Analysis of xx-top500-290-base.sdk
Contents
Original Sudoku
level: medium
position: .68...3.....7.1.............3..8.6..7......4..........1..4...574...6.......2..... initial
Autosolve
position: .68...371.4.7.1.86...8.64...34.8761.78.6...436..3..7.81264938574..168.3.893275164 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A2: 2,5 => CTR => A2: 3,9 * DIS # A3: 2,5 => CTR => A3: 3,9 * DIS # A4: 9 => CTR => A4: 2,5 * DIS # I3: 2,9 => CTR => I3: 5 * PRF # A4: 5,9 => SOL * DIS # A4: 2 => CTR => A4: 5,9 * DIS # I4: 5,9 => CTR => I4: 2 * PRF # I4: 2 => SOL * DIS # G5: 2,9 => CTR => G5: 5 * DIS # G5: 2,9 => CTR => G5: 5 * DIS # G5: 2,9 => CTR => G5: 5 * DIS # I3: 2,9 => CTR => I3: 5 * CNT 12 HDP CHAINS / 40 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A2: 2,5 => CTR => A2: 3,9 * DIS A2: 3,9 # A3: 2,5 => CTR => A3: 3,9 * DIS A2: 3,9 + A3: 3,9 # E1: 2,5 => CTR => E1: 4 * DIS A2: 3,9 + A3: 3,9 + E1: 4 # I3: 2,9 => CTR => I3: 5 * DIS A2: 3,9 + A3: 3,9 + E1: 4 + I3: 5 # C6: 1,5 => CTR => C6: 2,9 * PRF A2: 3,9 + A3: 3,9 + E1: 4 + I3: 5 + C6: 2,9 # E2: 2,5 => SOL * STA A2: 3,9 + A3: 3,9 + E1: 4 + I3: 5 + C6: 2,9 + E2: 2,5 * CNT 6 HDP CHAINS / 8 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .68...3.....7.1.............3..8.6..7......4..........1..4...574...6.......2..... | initial |
| .68...371.4.7.1.86...8.64...34.8761.78.6...436..3..7.81264938574..168.3.893275164 | autosolve |
| 268549371345721986971836425534987612789612543612354798126493857457168239893275164 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) A1: 2,5 B3: 1,7 C3: 1,7 D1: 5,9 H3: 2,9 B6: 1,5 D4: 5,9 F5: 2,9 H6: 2,9 B8: 5,7 C8: 5,7 G8: 2,9 I8: 2,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B3,C3: 1.. / B3 = 1 => 10 pairs (_) / C3 = 1 => 8 pairs (_) E5,E6: 1.. / E5 = 1 => 13 pairs (_) / E6 = 1 => 14 pairs (_) C5,E5: 1.. / C5 = 1 => 14 pairs (_) / E5 = 1 => 13 pairs (_) B3,B6: 1.. / B3 = 1 => 10 pairs (_) / B6 = 1 => 8 pairs (_) G8,I8: 2.. / G8 = 2 => 16 pairs (_) / I8 = 2 => 0 pairs (X) A4,I4: 2.. / A4 = 2 => 0 pairs (X) / I4 = 2 => 0 pairs (_) H3,H6: 2.. / H3 = 2 => 17 pairs (_) / H6 = 2 => 0 pairs (X) A2,A3: 3.. / A2 = 3 => 14 pairs (_) / A3 = 3 => 15 pairs (_) E2,E3: 3.. / E2 = 3 => 15 pairs (_) / E3 = 3 => 14 pairs (_) A2,E2: 3.. / A2 = 3 => 14 pairs (_) / E2 = 3 => 15 pairs (_) A3,E3: 3.. / A3 = 3 => 15 pairs (_) / E3 = 3 => 14 pairs (_) E1,F1: 4.. / E1 = 4 => 14 pairs (_) / F1 = 4 => 22 pairs (_) E6,F6: 4.. / E6 = 4 => 22 pairs (_) / F6 = 4 => 14 pairs (_) E1,E6: 4.. / E1 = 4 => 14 pairs (_) / E6 = 4 => 22 pairs (_) F1,F6: 4.. / F1 = 4 => 22 pairs (_) / F6 = 4 => 14 pairs (_) G2,I3: 5.. / G2 = 5 => 0 pairs (X) / I3 = 5 => 17 pairs (_) I4,G5: 5.. / I4 = 5 => 0 pairs (X) / G5 = 5 => 17 pairs (_) B8,C8: 5.. / B8 = 5 => 8 pairs (_) / C8 = 5 => 10 pairs (_) B6,B8: 5.. / B6 = 5 => 10 pairs (_) / B8 = 5 => 8 pairs (_) D1,D4: 5.. / D1 = 5 => 0 pairs (*) / D4 = 5 => 0 pairs (X) G2,G5: 5.. / G2 = 5 => 0 pairs (X) / G5 = 5 => 17 pairs (_) I3,I4: 5.. / I3 = 5 => 17 pairs (_) / I4 = 5 => 0 pairs (X) B3,C3: 7.. / B3 = 7 => 8 pairs (_) / C3 = 7 => 10 pairs (_) B8,C8: 7.. / B8 = 7 => 10 pairs (_) / C8 = 7 => 8 pairs (_) B3,B8: 7.. / B3 = 7 => 8 pairs (_) / B8 = 7 => 10 pairs (_) C3,C8: 7.. / C3 = 7 => 10 pairs (_) / C8 = 7 => 8 pairs (_) D1,F1: 9.. / D1 = 9 => 20 pairs (_) / F1 = 9 => 0 pairs (*) G8,I8: 9.. / G8 = 9 => 0 pairs (X) / I8 = 9 => 16 pairs (_) D1,D4: 9.. / D1 = 9 => 20 pairs (_) / D4 = 9 => 0 pairs (*) H3,H6: 9.. / H3 = 9 => 0 pairs (X) / H6 = 9 => 17 pairs (_) * DURATION: 0:00:53.348310 START: 12:51:39.351637 END: 12:52:32.699947 2017-05-04 * CP COUNT: (30) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B3,B6,B8,C3,C8,D1,D4,F5,G8,H3,H6,I8) * .68...371.4.7.1.86...8.64...34.8761.78.6...436..3..7.81264938574..168.3.893275164 * PAIR A1: 2,5 BLK 1 A2: 2,5,3,9 # reduction candidate for 2,5 A2: 2,5 => CTR * .68...371.4.731.863..8.64..93458761278.6..5436..3..7981264938574..168239893275164 A2: 3,9 # 14 pairs C2: 2,5,9 # reduction candidate for 2,5 C2: 2,5 # 17 pairs A3: 2,5,3,9 # reduction candidate for 2,5 A3: 2,5 => CTR * .68...3713497.1.86...8364..93458761278.6..5436..3..7981264938574..168.3.893275164 A3: 3,9 # 14 pairs * PAIR A1: 2,5 ROW 1 E1: 2,5,4 # reduction candidate for 2,5 E1: 2,5 # 22 pairs E1: 4 # 14 pairs * PAIR A1: 2,5 COL A A4: 2,5,9 # reduction candidate for 2,5 A4: 9 => CTR * .68...371.4.7.1.86...8.64..93458761278.6..5436..3..7981264938574..168239893275164 A4: 2,5 # 17 pairs * PAIR H3: 2,9 BLK 3 G2: 2,9,5 # reduction candidate for 2,9 G2: 2,9 # 17 pairs I3: 2,9,5 # reduction candidate for 2,9 I3: 2,9 => CTR * .685.9371.4.7.15865..8364..234.8761578.6...436..3..7.81264938574..168.3.893275164 I3: 5 # 17 pairs * PAIR H3: 2,9 ROW 3 A3: 2,9,3,5 # reduction candidate for 2,9 A3: 2,9 # 18 pairs A3: 3,5 # 15 pairs * PAIR B6: 1,5 BLK 4 C5: 1,5,2,9 # reduction candidate for 1,5 C5: 1,5 # 20 pairs C6: 1,5,2,9 # reduction candidate for 1,5 C6: 1,5 # 22 pairs * PAIR B6: 1,5 ROW 6 E6: 1,5,2,4 # reduction candidate for 1,5 E6: 2,4 # 22 pairs E6: 1,5 # 17 pairs * PAIR D4: 5,9 ROW 4 A4: 5,9,2 # reduction candidate for 5,9 A4: 5,9 => SOLVED * 268549371345721986971836425534987612789612543612354798126493857457168239893275164 A4: 2 => CTR * 5689..371.427.1.86...8.64..23458761978.6..5436..3..7281264938574..168.3.893275164 I4: 5,9,2 # reduction candidate for 5,9 I4: 5,9 => CTR * 5689..371.427.1.86...8.64..23458761978.6..5436..3..7281264938574..168.3.893275164 I4: 2 => SOLVED * 268549371345721986971836425534987612789612543612354798126493857457168239893275164 * PAIR F5: 2,9 BLK 5 F6: 2,9,4 # reduction candidate for 2,9 F6: 2,9 # 22 pairs F6: 4 # 14 pairs * PAIR F5: 2,9 ROW 5 C5: 2,9,1,5 # reduction candidate for 2,9 C5: 2,9 # 17 pairs G5: 2,9,5 # reduction candidate for 2,9 G5: 2,9 => CTR * .685.9371.4.7.15865..8364..234.8761578.6...436..3..7.81264938574..168.3.893275164 G5: 5 # 17 pairs * PAIR F5: 2,9 COL F F1: 2,9,4 # reduction candidate for 2,9 F1: 4 # 22 pairs F1: 2,9 # 14 pairs * PAIR H6: 2,9 BLK 6 I4: 2,9,5 # reduction candidate for 2,9 I4: 2,9 # 17 pairs G5: 2,9,5 # reduction candidate for 2,9 G5: 2,9 => CTR * .685.9371.4.7.15865..8364..234.8761578.6...436..3..7.81264938574..168.3.893275164 G5: 5 # 17 pairs * PAIR H6: 2,9 ROW 6 C6: 2,9,1,5 # reduction candidate for 2,9 C6: 2,9 # 17 pairs F6: 2,9,4 # reduction candidate for 2,9 F6: 2,9 # 22 pairs * PAIR G8: 2,9 COL G G2: 2,9,5 # reduction candidate for 2,9 G2: 2,9 # 17 pairs G5: 2,9,5 # reduction candidate for 2,9 G5: 2,9 => CTR * .685.9371.4.7.15865..8364..234.8761578.6...436..3..7.81264938574..168.3.893275164 G5: 5 # 17 pairs * PAIR I8: 2,9 COL I I3: 2,9,5 # reduction candidate for 2,9 I3: 2,9 => CTR * .685.9371.4.7.15865..8364..234.8761578.6...436..3..7.81264938574..168.3.893275164 I3: 5 # 17 pairs I4: 2,9,5 # reduction candidate for 2,9 I4: 2,9 # 17 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-290-base-pr-000.dot * REASONING * DIS # A2: 2,5 => CTR => A2: 3,9 * DIS # A3: 2,5 => CTR => A3: 3,9 * DIS # A4: 9 => CTR => A4: 2,5 * DIS # I3: 2,9 => CTR => I3: 5 * PRF # A4: 5,9 => SOL * DIS # A4: 2 => CTR => A4: 5,9 * DIS # I4: 5,9 => CTR => I4: 2 * PRF # I4: 2 => SOL * DIS # G5: 2,9 => CTR => G5: 5 * DIS # G5: 2,9 => CTR => G5: 5 * DIS # G5: 2,9 => CTR => G5: 5 * DIS # I3: 2,9 => CTR => I3: 5 * CNT 12 HDP CHAINS / 40 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B3,B6,B8,C3,C8,D1,D4,F5,G8,H3,H6,I8) * .68...371.4.7.1.86...8.64...34.8761.78.6...436..3..7.81264938574..168.3.893275164 * PAIR A1: 2,5 BLK 1 A2: 2,5,3,9 # reduction candidate for 2,5 A2: 2,5 => CTR * .68...371.4.731.863..8.64..93458761278.6..5436..3..7981264938574..168239893275164 C2: 2,5,9 # reduction candidate for 2,5 C2: 2,5 # 17 pairs A3: 2,5,3,9 # reduction candidate for 2,5 A3: 2,5 => CTR * .68...3713497.1.86...8364..93458761278.6..5436..3..7981264938574..168.3.893275164 * RESTART * PAIR A1: 2,5 ROW 1 E1: 2,5,4 # reduction candidate for 2,5 E1: 2,5 => CTR * 5689243719427.1.86...8.64...3458761978.61.5436..34.7281264938574..168932893275164 * PAIR RESTART * PAIR H3: 2,9 BLK 3 G2: 2,9,5 # reduction candidate for 2,9 G2: 2,9 # 22 pairs I3: 2,9,5 # reduction candidate for 2,9 I3: 2,9 => CTR * .68.4.371.4.7.1586...8564...345876197856192436..3.47.81264938574..168.3.893275164 * RESTART * PAIR B6: 1,5 BLK 4 C6: 1,5,2,9 # reduction candidate for 1,5 C6: 1,5 => CTR * .68.4.371.4.7.1.86...8.64.5.34.8761.7896125436..3547.81264938574..168.3.893275164 * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A1,A2,A3,A4,B3,B6,B8,C2,C3,C5,C6,C8,D1,D4,E3,E5,E6,F1,F5,G2,G8,H3,H6,I4,I8) * .68.4.371.4.7.1.86...8.64.5.34.8761.78.6..5436..3.47.81264938574..168.3.893275164 * PAIR C2: 2,5 ROW 2 E2: 2,5,3 # reduction candidate for 2,5 E2: 2,5 => SOLVED * 268549371345721986971836425534987612789612543612354798126493857457168239893275164 * DURATION: 0:00:12.167709 START: 12:53:11.138281 END: 12:53:23.305990 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-290-base-pr-001.dot * REASONING * DIS # A2: 2,5 => CTR => A2: 3,9 * DIS A2: 3,9 # A3: 2,5 => CTR => A3: 3,9 * DIS A2: 3,9 + A3: 3,9 # E1: 2,5 => CTR => E1: 4 * DIS A2: 3,9 + A3: 3,9 + E1: 4 # I3: 2,9 => CTR => I3: 5 * DIS A2: 3,9 + A3: 3,9 + E1: 4 + I3: 5 # C6: 1,5 => CTR => C6: 2,9 * PRF A2: 3,9 + A3: 3,9 + E1: 4 + I3: 5 + C6: 2,9 # E2: 2,5 => SOL * STA A2: 3,9 + A3: 3,9 + E1: 4 + I3: 5 + C6: 2,9 + E2: 2,5 * CNT 6 HDP CHAINS / 8 HYP OPENED
Header Info
Top 500 Minimum 17 290 solution: 268549371345721986971836425534987612789612543612354798126493857457168239893275164 info: 2397 FNBHWXY S8.f 21970 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 268549371345721986971836425534987612789612543612354798126493857457168239893275164 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 # A2: 2,5 => CTR => A2: 3,9 * INC # A2: 3,9 => UNS * INC # C2: 2,5 => UNS * DIS # A3: 2,5 => CTR => A3: 3,9 * INC # A3: 3,9 => UNS * INC # E1: 2,5 => UNS * INC # E1: 4 => UNS * INC # A4: 2,5 => UNS * DIS # A4: 9 => CTR => A4: 2,5 * INC # G2: 2,9 => UNS * DIS # I3: 2,9 => CTR => I3: 5 * INC # I3: 5 => UNS * INC # A3: 2,9 => UNS * INC # A3: 3,5 => UNS * INC # C5: 1,5 => UNS * INC # C6: 1,5 => UNS * INC # E6: 1,5 => UNS * INC # E6: 2,4 => UNS * PRF # A4: 5,9 => SOL * DIS # A4: 2 => CTR => A4: 5,9 * DIS # I4: 5,9 => CTR => I4: 2 * PRF # I4: 2 => SOL * INC # F6: 2,9 => UNS * INC # F6: 4 => UNS * INC # C5: 2,9 => UNS * DIS # G5: 2,9 => CTR => G5: 5 * INC # G5: 5 => UNS * INC # F1: 2,9 => UNS * INC # F1: 4 => UNS * INC # I4: 2,9 => UNS * DIS # G5: 2,9 => CTR => G5: 5 * INC # G5: 5 => UNS * INC # C6: 2,9 => UNS * INC # F6: 2,9 => UNS * INC # G2: 2,9 => UNS * DIS # G5: 2,9 => CTR => G5: 5 * INC # G5: 5 => UNS * DIS # I3: 2,9 => CTR => I3: 5 * INC # I3: 5 => UNS * INC # I4: 2,9 => UNS * CNT 40 HDP CHAINS / 40 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A2: 2,5 => CTR => A2: 3,9 * INC A2: 3,9 # C2: 2,5 => UNS * DIS A2: 3,9 # A3: 2,5 => CTR => A3: 3,9 * DIS A2: 3,9 + A3: 3,9 # E1: 2,5 => CTR => E1: 4 * INC A2: 3,9 + A3: 3,9 + E1: 4 # G2: 2,9 => UNS * DIS A2: 3,9 + A3: 3,9 + E1: 4 # I3: 2,9 => CTR => I3: 5 * DIS A2: 3,9 + A3: 3,9 + E1: 4 + I3: 5 # C6: 1,5 => CTR => C6: 2,9 * PRF A2: 3,9 + A3: 3,9 + E1: 4 + I3: 5 + C6: 2,9 # E2: 2,5 => SOL * STA A2: 3,9 + A3: 3,9 + E1: 4 + I3: 5 + C6: 2,9 + E2: 2,5 * CNT 8 HDP CHAINS / 8 HYP OPENED