 2,6 C5: 2,6 => CTR * 967513482243698517158274936.3.7.519..1.9......951.....529.678.1374851269681.29... C5: 5,7 # 15 pairs C6: 2,6,5,7 # reduction candidate for 2,6 C6: 2,6 => CTR * 967513482243698517158274936.3.7.519..159......9.1.....529.678.1374851269681.29... C6: 5,7 # 15 pairs * PAIR B6: 6,9 ROW 6 G6: 6,9,3,7 # reduction candidate for 6,9 G6: 3,7 => CTR * ...513482243698517158274936.367.512..1.9..6...9.1.6...529367841374851269681429... G6: 6,9 # 16 pairs * PAIR E4: 4,8 BLK 5 E5: 4,8,3 # reduction candidate for 4,8 E5: 4,8 # 15 pairs E6: 4,8,3 # reduction candidate for 4,8 E6: 4,8 # 16 pairs * PAIR E4: 4,8 ROW 4 A4: 4,8,9 # reduction candidate for 4,8 A4: 4,8 => CTR * ...513482243698517158274936.3.7.519..1.9........1.....529.678.1374851269681.29... A4: 9 => SOLVED * 796513482243698517158274693932785146817946325465132978529467831374851269681329754 I4: 4,8,6 # reduction candidate for 4,8 I4: 4,8 => CTR * ...513482243698517158274....367.512..1.9......9.1.....529.678.1374851269681.29... I4: 6 => SOLVED * 796513482243698517158274693932785146817946325465132978529467831374851269681329754 * PAIR F5: 2,6 ROW 5 C5: 2,6,5,7 # reduction candidate for 2,6 C5: 2,6 => CTR * 967513482243698517158274936.3.7.519..1.9......951.....529.678.1374851269681.29... C5: 5,7 # 15 pairs * PAIR F6: 2,6 ROW 6 C6: 2,6,5,7 # reduction candidate for 2,6 C6: 2,6 => CTR * 967513482243698517158274936.3.7.519..159......9.1.....529.678.1374851269681.29... C6: 5,7 # 15 pairs * PAIR D9: 3,4 ROW 9 H9: 3,4,5,7 # reduction candidate for 3,4 H9: 3,4 => CTR * ...513482243698517158274.9.93.7.512..1.9......6.1.....529.678.1374851269681.297.5 H9: 5,7 # 15 pairs I9: 3,4,5 # reduction candidate for 3,4 I9: 3,4 # 15 pairs * PAIR H7: 3,4 BLK 9 H9: 3,4,5,7 # reduction candidate for 3,4 H9: 3,4 => CTR * ...513482243698517158274.9.93.7.512..1.9......6.1.....529.678.1374851269681.297.5 H9: 5,7 # 15 pairs I9: 3,4,5 # reduction candidate for 3,4 I9: 3,4 # 15 pairs * PAIR H7: 3,4 COL H H5: 3,4,2,5,7 # reduction candidate for 3,4 H5: 3,4 => CTR * ...513482243698517158274.9.93.7.512..1.9......6.1.....529.678.1374851269681.29... H5: 2,5,7 # 14 pairs H6: 3,4,2,5,7,9 # reduction candidate for 3,4 H6: 3,4 => CTR * ...513482243698517158274.9.93.7.512..1.9......6.1.....529.678.1374851269681.29... H6: 2,5,7,9 # 14 pairs * PAIR G9: 3,7 BLK 9 H9: 3,7,4,5 # reduction candidate for 3,7 H9: 4,5 # 15 pairs H9: 3,7 # 13 pairs * PAIR G9: 3,7 COL G G5: 3,7,6 # reduction candidate for 3,7 G5: 3,7 # 16 pairs G6: 3,7,6,9 # reduction candidate for 3,7 G6: 3,7 => CTR * ...513482243698517158274936.367.512..1.9..6...9.1.6...529367841374851269681429... G6: 6,9 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-464-base-pr-000.dot * REASONING * DIS # A6: 7,9 => CTR => A6: 4,8 * PRF # C5: 6,7 => SOL * DIS # C6: 6,7 => CTR => C6: 2,5 * DIS # G3: 3,9 => CTR => G3: 6 * PRF # G3: 6 => SOL * DIS # H6: 3,9 => CTR => H6: 2,4,5,7 * PRF # G3: 3,6 => SOL * DIS # G3: 9 => CTR => G3: 3,6 * DIS # I5: 3,6 => CTR => I5: 4,5,8 * DIS # I6: 3,6 => CTR => I6: 4,5,8 * DIS # C5: 2,6 => CTR => C5: 5,7 * DIS # C6: 2,6 => CTR => C6: 5,7 * DIS # G6: 3,7 => CTR => G6: 6,9 * DIS # A4: 4,8 => CTR => A4: 9 * PRF # A4: 9 => SOL * DIS # I4: 4,8 => CTR => I4: 6 * PRF # I4: 6 => SOL * DIS # C5: 2,6 => CTR => C5: 5,7 * DIS # C6: 2,6 => CTR => C6: 5,7 * DIS # H9: 3,4 => CTR => H9: 5,7 * DIS # H9: 3,4 => CTR => H9: 5,7 * DIS # H5: 3,4 => CTR => H5: 2,5,7 * DIS # H6: 3,4 => CTR => H6: 2,5,7,9 * DIS # G6: 3,7 => CTR => G6: 6,9 * CNT 24 HDP CHAINS / 47 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B1,B6,C1,C4,D7,D9,E4,F5,F6,G9,H3,H7,I3) * ...513482243698517158274....3.7.51...1.9........1.....529.678.1374851269681.29... * PAIR A1: 7,9 COL A A6: 7,9,4,8 # reduction candidate for 7,9 A6: 7,9 => CTR * ...513482243698517158274..3.3.7.519..1.9........1.....529.678.1374851269681.29... * PAIR RESTART * PAIR C1: 6,7 COL C C5: 6,7,2,5 # reduction candidate for 6,7 C5: 6,7 => SOLVED * 796513482243698517158274693932785146817946325465132978529467831374851269681329754 * DURATION: 0:00:04.332000 START: 18:36:17.272955 END: 18:36:21.604955 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-464-base-pr-001.dot * REASONING * DIS # A6: 7,9 => CTR => A6: 4,8 * PRF A6: 4,8 # C5: 6,7 => SOL * STA A6: 4,8 + C5: 6,7 * CNT 2 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 464 solution: 796513482243698517158274693932785146817946325465132978529467831374851269681329754 info: 95546 FNBTYK S8.f 41846 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 796513482243698517158274693932785146817946325465132978529467831374851269681329754 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 # A6: 7,9 => CTR => A6: 4,8 * INC # A6: 4,8 => UNS * PRF # C5: 6,7 => SOL * INC # C5: 2,5 => UNS * DIS # C6: 6,7 => CTR => C6: 2,5 * INC # C6: 2,5 => UNS * DIS # G3: 3,9 => CTR => G3: 6 * PRF # G3: 6 => SOL * DIS # H6: 3,9 => CTR => H6: 2,4,5,7 * INC # H6: 2,4,5,7 => UNS * PRF # G3: 3,6 => SOL * DIS # G3: 9 => CTR => G3: 3,6 * DIS # I5: 3,6 => CTR => I5: 4,5,8 * INC # I5: 4,5,8 => UNS * DIS # I6: 3,6 => CTR => I6: 4,5,8 * INC # I6: 4,5,8 => UNS * DIS # C5: 2,6 => CTR => C5: 5,7 * INC # C5: 5,7 => UNS * DIS # C6: 2,6 => CTR => C6: 5,7 * INC # C6: 5,7 => UNS * INC # G6: 6,9 => UNS * DIS # G6: 3,7 => CTR => G6: 6,9 * INC # E5: 4,8 => UNS * INC # E6: 4,8 => UNS * DIS # A4: 4,8 => CTR => A4: 9 * PRF # A4: 9 => SOL * DIS # I4: 4,8 => CTR => I4: 6 * PRF # I4: 6 => SOL * DIS # C5: 2,6 => CTR => C5: 5,7 * INC # C5: 5,7 => UNS * DIS # C6: 2,6 => CTR => C6: 5,7 * INC # C6: 5,7 => UNS * DIS # H9: 3,4 => CTR => H9: 5,7 * INC # H9: 5,7 => UNS * INC # I9: 3,4 => UNS * DIS # H9: 3,4 => CTR => H9: 5,7 * INC # H9: 5,7 => UNS * INC # I9: 3,4 => UNS * DIS # H5: 3,4 => CTR => H5: 2,5,7 * INC # H5: 2,5,7 => UNS * DIS # H6: 3,4 => CTR => H6: 2,5,7,9 * INC # H6: 2,5,7,9 => UNS * INC # H9: 3,7 => UNS * INC # H9: 4,5 => UNS * INC # G5: 3,7 => UNS * DIS # G6: 3,7 => CTR => G6: 6,9 * INC # G6: 6,9 => UNS * CNT 47 HDP CHAINS / 47 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A6: 7,9 => CTR => A6: 4,8 * PRF A6: 4,8 # C5: 6,7 => SOL * STA A6: 4,8 + C5: 6,7 * CNT 2 HDP CHAINS / 2 HYP OPENED