Analysis of xx-top500-241-base.sdk
Contents
Original Sudoku
level: medium
position: 2...3......4...6.......8....3.6........4..1.......54..78......3....4..2....1..... initial
Autosolve
position: 268.34.1.3.4...682.1.2683.443.6..2..8..4.213.12.3.54..781.26.436.384..21.421.38.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C3: 5,9 => CTR => C3: 7 * DIS # H3: 7 => CTR => H3: 5,9 * DIS # E2: 1,9 => CTR => E2: 5 * DIS # F4: 1,9 => CTR => F4: 7 * PRF # F4: 7 => SOL * DIS # E4: 7,9 => CTR => E4: 1,8 * DIS # E6: 7,9 => CTR => E6: 8 * DIS # C5: 7,9 => CTR => C5: 5,6 * DIS # I5: 7,9 => CTR => I5: 5,6 * DIS # E9: 5 => CTR => E9: 7,9 * DIS # G8: 5,9 => CTR => G8: 7 * PRF # G8: 7 => SOL * DIS # B5: 5,9 => CTR => B5: 7 * DIS # E9: 5,9 => CTR => E9: 7 * PRF # E9: 7 => SOL * DIS # H9: 5,9 => CTR => H9: 6,7 * PRF # I9: 5,9 => SOL * DIS # E9: 5,9 => CTR => E9: 7 * PRF # E9: 7 => SOL * DIS # D2: 5,9 => CTR => D2: 7 * DIS # E9: 5 => CTR => E9: 7,9 * DIS # G8: 5 => CTR => G8: 7,9 * DIS # F4: 1 => CTR => F4: 7,9 * DIS # G8: 5,9 => CTR => G8: 7 * PRF # G8: 7 => SOL * DIS # H9: 5,9 => CTR => H9: 6,7 * PRF # I9: 5,9 => SOL * PRF # G1: 5,9 => SOL * DIS # G1: 7 => CTR => G1: 5,9 * CNT 29 HDP CHAINS / 51 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C3: 5,9 => CTR => C3: 7 * DIS C3: 7 # G8: 5,9 => CTR => G8: 7 * PRF C3: 7 + G8: 7 => SOL * STA C3: 7 + G8: 7 * CNT 3 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 2...3......4...6.......8....3.6........4..1.......54..78......3....4..2....1..... | initial |
| 268.34.1.3.4...682.1.2683.443.6..2..8..4.213.12.3.54..781.26.436.384..21.421.38.. | autosolve |
| 268934517394751682517268394439617258875492136126385479781526943653849721942173865 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) A3: 5,9 F2: 1,9 E5: 7,9 B8: 5,9 A9: 5,9 D7: 5,9 F8: 7,9 G7: 5,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E2,F2: 1.. / E2 = 1 => 0 pairs (X) / F2 = 1 => 9 pairs (_) E4,F4: 1.. / E4 = 1 => 9 pairs (_) / F4 = 1 => 0 pairs (X) E2,E4: 1.. / E2 = 1 => 0 pairs (X) / E4 = 1 => 9 pairs (_) F2,F4: 1.. / F2 = 1 => 9 pairs (_) / F4 = 1 => 0 pairs (X) B8,A9: 5.. / B8 = 5 => 15 pairs (_) / A9 = 5 => 0 pairs (X) D7,E9: 5.. / D7 = 5 => 13 pairs (_) / E9 = 5 => 0 pairs (X) D7,G7: 5.. / D7 = 5 => 13 pairs (_) / G7 = 5 => 0 pairs (X) B8,G8: 5.. / B8 = 5 => 15 pairs (_) / G8 = 5 => 0 pairs (X) A3,A9: 5.. / A3 = 5 => 15 pairs (_) / A9 = 5 => 0 pairs (X) E2,E9: 5.. / E2 = 5 => 13 pairs (_) / E9 = 5 => 0 pairs (X) C5,C6: 6.. / C5 = 6 => 9 pairs (_) / C6 = 6 => 10 pairs (_) H9,I9: 6.. / H9 = 6 => 9 pairs (_) / I9 = 6 => 9 pairs (_) C5,I5: 6.. / C5 = 6 => 9 pairs (_) / I5 = 6 => 10 pairs (_) H6,H9: 6.. / H6 = 6 => 9 pairs (_) / H9 = 6 => 9 pairs (_) B2,C3: 7.. / B2 = 7 => 0 pairs (X) / C3 = 7 => 18 pairs (_) D1,D2: 7.. / D1 = 7 => 0 pairs (X) / D2 = 7 => 18 pairs (_) F8,E9: 7.. / F8 = 7 => 0 pairs (X) / E9 = 7 => 0 pairs (_) B2,D2: 7.. / B2 = 7 => 0 pairs (X) / D2 = 7 => 18 pairs (_) C3,H3: 7.. / C3 = 7 => 18 pairs (_) / H3 = 7 => 0 pairs (X) F8,G8: 7.. / F8 = 7 => 0 pairs (X) / G8 = 7 => 0 pairs (_) B2,B5: 7.. / B2 = 7 => 0 pairs (X) / B5 = 7 => 18 pairs (_) F4,F8: 7.. / F4 = 7 => 0 pairs (*) / F8 = 7 => 0 pairs (X) G1,G8: 7.. / G1 = 7 => 0 pairs (X) / G8 = 7 => 0 pairs (_) E4,E6: 8.. / E4 = 8 => 0 pairs (X) / E6 = 8 => 8 pairs (_) I4,I6: 8.. / I4 = 8 => 8 pairs (_) / I6 = 8 => 0 pairs (X) E4,I4: 8.. / E4 = 8 => 0 pairs (X) / I4 = 8 => 8 pairs (_) E6,I6: 8.. / E6 = 8 => 8 pairs (_) / I6 = 8 => 0 pairs (X) B8,A9: 9.. / B8 = 9 => 0 pairs (X) / A9 = 9 => 15 pairs (_) D7,G7: 9.. / D7 = 9 => 0 pairs (X) / G7 = 9 => 13 pairs (_) A3,A9: 9.. / A3 = 9 => 0 pairs (X) / A9 = 9 => 15 pairs (_) * DURATION: 0:00:48.119239 START: 11:02:26.868593 END: 11:03:14.987832 2017-05-04 * CP COUNT: (30) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A9,B8,D7,E5,F2,F8,G7) * 268.34.1.3.4...682.1.2683.443.6..2..8..4.213.12.3.54..781.26.436.384..21.421.38.. * PAIR A3: 5,9 BLK 1 B2: 5,9,7 # reduction candidate for 5,9 B2: 5,9 # 18 pairs C3: 5,9,7 # reduction candidate for 5,9 C3: 5,9 => CTR * 268734.1.374.51682.1.26837443.6172.88..49213.12.3854..7815269436.384.721.421738.. C3: 7 # 18 pairs * PAIR A3: 5,9 ROW 3 H3: 5,9,7 # reduction candidate for 5,9 H3: 7 => CTR * 268734.1.374.51682.1.26837443.6172.88..49213.12.3854..7815269436.384.721.421738.. H3: 5,9 # 18 pairs * PAIR F2: 1,9 BLK 2 E2: 1,9,5 # reduction candidate for 1,9 E2: 1,9 => CTR * 268.34.1.3.4...68251.2683.443.6..25.8.54.21361263.54..781926543653847921942153867 E2: 5 # 13 pairs * PAIR F2: 1,9 COL F F4: 1,9,7 # reduction candidate for 1,9 F4: 1,9 => CTR * 268.3471.3.47..682.172683.443.6..2..87.49213.12.3.54..7819265436538479219421538.. F4: 7 => SOLVED * 268934517394751682517268394439617258875492136126385479781526943653849721942173865 * PAIR E5: 7,9 BLK 5 E4: 7,9,1,8 # reduction candidate for 7,9 E4: 7,9 => CTR * 268.34719374.19682.1.2683.443.6.12.88..4.213.12.3854..7819265436538479219421538.. E4: 1,8 # 9 pairs F4: 7,9,1 # reduction candidate for 7,9 F4: 7,9 # 9 pairs E6: 7,9,8 # reduction candidate for 7,9 E6: 7,9 => CTR * 268.3471.3.4719682.172683.443.6812..87.49213.12.3754.87819265436.3847.21.421.38.. E6: 8 # 8 pairs * PAIR E5: 7,9 ROW 5 B5: 7,9,5 # reduction candidate for 7,9 B5: 7,9 # 12 pairs C5: 7,9,5,6 # reduction candidate for 7,9 C5: 7,9 => CTR * 268.3471.374...682.1.2683.443.6..2..85.4.21361263.54..781.26.43693847521542193867 C5: 5,6 # 9 pairs I5: 7,9,5,6 # reduction candidate for 7,9 I5: 7,9 => CTR * 268.3471.374...682.1.2683.443.6..2..8564.213.12.3.54..781.26.436938475215421938.. I5: 5,6 # 9 pairs * PAIR E5: 7,9 COL E E9: 7,9,5 # reduction candidate for 7,9 E9: 5 => CTR * 268.3471.3.47..68251726839443.6..25.8754921361263.5479781926.436.3847.21.421538.. E9: 7,9 # 13 pairs * PAIR B8: 5,9 ROW 8 G8: 5,9,7 # reduction candidate for 5,9 G8: 5,9 => CTR * 2685347193547..682.172683.443.6..2..87.49213.12.3.54..781.26.436.3847.21.421538.. G8: 7 => SOLVED * 268934517394751682517268394439617258875492136126385479781526943653849721942173865 * PAIR B8: 5,9 COL B B2: 5,9,7 # reduction candidate for 5,9 B2: 5,9 # 18 pairs B5: 5,9,7 # reduction candidate for 5,9 B5: 5,9 => CTR * 268734.1.374.51682.1.26837443.6172.88..49213.12.3854..7815269436.384.721.421738.. B5: 7 # 18 pairs * PAIR A9: 5,9 ROW 9 E9: 5,9,7 # reduction candidate for 5,9 E9: 5,9 => CTR * 268.3471.3.47..682.172683.443.6..2..87.49213.12.3.54..7819265436538479219421538.. E9: 7 => SOLVED * 268934517394751682517268394439617258875492136126385479781526943653849721942173865 H9: 5,9,6,7 # reduction candidate for 5,9 H9: 5,9 => CTR * 268.3451.39475168251.2683.443.6172.88.649213.12.38546.781526943653849721942173856 H9: 6,7 # 9 pairs I9: 5,9,6,7 # reduction candidate for 5,9 I9: 5,9 => SOLVED * 268934517394751682517268394439617258875492136126385479781526943653849721942173865 I9: 6,7 # 9 pairs * PAIR D7: 5,9 BLK 8 E9: 5,9,7 # reduction candidate for 5,9 E9: 5,9 => CTR * 268.3471.3.47..682.172683.443.6..2..87.49213.12.3.54..7819265436538479219421538.. E9: 7 => SOLVED * 268934517394751682517268394439617258875492136126385479781526943653849721942173865 * PAIR D7: 5,9 COL D D1: 5,9,7 # reduction candidate for 5,9 D1: 5,9 # 18 pairs D2: 5,9,7 # reduction candidate for 5,9 D2: 5,9 => CTR * 268734.1.374.51682.1.26837443.6172.88..49213.12.3854..7815269436.384.721.421738.. D2: 7 # 18 pairs * PAIR F8: 7,9 BLK 8 E9: 7,9,5 # reduction candidate for 7,9 E9: 5 => CTR * 268.3471.3.47..68251726839443.6..25.8754921361263.5479781926.436.3847.21.421538.. E9: 7,9 # 13 pairs * PAIR F8: 7,9 ROW 8 G8: 7,9,5 # reduction candidate for 7,9 G8: 5 => CTR * 268.3471.3.47..682.172683.443.6..2..87.49213.12.3.54..781.269436.384..21.421.38.. G8: 7,9 # 15 pairs * PAIR F8: 7,9 COL F F4: 7,9,1 # reduction candidate for 7,9 F4: 1 => CTR * 268.3471.3.4719682.172683.443.6.12..87.49213.12.3.54..7819265436.3847.21.421.38.. F4: 7,9 # 9 pairs * PAIR G7: 5,9 BLK 9 G8: 5,9,7 # reduction candidate for 5,9 G8: 5,9 => CTR * 2685347193547..682.172683.443.6..2..87.49213.12.3.54..781.26.436.3847.21.421538.. G8: 7 => SOLVED * 268934517394751682517268394439617258875492136126385479781526943653849721942173865 H9: 5,9,6,7 # reduction candidate for 5,9 H9: 5,9 => CTR * 268.3451.39475168251.2683.443.6172.88.649213.12.38546.781526943653849721942173856 H9: 6,7 # 9 pairs I9: 5,9,6,7 # reduction candidate for 5,9 I9: 5,9 => SOLVED * 268934517394751682517268394439617258875492136126385479781526943653849721942173865 I9: 6,7 # 9 pairs * PAIR G7: 5,9 COL G G1: 5,9,7 # reduction candidate for 5,9 G1: 5,9 => SOLVED * 268934517394751682517268394439617258875492136126385479781526943653849721942173865 G1: 7 => CTR * 2685347193547..682.172683.443.6..2..87.49213.12.3.54..781.26.436.3847.21.421538.. * INCONCLUSIVE * SAVE PR GRAPH xx-top500-241-base-pr-000.dot * REASONING * DIS # C3: 5,9 => CTR => C3: 7 * DIS # H3: 7 => CTR => H3: 5,9 * DIS # E2: 1,9 => CTR => E2: 5 * DIS # F4: 1,9 => CTR => F4: 7 * PRF # F4: 7 => SOL * DIS # E4: 7,9 => CTR => E4: 1,8 * DIS # E6: 7,9 => CTR => E6: 8 * DIS # C5: 7,9 => CTR => C5: 5,6 * DIS # I5: 7,9 => CTR => I5: 5,6 * DIS # E9: 5 => CTR => E9: 7,9 * DIS # G8: 5,9 => CTR => G8: 7 * PRF # G8: 7 => SOL * DIS # B5: 5,9 => CTR => B5: 7 * DIS # E9: 5,9 => CTR => E9: 7 * PRF # E9: 7 => SOL * DIS # H9: 5,9 => CTR => H9: 6,7 * PRF # I9: 5,9 => SOL * DIS # E9: 5,9 => CTR => E9: 7 * PRF # E9: 7 => SOL * DIS # D2: 5,9 => CTR => D2: 7 * DIS # E9: 5 => CTR => E9: 7,9 * DIS # G8: 5 => CTR => G8: 7,9 * DIS # F4: 1 => CTR => F4: 7,9 * DIS # G8: 5,9 => CTR => G8: 7 * PRF # G8: 7 => SOL * DIS # H9: 5,9 => CTR => H9: 6,7 * PRF # I9: 5,9 => SOL * PRF # G1: 5,9 => SOL * DIS # G1: 7 => CTR => G1: 5,9 * CNT 29 HDP CHAINS / 51 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A9,B8,D7,E5,F2,F8,G7) * 268.34.1.3.4...682.1.2683.443.6..2..8..4.213.12.3.54..781.26.436.384..21.421.38.. * PAIR A3: 5,9 BLK 1 B2: 5,9,7 # reduction candidate for 5,9 B2: 5,9 # 18 pairs C3: 5,9,7 # reduction candidate for 5,9 C3: 5,9 => CTR * 268734.1.374.51682.1.26837443.6172.88..49213.12.3854..7815269436.384.721.421738.. * RESTART * PAIR B8: 5,9 ROW 8 G8: 5,9,7 # reduction candidate for 5,9 G8: 5,9 => CTR * 2685347193547..682.172683.443.6..2..87.49213.12.3.54..781.26.436.3847.21.421538.. G8: 7 => SOLVED * 268934517394751682517268394439617258875492136126385479781526943653849721942173865 * DURATION: 0:00:04.856749 START: 11:04:02.871099 END: 11:04:07.727848 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-241-base-pr-001.dot * REASONING * DIS # C3: 5,9 => CTR => C3: 7 * DIS C3: 7 # G8: 5,9 => CTR => G8: 7 * PRF C3: 7 + G8: 7 => SOL * STA C3: 7 + G8: 7 * CNT 3 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 241 solution: 268934517394751682517268394439617258875492136126385479781526943653849721942173865 info: 2069 FNBWXY S8.f 27320 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 268934517394751682517268394439617258875492136126385479781526943653849721942173865 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 # B2: 5,9 => UNS * DIS # C3: 5,9 => CTR => C3: 7 * INC # C3: 7 => UNS * INC # H3: 5,9 => UNS * DIS # H3: 7 => CTR => H3: 5,9 * DIS # E2: 1,9 => CTR => E2: 5 * INC # E2: 5 => UNS * DIS # F4: 1,9 => CTR => F4: 7 * PRF # F4: 7 => SOL * DIS # E4: 7,9 => CTR => E4: 1,8 * INC # E4: 1,8 => UNS * INC # F4: 7,9 => UNS * DIS # E6: 7,9 => CTR => E6: 8 * INC # E6: 8 => UNS * INC # B5: 7,9 => UNS * DIS # C5: 7,9 => CTR => C5: 5,6 * INC # C5: 5,6 => UNS * DIS # I5: 7,9 => CTR => I5: 5,6 * INC # I5: 5,6 => UNS * INC # E9: 7,9 => UNS * DIS # E9: 5 => CTR => E9: 7,9 * DIS # G8: 5,9 => CTR => G8: 7 * PRF # G8: 7 => SOL * INC # B2: 5,9 => UNS * DIS # B5: 5,9 => CTR => B5: 7 * INC # B5: 7 => UNS * DIS # E9: 5,9 => CTR => E9: 7 * PRF # E9: 7 => SOL * DIS # H9: 5,9 => CTR => H9: 6,7 * INC # H9: 6,7 => UNS * PRF # I9: 5,9 => SOL * INC # I9: 6,7 => UNS * DIS # E9: 5,9 => CTR => E9: 7 * PRF # E9: 7 => SOL * INC # D1: 5,9 => UNS * DIS # D2: 5,9 => CTR => D2: 7 * INC # D2: 7 => UNS * INC # E9: 7,9 => UNS * DIS # E9: 5 => CTR => E9: 7,9 * INC # G8: 7,9 => UNS * DIS # G8: 5 => CTR => G8: 7,9 * INC # F4: 7,9 => UNS * DIS # F4: 1 => CTR => F4: 7,9 * DIS # G8: 5,9 => CTR => G8: 7 * PRF # G8: 7 => SOL * DIS # H9: 5,9 => CTR => H9: 6,7 * INC # H9: 6,7 => UNS * PRF # I9: 5,9 => SOL * INC # I9: 6,7 => UNS * PRF # G1: 5,9 => SOL * DIS # G1: 7 => CTR => G1: 5,9 * CNT 51 HDP CHAINS / 51 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B2: 5,9 => UNS * DIS # C3: 5,9 => CTR => C3: 7 * DIS C3: 7 # G8: 5,9 => CTR => G8: 7 * PRF C3: 7 + G8: 7 => SOL * STA C3: 7 + G8: 7 * CNT 4 HDP CHAINS / 3 HYP OPENED