Analysis of xx-top500-280-base.sdk
Contents
Original Sudoku
level: medium
position: .3.6...9.1...8..............2.57.........21........4.87.1.........3...5.4........ initial
Autosolve
position: 23.6...9.1...8.............824571...3..8421755179..4287.1........23...5.4.3...... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # G1: 5,8 => CTR => G1: 7 * PRF # G1: 7 => SOL * DIS # F2: 4,7 => CTR => F2: 3,5,9 * DIS # I2: 4,7 => CTR => I2: 2,3,6 * DIS # D3: 4,7 => CTR => D3: 1,2 * DIS # F3: 4,7 => CTR => F3: 3,5,9 * DIS # E3: 1,5 => CTR => E3: 2,3,9 * DIS # E9: 1,5 => CTR => E9: 2,6,9 * DIS # B8: 6,9 => CTR => B8: 8 * DIS # H3: 3,6 => CTR => H3: 1,4,8 * DIS # H7: 3,6 => CTR => H7: 4,8 * DIS # B8: 6,9 => CTR => B8: 8 * DIS # E8: 6,9 => CTR => E8: 1 * PRF # E8: 1 => SOL * DIS # F8: 6,9 => CTR => F8: 4,7,8 * PRF # G8: 6,9 => SOL * DIS # I8: 6,9 => CTR => I8: 1,4,7 * DIS # I7: 2,4 => CTR => I7: 3,6,9 * DIS # D3: 2,4 => CTR => D3: 1,7 * CNT 19 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 # G1: 5,8 => CTR => G1: 7 * PRF G1: 7 => SOL * STA G1: 7 * CNT 2 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...5.4........ | initial |
| 23.6...9.1...8.............824571...3..8421755179..4287.1........23...5.4.3...... | autosolve |
| 238654791146789532975123846824571369369842175517936428791465283682317954453298617 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (12) C1: 5,8 B2: 4,7 A3: 6,9 B3: 4,7 E1: 1,5 B5: 6,9 C5: 6,9 E6: 3,6 F6: 3,6 H4: 3,6 A8: 6,9 D7: 2,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) 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) H3,H9: 1.. / H3 = 1 => 0 pairs (X) / H9 = 1 => 0 pairs (_) E6,F6: 3.. / E6 = 3 => 10 pairs (_) / F6 = 3 => 0 pairs (X) E3,E6: 3.. / E3 = 3 => 0 pairs (X) / E6 = 3 => 10 pairs (_) B2,B3: 4.. / B2 = 4 => 14 pairs (_) / B3 = 4 => 13 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 (_) B7,B9: 5.. / B7 = 5 => 12 pairs (_) / B9 = 5 => 12 pairs (_) B5,C5: 6.. / B5 = 6 => 11 pairs (_) / C5 = 6 => 11 pairs (_) E6,F6: 6.. / E6 = 6 => 0 pairs (X) / F6 = 6 => 10 pairs (_) A3,A8: 6.. / A3 = 6 => 11 pairs (_) / A8 = 6 => 11 pairs (_) B2,B3: 7.. / B2 = 7 => 13 pairs (_) / B3 = 7 => 14 pairs (_) C1,C3: 8.. / C1 = 8 => 12 pairs (_) / C3 = 8 => 0 pairs (X) C1,G1: 8.. / C1 = 8 => 12 pairs (_) / G1 = 8 => 0 pairs (X) B5,C5: 9.. / B5 = 9 => 11 pairs (_) / C5 = 9 => 11 pairs (_) G4,I4: 9.. / G4 = 9 => 13 pairs (_) / I4 = 9 => 13 pairs (_) C2,F2: 9.. / C2 = 9 => 11 pairs (_) / F2 = 9 => 13 pairs (_) A3,A8: 9.. / A3 = 9 => 11 pairs (_) / A8 = 9 => 11 pairs (_) * DURATION: 0:00:28.013633 START: 12:31:10.091082 END: 12:31:38.104715 2017-05-04 * CP COUNT: (20) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A8,B2,B3,B5,C1,C5,D7,E1,E6,F6,H4) * 23.6...9.1...8.............824571...3..8421755179..4287.1........23...5.4.3...... * PAIR C1: 5,8 BLK 1 C3: 5,8,6,9 # reduction candidate for 5,8 C3: 5,8 # 14 pairs C3: 6,9 # 13 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...........1.824571...3..8421755179..4287.1........23.47514.31.7... G1: 7 => SOLVED * 238654791146789532975123846824571369369842175517936428791465283682317954453298617 * PAIR B2: 4,7 ROW 2 D2: 4,7,2 # reduction candidate for 4,7 D2: 4,7 # 16 pairs F2: 4,7,3,5,9 # reduction candidate for 4,7 F2: 4,7 => CTR * 2386.47911492875..6751..842824571...3968421755179..4287.14...8.9.231.6544.37...19 F2: 3,5,9 # 12 pairs I2: 4,7,2,3,6 # reduction candidate for 4,7 I2: 4,7 => CTR * 23.6.4.9.14.28...7.7.1...4.824571...3..8421755179..4287.14...8...231..544.37...1. I2: 2,3,6 # 12 pairs * PAIR A3: 6,9 BLK 1 C2: 6,9,5 # reduction candidate for 6,9 C2: 6,9 # 14 pairs C3: 6,9,5,8 # reduction candidate for 6,9 C3: 6,9 # 13 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...........1.824571...3..8421755179..4287.1........23.47514.31.7... D3: 1,2 # 13 pairs F3: 4,7,3,5,9 # reduction candidate for 4,7 F3: 4,7 => CTR * 2386.47911..78.............824571...3..8421755179..4287.14.......23...544.3.....7 F3: 3,5,9 # 12 pairs I3: 4,7,1,2,3,6 # reduction candidate for 4,7 I3: 4,7 # 14 pairs * PAIR E1: 1,5 BLK 2 E3: 1,5,2,3,9 # reduction candidate for 1,5 E3: 1,5 => CTR * 23.6.4.9.1...8.............824571...3..8421755179364287.14.......231..544.37..... E3: 2,3,9 # 12 pairs * PAIR E1: 1,5 COL E E9: 1,5,2,6,9 # reduction candidate for 1,5 E9: 1,5 => CTR * 23.61..9.1...8...........1.824571...3..8421755179..4287.1........23.47514.3157... E9: 2,6,9 # 12 pairs * PAIR B5: 6,9 COL B B7: 6,9,5,8 # reduction candidate for 6,9 B7: 6,9 # 13 pairs B8: 6,9,8 # reduction candidate for 6,9 B8: 6,9 => CTR * 2386547911..78.....7.12....824571...3..8421755179..4287.14.......231.8544.3....17 B8: 8 # 12 pairs B9: 6,9,5,8 # reduction candidate for 6,9 B9: 6,9 # 13 pairs * PAIR C5: 6,9 COL C C2: 6,9,5 # reduction candidate for 6,9 C2: 6,9 # 14 pairs C3: 6,9,5,8 # reduction candidate for 6,9 C3: 6,9 # 13 pairs * PAIR H4: 3,6 BLK 6 G4: 3,6,9 # reduction candidate for 3,6 G4: 3,6 # 13 pairs I4: 3,6,9 # reduction candidate for 3,6 I4: 3,6 # 13 pairs * PAIR H4: 3,6 COL H H2: 3,6,4 # reduction candidate for 3,6 H2: 3,6 # 15 pairs H3: 3,6,1,4,8 # reduction candidate for 3,6 H3: 3,6 => CTR * 23865479117.28..4..4.1.78.2824571...3..8421755179..4287.14...8...231..544.37...1. H3: 1,4,8 # 12 pairs H7: 3,6,4,8 # reduction candidate for 3,6 H7: 3,6 => CTR * 2386547911...8.......1...8.824571...3..8421755179..4287.14.......2317.544.32...17 H7: 4,8 # 13 pairs * PAIR A8: 6,9 BLK 7 B7: 6,9,5,8 # reduction candidate for 6,9 B7: 6,9 # 13 pairs B8: 6,9,8 # reduction candidate for 6,9 B8: 6,9 => CTR * 2386547911..78.....7.12....824571...3..8421755179..4287.14.......231.8544.3....17 B8: 8 # 12 pairs B9: 6,9,5,8 # reduction candidate for 6,9 B9: 6,9 # 13 pairs * PAIR A8: 6,9 ROW 8 E8: 6,9,1 # reduction candidate for 6,9 E8: 6,9 => CTR * 23.61..9.1...8...........1.824571...3..8421755179..4287.1........23.47514.31.7... E8: 1 => SOLVED * 238654791146789532975123846824571369369842175517936428791465283682317954453298617 F8: 6,9,4,7,8 # reduction candidate for 6,9 F8: 6,9 => CTR * 23.6.4.9.1...8.............824571...3..8421755179..4287.14.......231.7544.3...... F8: 4,7,8 # 12 pairs G8: 6,9,7,8 # reduction candidate for 6,9 G8: 6,9 => SOLVED * 238654791146789532975123846824571369369842175517936428791465283682317954453298617 G8: 7,8 # 13 pairs I8: 6,9,1,4,7 # reduction candidate for 6,9 I8: 6,9 => CTR * 23.6...9.1...8.............824571...3..8421755179..4287.1........231475.4.3...... I8: 1,4,7 # 12 pairs * PAIR D7: 2,4 ROW 7 I7: 2,4,3,6,9 # reduction candidate for 2,4 I7: 2,4 => CTR * 2386547911..78.2...7.12.5..824571...3..8421755179..4287.14....2..2317.544.32...17 I7: 3,6,9 # 12 pairs * PAIR D7: 2,4 COL D D2: 2,4,7 # reduction candidate for 2,4 D2: 2,4 # 15 pairs D3: 2,4,1,7 # reduction candidate for 2,4 D3: 2,4 => CTR * 23.61..9.14.78.....7.....1.824571...3..8421755179..4287.1....4...23.47514.31.7.8. D3: 1,7 # 13 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-280-base-pr-000.dot * REASONING * DIS # G1: 5,8 => CTR => G1: 7 * PRF # G1: 7 => SOL * DIS # F2: 4,7 => CTR => F2: 3,5,9 * DIS # I2: 4,7 => CTR => I2: 2,3,6 * DIS # D3: 4,7 => CTR => D3: 1,2 * DIS # F3: 4,7 => CTR => F3: 3,5,9 * DIS # E3: 1,5 => CTR => E3: 2,3,9 * DIS # E9: 1,5 => CTR => E9: 2,6,9 * DIS # B8: 6,9 => CTR => B8: 8 * DIS # H3: 3,6 => CTR => H3: 1,4,8 * DIS # H7: 3,6 => CTR => H7: 4,8 * DIS # B8: 6,9 => CTR => B8: 8 * DIS # E8: 6,9 => CTR => E8: 1 * PRF # E8: 1 => SOL * DIS # F8: 6,9 => CTR => F8: 4,7,8 * PRF # G8: 6,9 => SOL * DIS # I8: 6,9 => CTR => I8: 1,4,7 * DIS # I7: 2,4 => CTR => I7: 3,6,9 * DIS # D3: 2,4 => CTR => D3: 1,7 * CNT 19 HDP CHAINS / 50 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A8,B2,B3,B5,C1,C5,D7,E1,E6,F6,H4) * 23.6...9.1...8.............824571...3..8421755179..4287.1........23...5.4.3...... * PAIR C1: 5,8 BLK 1 C3: 5,8,6,9 # reduction candidate for 5,8 C3: 5,8 # 14 pairs C3: 6,9 # 13 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...........1.824571...3..8421755179..4287.1........23.47514.31.7... G1: 7 => SOLVED * 238654791146789532975123846824571369369842175517936428791465283682317954453298617 * DURATION: 0:00:04.601785 START: 12:32:15.686845 END: 12:32:20.288630 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-280-base-pr-001.dot * REASONING * DIS # G1: 5,8 => CTR => G1: 7 * PRF G1: 7 => SOL * STA G1: 7 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 280 solution: 238654791146789532975123846824571369369842175517936428791465283682317954453298617 info: 2264 FNBHWY S8.f 18015 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 238654791146789532975123846824571369369842175517936428791465283682317954453298617 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 * INC # C3: 6,9 => UNS * 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 # I2: 4,7 => CTR => I2: 2,3,6 * INC # I2: 2,3,6 => UNS * INC # C2: 6,9 => UNS * INC # C3: 6,9 => 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 * INC # I3: 4,7 => UNS * DIS # E3: 1,5 => CTR => E3: 2,3,9 * INC # E3: 2,3,9 => UNS * DIS # E9: 1,5 => CTR => E9: 2,6,9 * INC # E9: 2,6,9 => UNS * INC # B7: 6,9 => UNS * DIS # B8: 6,9 => CTR => B8: 8 * INC # B8: 8 => UNS * INC # B9: 6,9 => UNS * INC # C2: 6,9 => UNS * INC # C3: 6,9 => UNS * INC # G4: 3,6 => UNS * INC # I4: 3,6 => UNS * INC # H2: 3,6 => UNS * DIS # H3: 3,6 => CTR => H3: 1,4,8 * INC # H3: 1,4,8 => UNS * DIS # H7: 3,6 => CTR => H7: 4,8 * INC # H7: 4,8 => UNS * INC # B7: 6,9 => UNS * DIS # B8: 6,9 => CTR => B8: 8 * INC # B8: 8 => UNS * INC # B9: 6,9 => UNS * DIS # E8: 6,9 => CTR => E8: 1 * PRF # E8: 1 => SOL * DIS # F8: 6,9 => CTR => F8: 4,7,8 * INC # F8: 4,7,8 => UNS * PRF # G8: 6,9 => SOL * INC # G8: 7,8 => UNS * DIS # I8: 6,9 => CTR => I8: 1,4,7 * INC # I8: 1,4,7 => UNS * DIS # I7: 2,4 => CTR => I7: 3,6,9 * INC # I7: 3,6,9 => UNS * INC # D2: 2,4 => UNS * DIS # D3: 2,4 => CTR => D3: 1,7 * INC # D3: 1,7 => UNS * CNT 50 HDP CHAINS / 50 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C3: 5,8 => UNS * INC # C3: 6,9 => UNS * DIS # G1: 5,8 => CTR => G1: 7 * PRF G1: 7 => SOL * STA G1: 7 * CNT 4 HDP CHAINS / 3 HYP OPENED