Analysis of xx-top500-287-base.sdk
Contents
Original Sudoku
level: medium
position: 7.2....5.....41............16..3...4...2..58.............5..2..31........4....... initial
Autosolve
position: 7.23..451653.41..24.1.5236.16..35.2493421.58.52.4..13.87659421331.62..4.24.1.36.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # F1: 6 => SOL * DIS # D3: 8,9 => CTR => D3: 7 * PRF # F1: 6,8 => SOL * DIS # F1: 9 => CTR => F1: 6,8 * PRF # E6: 6,8 => SOL * DIS # E6: 7 => CTR => E6: 6,8 * DIS # G2: 7,9 => CTR => G2: 8 * DIS # D2: 8 => CTR => D2: 7,9 * DIS # F6: 7,8 => CTR => F6: 6,9 * DIS # F6: 6,7 => CTR => F6: 8,9 * DIS # D3: 8,9 => CTR => D3: 7 * DIS # F6: 6,7 => CTR => F6: 8,9 * PRF # I6: 7,9 => SOL * DIS # I6: 6 => CTR => I6: 7,9 * DIS # G2: 7,9 => CTR => G2: 8 * PRF # I6: 6,7 => SOL * DIS # I6: 9 => CTR => I6: 6,7 * DIS # I8: 7,8 => CTR => I8: 5,9 * DIS # I9: 5,9 => CTR => I9: 7,8 * DIS # I8: 7,8 => CTR => I8: 5,9 * DIS # F6: 7,8 => CTR => F6: 6,9 * DIS # I9: 5,9 => CTR => I9: 7,8 * PRF # E6: 6 => SOL * DIS # I8: 7,9 => CTR => I8: 5,8 * DIS # I9: 7,9 => CTR => I9: 5,8 * 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:
* PRF # F1: 6 => SOL * STA F1: 6 * CNT 1 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 7.2....5.....41............16..3...4...2..58.............5..2..31........4....... | initial |
| 7.23..451653.41..24.1.5236.16..35.2493421.58.52.4..13.87659421331.62..4.24.1.36.. | autosolve |
| 792386451653941872481752369167835924934217586528469137876594213319628745245173698 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) B1: 8,9 B3: 8,9 E1: 6,8 H2: 7,9 C4: 7,8 C6: 7,8 D4: 8,9 F5: 6,7 G4: 7,9 I5: 6,7 C8: 5,9 C9: 5,9 F8: 7,8 E9: 7,8 H9: 7,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C8,C9: 5.. / C8 = 5 => 0 pairs (X) / C9 = 5 => 14 pairs (_) I8,I9: 5.. / I8 = 5 => 14 pairs (_) / I9 = 5 => 0 pairs (X) C8,I8: 5.. / C8 = 5 => 0 pairs (X) / I8 = 5 => 14 pairs (_) C9,I9: 5.. / C9 = 5 => 14 pairs (_) / I9 = 5 => 0 pairs (X) E1,F1: 6.. / E1 = 6 => 18 pairs (_) / F1 = 6 => 0 pairs (*) I5,I6: 6.. / I5 = 6 => 0 pairs (*) / I6 = 6 => 0 pairs (X) F5,I5: 6.. / F5 = 6 => 0 pairs (X) / I5 = 6 => 0 pairs (_) E1,E6: 6.. / E1 = 6 => 18 pairs (_) / E6 = 6 => 0 pairs (*) D2,D3: 7.. / D2 = 7 => 0 pairs (X) / D3 = 7 => 17 pairs (_) C4,C6: 7.. / C4 = 7 => 0 pairs (*) / C6 = 7 => 0 pairs (X) F8,E9: 7.. / F8 = 7 => 0 pairs (X) / E9 = 7 => 0 pairs (_) D3,I3: 7.. / D3 = 7 => 17 pairs (_) / I3 = 7 => 0 pairs (X) C4,G4: 7.. / C4 = 7 => 0 pairs (*) / G4 = 7 => 0 pairs (X) F5,I5: 7.. / F5 = 7 => 0 pairs (*) / I5 = 7 => 0 pairs (X) E6,E9: 7.. / E6 = 7 => 0 pairs (X) / E9 = 7 => 0 pairs (_) H2,H9: 7.. / H2 = 7 => 16 pairs (_) / H9 = 7 => 0 pairs (X) B1,B3: 8.. / B1 = 8 => 0 pairs (X) / B3 = 8 => 0 pairs (_) G2,I3: 8.. / G2 = 8 => 20 pairs (_) / I3 = 8 => 0 pairs (X) C4,C6: 8.. / C4 = 8 => 0 pairs (X) / C6 = 8 => 0 pairs (_) F8,E9: 8.. / F8 = 8 => 0 pairs (*) / E9 = 8 => 0 pairs (X) D2,G2: 8.. / D2 = 8 => 0 pairs (X) / G2 = 8 => 20 pairs (_) C4,D4: 8.. / C4 = 8 => 0 pairs (X) / D4 = 8 => 0 pairs (_) E9,I9: 8.. / E9 = 8 => 0 pairs (X) / I9 = 8 => 0 pairs (_) G2,G8: 8.. / G2 = 8 => 20 pairs (_) / G8 = 8 => 0 pairs (X) B1,B3: 9.. / B1 = 9 => 0 pairs (*) / B3 = 9 => 0 pairs (X) D4,F6: 9.. / D4 = 9 => 0 pairs (X) / F6 = 9 => 0 pairs (_) G4,I6: 9.. / G4 = 9 => 0 pairs (*) / I6 = 9 => 0 pairs (X) C8,C9: 9.. / C8 = 9 => 14 pairs (_) / C9 = 9 => 0 pairs (X) B1,F1: 9.. / B1 = 9 => 0 pairs (*) / F1 = 9 => 0 pairs (X) D4,G4: 9.. / D4 = 9 => 0 pairs (X) / G4 = 9 => 0 pairs (_) F6,I6: 9.. / F6 = 9 => 0 pairs (*) / I6 = 9 => 0 pairs (X) F1,F6: 9.. / F1 = 9 => 0 pairs (X) / F6 = 9 => 0 pairs (_) H2,H9: 9.. / H2 = 9 => 0 pairs (X) / H9 = 9 => 16 pairs (_) * DURATION: 0:01:03.608736 START: 12:44:43.474403 END: 12:45:47.083139 2017-05-04 * CP COUNT: (33) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,B3,C4,C6,C8,C9,D4,E1,E9,F5,F8,G4,H2,H9,I5) * 7.23..451653.41..24.1.5236.16..35.2493421.58.52.4..13.87659421331.62..4.24.1.36.. * PAIR B1: 8,9 ROW 1 F1: 8,9,6 # reduction candidate for 8,9 F1: 6 => SOLVED * 792386451653941872481752369167835924934217586528469137876594213319628745245173698 F1: 8,9 # 18 pairs * PAIR B3: 8,9 ROW 3 D3: 8,9,7 # reduction candidate for 8,9 D3: 8,9 => CTR * 7.23..4516537418924.1.5236716..357249342175865274..13987659421331.62894524.1.36.. D3: 7 # 17 pairs I3: 8,9,7 # reduction candidate for 8,9 I3: 8,9 # 17 pairs * PAIR E1: 6,8 BLK 2 F1: 6,8,9 # reduction candidate for 6,8 F1: 6,8 => SOLVED * 792386451653941872481752369167835924934217586528469137876594213319628745245173698 F1: 9 => CTR * 7.2369451653.41..2491.5236.16.93572493421758652748613987659421331.62894724.1.36.. * PAIR E1: 6,8 COL E E6: 6,8,7 # reduction candidate for 6,8 E6: 6,8 => SOLVED * 792386451653941872481752369167835924934217586528469137876594213319628745245173698 E6: 7 => CTR * 7.236.451653.41..24.1.5236.16783592493421.58.52.47.13.87659421331.627.4.24.1836.. * PAIR H2: 7,9 BLK 3 G2: 7,9,8 # reduction candidate for 7,9 G2: 7,9 => CTR * 7.23..451653841..24.17523681689357249342175865274..13987659421331.628.4.24.1.36.. G2: 8 # 20 pairs I3: 7,9,8 # reduction candidate for 7,9 I3: 7,9 # 20 pairs * PAIR H2: 7,9 ROW 2 D2: 7,9,8 # reduction candidate for 7,9 D2: 8 => CTR * 7.23..451653841..24.17523681689357249342175865274..13987659421331.628.4.24.1.36.. D2: 7,9 # 20 pairs * PAIR C6: 7,8 ROW 6 E6: 7,8,6 # reduction candidate for 7,8 E6: 7,8 # 18 pairs F6: 7,8,6,9 # reduction candidate for 7,8 F6: 7,8 => CTR * 7.23.9451653.41..2491.5236.16.93572493421.58.52.4..13.87659421331.62..4.24.1.36.. F6: 6,9 # 16 pairs * PAIR D4: 8,9 BLK 5 F6: 8,9,6,7 # reduction candidate for 8,9 F6: 6,7 => CTR * 7.23.9451653.41..2491.5236.16.93572493421758652748613987659421331.62894724.1.36.. F6: 8,9 # 17 pairs * PAIR D4: 8,9 COL D D2: 8,9,7 # reduction candidate for 8,9 D2: 8,9 # 17 pairs D3: 8,9,7 # reduction candidate for 8,9 D3: 8,9 => CTR * 7.23..4516537418924.1.5236716..357249342175865274..13987659421331.62894524.1.36.. D3: 7 # 17 pairs * PAIR F5: 6,7 BLK 5 E6: 6,7,8 # reduction candidate for 6,7 E6: 6,7 # 17 pairs F6: 6,7,8,9 # reduction candidate for 6,7 F6: 6,7 => CTR * 7.23.9451653.41..2491.5236.16.93572493421758652748613987659421331.62894724.1.36.. F6: 8,9 # 17 pairs * PAIR G4: 7,9 BLK 6 I6: 7,9,6 # reduction candidate for 7,9 I6: 7,9 => SOLVED * 792386451653941872481752369167835924934217586528469137876594213319628745245173698 I6: 6 => CTR * 792368451653.417924.1.5236.16..3592493421.58752.4.913687659421331.62784.24.18367. * PAIR G4: 7,9 COL G G2: 7,9,8 # reduction candidate for 7,9 G2: 7,9 => CTR * 7.23..451653841..24.17523681689357249342175865274..13987659421331.628.4.24.1.36.. G2: 8 # 20 pairs G8: 7,9,8 # reduction candidate for 7,9 G8: 7,9 # 20 pairs * PAIR I5: 6,7 BLK 6 I6: 6,7,9 # reduction candidate for 6,7 I6: 6,7 => SOLVED * 792386451653941872481752369167835924934217586528469137876594213319628745245173698 I6: 9 => CTR * 7.23.9451653.41..2491.5236.16.9357249342175865274.613987659421331.62894724.1.36.. * PAIR C8: 5,9 ROW 8 I8: 5,9,7,8 # reduction candidate for 5,9 I8: 7,8 => CTR * 7.23..451653.418924.1.5236716.9357249342175865274..13987659421331562894.2491.3675 I8: 5,9 # 17 pairs * PAIR C9: 5,9 ROW 9 I9: 5,9,7,8 # reduction candidate for 5,9 I9: 5,9 => CTR * 7.236.451653.41.924.1.5236.16783592493421.58.52.47.13.87659421331.627.4.24.18367. I9: 7,8 # 16 pairs * PAIR F8: 7,8 ROW 8 G8: 7,8,9 # reduction candidate for 7,8 G8: 7,8 # 17 pairs I8: 7,8,5,9 # reduction candidate for 7,8 I8: 7,8 => CTR * 7.23..451653.418924.1.5236716.9357249342175865274..13987659421331562894.2491.3675 I8: 5,9 # 17 pairs * PAIR F8: 7,8 COL F F6: 7,8,6,9 # reduction candidate for 7,8 F6: 7,8 => CTR * 7.23.9451653.41..2491.5236.16.93572493421.58.52.4..13.87659421331.62..4.24.1.36.. F6: 6,9 # 16 pairs * PAIR E9: 7,8 ROW 9 I9: 7,8,5,9 # reduction candidate for 7,8 I9: 5,9 => CTR * 7.236.451653.41.924.1.5236.16783592493421.58.52.47.13.87659421331.627.4.24.18367. I9: 7,8 # 16 pairs * PAIR E9: 7,8 COL E E6: 7,8,6 # reduction candidate for 7,8 E6: 6 => SOLVED * 792386451653941872481752369167835924934217586528469137876594213319628745245173698 E6: 7,8 # 18 pairs * PAIR H9: 7,9 BLK 9 G8: 7,9,8 # reduction candidate for 7,9 G8: 7,9 # 20 pairs I8: 7,9,5,8 # reduction candidate for 7,9 I8: 7,9 => CTR * 782369451653.41.924.1.5236816..35.2493421.58.52.47.13.876594213315627849249183675 I8: 5,8 # 16 pairs I9: 7,9,5,8 # reduction candidate for 7,9 I9: 7,9 => CTR * 782369451653841..249175236816..35.2493421.58.52.47.13.8765942133196278452451836.. I9: 5,8 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-287-base-pr-000.dot * REASONING * PRF # F1: 6 => SOL * DIS # D3: 8,9 => CTR => D3: 7 * PRF # F1: 6,8 => SOL * DIS # F1: 9 => CTR => F1: 6,8 * PRF # E6: 6,8 => SOL * DIS # E6: 7 => CTR => E6: 6,8 * DIS # G2: 7,9 => CTR => G2: 8 * DIS # D2: 8 => CTR => D2: 7,9 * DIS # F6: 7,8 => CTR => F6: 6,9 * DIS # F6: 6,7 => CTR => F6: 8,9 * DIS # D3: 8,9 => CTR => D3: 7 * DIS # F6: 6,7 => CTR => F6: 8,9 * PRF # I6: 7,9 => SOL * DIS # I6: 6 => CTR => I6: 7,9 * DIS # G2: 7,9 => CTR => G2: 8 * PRF # I6: 6,7 => SOL * DIS # I6: 9 => CTR => I6: 6,7 * DIS # I8: 7,8 => CTR => I8: 5,9 * DIS # I9: 5,9 => CTR => I9: 7,8 * DIS # I8: 7,8 => CTR => I8: 5,9 * DIS # F6: 7,8 => CTR => F6: 6,9 * DIS # I9: 5,9 => CTR => I9: 7,8 * PRF # E6: 6 => SOL * DIS # I8: 7,9 => CTR => I8: 5,8 * DIS # I9: 7,9 => CTR => I9: 5,8 * CNT 25 HDP CHAINS / 50 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,B3,C4,C6,C8,C9,D4,E1,E9,F5,F8,G4,H2,H9,I5) * 7.23..451653.41..24.1.5236.16..35.2493421.58.52.4..13.87659421331.62..4.24.1.36.. * PAIR B1: 8,9 ROW 1 F1: 8,9,6 # reduction candidate for 8,9 F1: 6 => SOLVED * 792386451653941872481752369167835924934217586528469137876594213319628745245173698 * DURATION: 0:00:02.942394 START: 12:46:40.862157 END: 12:46:43.804551 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-287-base-pr-001.dot * REASONING * PRF # F1: 6 => SOL * STA F1: 6 * CNT 1 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 287 solution: 792386451653941872481752369167835924934217586528469137876594213319628745245173698 info: 2334 FNBTWXY S8.f 37281 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 792386451653941872481752369167835924934217586528469137876594213319628745245173698 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 # F1: 8,9 => UNS * PRF # F1: 6 => SOL * DIS # D3: 8,9 => CTR => D3: 7 * INC # D3: 7 => UNS * INC # I3: 8,9 => UNS * PRF # F1: 6,8 => SOL * DIS # F1: 9 => CTR => F1: 6,8 * PRF # E6: 6,8 => SOL * DIS # E6: 7 => CTR => E6: 6,8 * DIS # G2: 7,9 => CTR => G2: 8 * INC # G2: 8 => UNS * INC # I3: 7,9 => UNS * INC # D2: 7,9 => UNS * DIS # D2: 8 => CTR => D2: 7,9 * INC # E6: 7,8 => UNS * DIS # F6: 7,8 => CTR => F6: 6,9 * INC # F6: 6,9 => UNS * INC # F6: 8,9 => UNS * DIS # F6: 6,7 => CTR => F6: 8,9 * INC # D2: 8,9 => UNS * DIS # D3: 8,9 => CTR => D3: 7 * INC # D3: 7 => UNS * INC # E6: 6,7 => UNS * DIS # F6: 6,7 => CTR => F6: 8,9 * INC # F6: 8,9 => UNS * PRF # I6: 7,9 => SOL * DIS # I6: 6 => CTR => I6: 7,9 * DIS # G2: 7,9 => CTR => G2: 8 * INC # G2: 8 => UNS * INC # G8: 7,9 => UNS * PRF # I6: 6,7 => SOL * DIS # I6: 9 => CTR => I6: 6,7 * INC # I8: 5,9 => UNS * DIS # I8: 7,8 => CTR => I8: 5,9 * DIS # I9: 5,9 => CTR => I9: 7,8 * INC # I9: 7,8 => UNS * INC # G8: 7,8 => UNS * DIS # I8: 7,8 => CTR => I8: 5,9 * INC # I8: 5,9 => UNS * DIS # F6: 7,8 => CTR => F6: 6,9 * INC # F6: 6,9 => UNS * INC # I9: 7,8 => UNS * DIS # I9: 5,9 => CTR => I9: 7,8 * INC # E6: 7,8 => UNS * PRF # E6: 6 => SOL * INC # G8: 7,9 => UNS * DIS # I8: 7,9 => CTR => I8: 5,8 * INC # I8: 5,8 => UNS * DIS # I9: 7,9 => CTR => I9: 5,8 * INC # I9: 5,8 => UNS * CNT 50 HDP CHAINS / 50 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # F1: 8,9 => UNS * PRF # F1: 6 => SOL * STA F1: 6 * CNT 2 HDP CHAINS / 2 HYP OPENED