Analysis of xx-top500-299-base.sdk
Contents
Original Sudoku
level: medium
position: .3.6...9.1...8..............2.57.........21........4.87.1.........3...6.4........ initial
Autosolve
position: 23.6...9.1...8....6........824571.3.3968421..5179..4287.1......9.23...6.4.3...... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C3: 9 => CTR => C3: 5,8 * DIS # G1: 5,8 => CTR => G1: 7 * PRF # G1: 7 => SOL * DIS # F2: 4,7 => CTR => F2: 3,5,9 * DIS # H2: 4,7 => CTR => H2: 5 * DIS # I2: 4,7 => CTR => I2: 2,3,5,6 * DIS # C3: 8 => CTR => C3: 5,9 * DIS # F2: 5,9 => CTR => F2: 3,4,7 * DIS # D3: 4,7 => CTR => D3: 1,2 * DIS # F3: 4,7 => CTR => F3: 3,5,9 * PRF # H3: 4,7 => SOL * PRF # I1: 1,5 => SOL * DIS # I1: 4,7 => CTR => I1: 1,5 * DIS # H3: 5,7 => CTR => H3: 1,4,8 * DIS # H9: 5,7 => CTR => H9: 1,8 * DIS # I1: 5,7 => CTR => I1: 1,4 * DIS # I2: 5,7 => CTR => I2: 2,3,4,6 * DIS # I8: 5,7 => CTR => I8: 1,4 * DIS # F8: 5,8 => CTR => F8: 4,7 * PRF # G8: 5,8 => SOL * DIS # G8: 7 => CTR => G8: 5,8 * PRF # I7: 2,4 => SOL * DIS # D3: 2,4 => CTR => D3: 1,7 * DIS # I8: 1,5 => CTR => I8: 4,7 * PRF # I8: 4,7 => SOL * CNT 25 HDP CHAINS / 50 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C3: 9 => CTR => C3: 5,8 * DIS C3: 5,8 # G1: 5,8 => CTR => G1: 7 * PRF C3: 5,8 + G1: 7 => SOL * STA C3: 5,8 + G1: 7 * CNT 3 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .3.6...9.1...8..............2.57.........21........4.87.1.........3...6.4........ | initial |
| 23.6...9.1...8....6........824571.3.3968421..5179..4287.1......9.23...6.4.3...... | autosolve |
| 238654791149783256675129843824571639396842175517936428761495382982317564453268917 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) C1: 5,8 B2: 4,7 C2: 5,9 B3: 4,7 E1: 1,5 E6: 3,6 F6: 3,6 G4: 6,9 I4: 6,9 H5: 5,7 I5: 5,7 B8: 5,8 D7: 2,4 E8: 1,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E1,D3: 1.. / E1 = 1 => 0 pairs (X) / D3 = 1 => 0 pairs (_) E8,D9: 1.. / E8 = 1 => 0 pairs (*) / D9 = 1 => 0 pairs (X) E1,I1: 1.. / E1 = 1 => 0 pairs (X) / I1 = 1 => 0 pairs (_) E8,I8: 1.. / E8 = 1 => 0 pairs (*) / I8 = 1 => 0 pairs (X) D3,D9: 1.. / D3 = 1 => 0 pairs (*) / D9 = 1 => 0 pairs (X) E1,E8: 1.. / E1 = 1 => 0 pairs (X) / E8 = 1 => 0 pairs (_) H3,H9: 1.. / H3 = 1 => 0 pairs (X) / H9 = 1 => 0 pairs (_) E6,F6: 3.. / E6 = 3 => 13 pairs (_) / F6 = 3 => 0 pairs (X) G7,I7: 3.. / G7 = 3 => 14 pairs (_) / I7 = 3 => 14 pairs (_) E3,E6: 3.. / E3 = 3 => 0 pairs (X) / E6 = 3 => 13 pairs (_) B2,B3: 4.. / B2 = 4 => 16 pairs (_) / B3 = 4 => 16 pairs (_) F1,I1: 4.. / F1 = 4 => 0 pairs (*) / I1 = 4 => 0 pairs (X) F8,I8: 4.. / F8 = 4 => 0 pairs (X) / I8 = 4 => 0 pairs (_) H5,I5: 5.. / H5 = 5 => 0 pairs (X) / I5 = 5 => 13 pairs (_) E1,E8: 5.. / E1 = 5 => 0 pairs (*) / E8 = 5 => 0 pairs (X) G2,I2: 6.. / G2 = 6 => 12 pairs (_) / I2 = 6 => 12 pairs (_) E6,F6: 6.. / E6 = 6 => 0 pairs (X) / F6 = 6 => 13 pairs (_) G4,I4: 6.. / G4 = 6 => 12 pairs (_) / I4 = 6 => 12 pairs (_) B7,B9: 6.. / B7 = 6 => 16 pairs (_) / B9 = 6 => 16 pairs (_) G2,G4: 6.. / G2 = 6 => 12 pairs (_) / G4 = 6 => 12 pairs (_) I2,I4: 6.. / I2 = 6 => 12 pairs (_) / I4 = 6 => 12 pairs (_) B2,B3: 7.. / B2 = 7 => 16 pairs (_) / B3 = 7 => 16 pairs (_) H5,I5: 7.. / H5 = 7 => 13 pairs (_) / I5 = 7 => 0 pairs (X) C1,C3: 8.. / C1 = 8 => 15 pairs (_) / C3 = 8 => 0 pairs (X) C1,G1: 8.. / C1 = 8 => 15 pairs (_) / G1 = 8 => 0 pairs (X) C2,C3: 9.. / C2 = 9 => 14 pairs (_) / C3 = 9 => 0 pairs (X) G4,I4: 9.. / G4 = 9 => 12 pairs (_) / I4 = 9 => 12 pairs (_) C2,F2: 9.. / C2 = 9 => 14 pairs (_) / F2 = 9 => 0 pairs (X) * DURATION: 0:00:40.773241 START: 13:10:43.270682 END: 13:11:24.043923 2017-05-04 * CP COUNT: (28) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B3,B8,C1,C2,D7,E1,E6,E8,F6,G4,H5,I4,I5) * 23.6...9.1...8....6........824571.3.3968421..5179..4287.1......9.23...6.4.3...... * PAIR C1: 5,8 BLK 1 C3: 5,8,9 # reduction candidate for 5,8 C3: 9 => CTR * 238654791175289.4.649137...824571.3.3968421755179634287.14.....9.231..644.37...1. C3: 5,8 # 14 pairs * PAIR C1: 5,8 ROW 1 G1: 5,8,7 # reduction candidate for 5,8 G1: 5,8 => CTR * 23.61..9.1...8....6......1.824571.3.3968421..5179..4287.1......9823547614.31.7... G1: 7 => SOLVED * 238654791149783256675129843824571639396842175517936428761495382982317564453268917 * PAIR B2: 4,7 ROW 2 D2: 4,7,2 # reduction candidate for 4,7 D2: 4,7 # 17 pairs F2: 4,7,3,5,9 # reduction candidate for 4,7 F2: 4,7 => CTR * 2386.4791149287.5.6751..842824571.3.3968421755179..4287.14...8.9.231.5644.37...19 F2: 3,5,9 # 14 pairs H2: 4,7,5 # reduction candidate for 4,7 H2: 4,7 => CTR * 23.654.911..28....6..1.7...824571.3.3968421.75179..4287.14.....9.231.7644.37...1. H2: 5 # 15 pairs I2: 4,7,2,3,5,6 # reduction candidate for 4,7 I2: 4,7 => CTR * 23.6.4.9.1.928365767.195...8245719363968421..5179364287.14.....9.23...644.3...... I2: 2,3,5,6 # 14 pairs * PAIR C2: 5,9 BLK 1 C3: 5,9,8 # reduction candidate for 5,9 C3: 8 => CTR * 2356148971.9.8....6.8....1.824571.3.3968421755179..4287.14.....98235.7614.31.7... C3: 5,9 # 15 pairs * PAIR C2: 5,9 ROW 2 F2: 5,9,3,4,7 # reduction candidate for 5,9 F2: 5,9 => CTR * 23.654.911.5289...6.9137...824571.3.3968421.75179634287.14.....9.231.7644.37...1. F2: 3,4,7 # 15 pairs * PAIR B3: 4,7 ROW 3 D3: 4,7,1,2 # reduction candidate for 4,7 D3: 4,7 => CTR * 23.61..9.1...8....6......1.824571.3.3968421..5179..4287.1......9823547614.31.7... D3: 1,2 # 15 pairs F3: 4,7,3,5,9 # reduction candidate for 4,7 F3: 4,7 => CTR * 2386.47911...8..4.64.1.7...824571.3.3968421..5179..4287.14.....9.231..644.37...1. F3: 3,5,9 # 14 pairs H3: 4,7,1,5,8 # reduction candidate for 4,7 H3: 4,7 => SOLVED * 238654791149783256675129843824571639396842175517936428761495382982317564453268917 H3: 1,5,8 # 14 pairs I3: 4,7,1,2,3,5 # reduction candidate for 4,7 I3: 4,7 # 18 pairs * PAIR E1: 1,5 ROW 1 I1: 1,5,4,7 # reduction candidate for 1,5 I1: 1,5 => SOLVED * 238654791149783256675129843824571639396842175517936428761495382982317564453268917 I1: 4,7 => CTR * 23.61..9.1...8....6......1.824571.3.3968421..5179..4287.1......9823547614.31.7... * PAIR H5: 5,7 COL H H2: 5,7,4 # reduction candidate for 5,7 H2: 5,7 # 17 pairs H3: 5,7,1,4,8 # reduction candidate for 5,7 H3: 5,7 => CTR * 23865479117.28..4.64.1.7852824571.3.3968421755179..4287.14...8.9.231.5644.37...19 H3: 1,4,8 # 14 pairs H9: 5,7,1,8 # reduction candidate for 5,7 H9: 5,7 => CTR * 23.61..9.1...8..4.64.....1.824571.3.3968421..5179..4287.14...8.9.235..6.4.31..... H9: 1,8 # 15 pairs * PAIR I5: 5,7 COL I I1: 5,7,1,4 # reduction candidate for 5,7 I1: 5,7 => CTR * 23.614.9.1...8....6........824571.3.3968421..5179..4287.14.....9.235..6.4.3...... I1: 1,4 # 15 pairs I2: 5,7,2,3,4,6 # reduction candidate for 5,7 I2: 5,7 => CTR * 23.654.911.92836..6.5197...8245719363968421..5179364287.14.....9.231.7644.37...1. I2: 2,3,4,6 # 14 pairs I3: 5,7,1,2,3,4 # reduction candidate for 5,7 I3: 5,7 # 19 pairs I8: 5,7,1,4 # reduction candidate for 5,7 I8: 5,7 => CTR * 23.6...9.1...8....6........824571.3.3968421..5179..4287.1......9.2314.6.4.3...... I8: 1,4 # 15 pairs I9: 5,7,1,2,9 # reduction candidate for 5,7 I9: 5,7 # 19 pairs * PAIR B8: 5,8 BLK 7 B7: 5,8,6 # reduction candidate for 5,8 B7: 5,8 # 16 pairs B9: 5,8,6 # reduction candidate for 5,8 B9: 5,8 # 16 pairs * PAIR B8: 5,8 ROW 8 F8: 5,8,4,7 # reduction candidate for 5,8 F8: 5,8 => CTR * 23.6.4.9.1...8....6........824571.3.3968421..5179..4287.14.....9.231.7644.3...... F8: 4,7 # 15 pairs G8: 5,8,7 # reduction candidate for 5,8 G8: 5,8 => SOLVED * 238654791149783256675129843824571639396842175517936428761495382982317564453268917 G8: 7 => CTR * 23.614.971...8....6......1.824571.3.3968421755179..4287.14.....98235.7614.31.7... * PAIR D7: 2,4 ROW 7 I7: 2,4,3,5,9 # reduction candidate for 2,4 I7: 2,4 => SOLVED * 238654791149783256675129843824571639396842175517936428761495382982317564453268917 I7: 3,5,9 # 14 pairs * PAIR D7: 2,4 COL D D2: 2,4,7 # reduction candidate for 2,4 D2: 2,4 # 17 pairs D3: 2,4,1,7 # reduction candidate for 2,4 D3: 2,4 => CTR * 23.61..9.1..78....67.....1.824571.3.3968421..5179..4287.1......9823547614.31.7... D3: 1,7 # 15 pairs * PAIR E8: 1,5 ROW 8 I8: 1,5,4,7 # reduction candidate for 1,5 I8: 1,5 => CTR * 23.617.941..48....6........824571.3.3968421..5179..4287.12...4.9823.476.4.3...... I8: 4,7 => SOLVED * 238654791149783256675129843824571639396842175517936428761495382982317564453268917 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-299-base-pr-000.dot * REASONING * DIS # C3: 9 => CTR => C3: 5,8 * DIS # G1: 5,8 => CTR => G1: 7 * PRF # G1: 7 => SOL * DIS # F2: 4,7 => CTR => F2: 3,5,9 * DIS # H2: 4,7 => CTR => H2: 5 * DIS # I2: 4,7 => CTR => I2: 2,3,5,6 * DIS # C3: 8 => CTR => C3: 5,9 * DIS # F2: 5,9 => CTR => F2: 3,4,7 * DIS # D3: 4,7 => CTR => D3: 1,2 * DIS # F3: 4,7 => CTR => F3: 3,5,9 * PRF # H3: 4,7 => SOL * PRF # I1: 1,5 => SOL * DIS # I1: 4,7 => CTR => I1: 1,5 * DIS # H3: 5,7 => CTR => H3: 1,4,8 * DIS # H9: 5,7 => CTR => H9: 1,8 * DIS # I1: 5,7 => CTR => I1: 1,4 * DIS # I2: 5,7 => CTR => I2: 2,3,4,6 * DIS # I8: 5,7 => CTR => I8: 1,4 * DIS # F8: 5,8 => CTR => F8: 4,7 * PRF # G8: 5,8 => SOL * DIS # G8: 7 => CTR => G8: 5,8 * PRF # I7: 2,4 => SOL * DIS # D3: 2,4 => CTR => D3: 1,7 * DIS # I8: 1,5 => CTR => I8: 4,7 * PRF # I8: 4,7 => SOL * CNT 25 HDP CHAINS / 50 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B3,B8,C1,C2,D7,E1,E6,E8,F6,G4,H5,I4,I5) * 23.6...9.1...8....6........824571.3.3968421..5179..4287.1......9.23...6.4.3...... * PAIR C1: 5,8 BLK 1 C3: 5,8,9 # reduction candidate for 5,8 C3: 9 => CTR * 238654791175289.4.649137...824571.3.3968421755179634287.14.....9.231..644.37...1. * PAIR C1: 5,8 ROW 1 G1: 5,8,7 # reduction candidate for 5,8 G1: 5,8 => CTR * 23.61..9.1.9.8....6......1.824571.3.3968421..5179..4287.1......9823547614.31.7... G1: 7 => SOLVED * 238654791149783256675129843824571639396842175517936428761495382982317564453268917 * DURATION: 0:00:04.784052 START: 13:12:05.557847 END: 13:12:10.341899 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-299-base-pr-001.dot * REASONING * DIS # C3: 9 => CTR => C3: 5,8 * DIS C3: 5,8 # G1: 5,8 => CTR => G1: 7 * PRF C3: 5,8 + G1: 7 => SOL * STA C3: 5,8 + G1: 7 * CNT 3 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 299 solution: 238654791149783256675129843824571639396842175517936428761495382982317564453268917 info: 2545 FNBTHWY S8.f 18016 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 238654791149783256675129843824571639396842175517936428761495382982317564453268917 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 # C3: 5,8 => UNS * DIS # C3: 9 => CTR => C3: 5,8 * DIS # G1: 5,8 => CTR => G1: 7 * PRF # G1: 7 => SOL * INC # D2: 4,7 => UNS * DIS # F2: 4,7 => CTR => F2: 3,5,9 * INC # F2: 3,5,9 => UNS * DIS # H2: 4,7 => CTR => H2: 5 * INC # H2: 5 => UNS * DIS # I2: 4,7 => CTR => I2: 2,3,5,6 * INC # I2: 2,3,5,6 => UNS * INC # C3: 5,9 => UNS * DIS # C3: 8 => CTR => C3: 5,9 * DIS # F2: 5,9 => CTR => F2: 3,4,7 * INC # F2: 3,4,7 => UNS * DIS # D3: 4,7 => CTR => D3: 1,2 * INC # D3: 1,2 => UNS * DIS # F3: 4,7 => CTR => F3: 3,5,9 * INC # F3: 3,5,9 => UNS * PRF # H3: 4,7 => SOL * INC # H3: 1,5,8 => UNS * INC # I3: 4,7 => UNS * PRF # I1: 1,5 => SOL * DIS # I1: 4,7 => CTR => I1: 1,5 * INC # H2: 5,7 => UNS * DIS # H3: 5,7 => CTR => H3: 1,4,8 * INC # H3: 1,4,8 => UNS * DIS # H9: 5,7 => CTR => H9: 1,8 * INC # H9: 1,8 => UNS * DIS # I1: 5,7 => CTR => I1: 1,4 * INC # I1: 1,4 => UNS * DIS # I2: 5,7 => CTR => I2: 2,3,4,6 * INC # I2: 2,3,4,6 => UNS * INC # I3: 5,7 => UNS * DIS # I8: 5,7 => CTR => I8: 1,4 * INC # I8: 1,4 => UNS * INC # I9: 5,7 => UNS * INC # B7: 5,8 => UNS * INC # B9: 5,8 => UNS * DIS # F8: 5,8 => CTR => F8: 4,7 * INC # F8: 4,7 => UNS * PRF # G8: 5,8 => SOL * DIS # G8: 7 => CTR => G8: 5,8 * PRF # I7: 2,4 => SOL * INC # I7: 3,5,9 => UNS * INC # D2: 2,4 => UNS * DIS # D3: 2,4 => CTR => D3: 1,7 * INC # D3: 1,7 => UNS * DIS # I8: 1,5 => CTR => I8: 4,7 * PRF # I8: 4,7 => SOL * CNT 50 HDP CHAINS / 50 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C3: 5,8 => UNS * DIS # C3: 9 => CTR => C3: 5,8 * DIS C3: 5,8 # G1: 5,8 => CTR => G1: 7 * PRF C3: 5,8 + G1: 7 => SOL * STA C3: 5,8 + G1: 7 * CNT 4 HDP CHAINS / 3 HYP OPENED