Analysis of xx-top500-382-base.sdk
Contents
Original Sudoku
level: medium
position: .84....6....32.............7.....5.......23...6...4.....2....483...5.......1..... initial
Autosolve
position: 284..5.63...32.48..3.48..5272....5.44....23.6.6...482...2....4834.2586..8.614.235 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E4: 1,9 => CTR => E4: 3,6 * DIS # B7: 7,9 => CTR => B7: 1,5 * CNT 2 HDP CHAINS / 26 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # E4: 1,9 => CTR => E4: 3,6 * DIS E4: 3,6 # B7: 7,9 => CTR => B7: 1,5 * DIS E4: 3,6 + B7: 1,5 # C8: 1 => CTR => C8: 7,9 * PRF E4: 3,6 + B7: 1,5 + C8: 7,9 # F2: 7,9 => SOL * STA E4: 3,6 + B7: 1,5 + C8: 7,9 + F2: 7,9 * CNT 4 HDP CHAINS / 31 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .84....6....32.............7.....5.......23...6...4.....2....483...5.......1..... | initial |
| 284..5.63...32.48..3.48..5272....5.44....23.6.6...482...2....4834.2586..8.614.235 | autosolve |
| 284915763651327489937486152728631594495872316163594827512763948349258671876149235 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (4) D1: 7,9 H4: 1,9 B9: 7,9 F9: 7,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E1,G1: 1.. / E1 = 1 => 11 pairs (_) / G1 = 1 => 15 pairs (_) C4,C6: 3.. / C4 = 3 => 6 pairs (_) / C6 = 3 => 6 pairs (_) E7,F7: 3.. / E7 = 3 => 15 pairs (_) / F7 = 3 => 8 pairs (_) C6,E6: 3.. / C6 = 3 => 6 pairs (_) / E6 = 3 => 6 pairs (_) F4,F7: 3.. / F4 = 3 => 15 pairs (_) / F7 = 3 => 8 pairs (_) D5,D6: 5.. / D5 = 5 => 6 pairs (_) / D6 = 5 => 5 pairs (_) A7,B7: 5.. / A7 = 5 => 5 pairs (_) / B7 = 5 => 8 pairs (_) A2,A3: 6.. / A2 = 6 => 5 pairs (_) / A3 = 6 => 4 pairs (_) F2,F3: 6.. / F2 = 6 => 4 pairs (_) / F3 = 6 => 5 pairs (_) D4,E4: 6.. / D4 = 6 => 8 pairs (_) / E4 = 6 => 5 pairs (_) D7,E7: 6.. / D7 = 6 => 5 pairs (_) / E7 = 6 => 8 pairs (_) A2,F2: 6.. / A2 = 6 => 5 pairs (_) / F2 = 6 => 4 pairs (_) A3,F3: 6.. / A3 = 6 => 4 pairs (_) / F3 = 6 => 5 pairs (_) D4,D7: 6.. / D4 = 6 => 8 pairs (_) / D7 = 6 => 5 pairs (_) E4,E7: 6.. / E4 = 6 => 5 pairs (_) / E7 = 6 => 8 pairs (_) H5,I6: 7.. / H5 = 7 => 7 pairs (_) / I6 = 7 => 10 pairs (_) B9,F9: 7.. / B9 = 7 => 9 pairs (_) / F9 = 7 => 10 pairs (_) H5,H8: 7.. / H5 = 7 => 7 pairs (_) / H8 = 7 => 10 pairs (_) C4,C5: 8.. / C4 = 8 => 9 pairs (_) / C5 = 8 => 4 pairs (_) D4,D5: 8.. / D4 = 8 => 4 pairs (_) / D5 = 8 => 9 pairs (_) C4,D4: 8.. / C4 = 8 => 9 pairs (_) / D4 = 8 => 4 pairs (_) C5,D5: 8.. / C5 = 8 => 4 pairs (_) / D5 = 8 => 9 pairs (_) B9,F9: 9.. / B9 = 9 => 10 pairs (_) / F9 = 9 => 9 pairs (_) * DURATION: 0:00:35.347358 START: 15:55:01.340346 END: 15:55:36.687704 2017-05-04 * CP COUNT: (23) * INCONCLUSIVE -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B9,D1,F9,H4) * 284..5.63...32.48..3.48..5272....5.44....23.6.6...482...2....4834.2586..8.614.235 * PAIR D1: 7,9 BLK 2 E1: 7,9,1 # reduction candidate for 7,9 E1: 7,9 # 15 pairs F2: 7,9,1,6 # reduction candidate for 7,9 F2: 7,9 # 13 pairs F3: 7,9,1,6 # reduction candidate for 7,9 F3: 7,9 # 12 pairs * PAIR D1: 7,9 ROW 1 G1: 7,9,1 # reduction candidate for 7,9 G1: 1 # 15 pairs G1: 7,9 # 11 pairs * PAIR D1: 7,9 COL D D5: 7,9,5,8 # reduction candidate for 7,9 D5: 7,9 # 6 pairs D6: 7,9,5 # reduction candidate for 7,9 D6: 7,9 # 6 pairs D7: 7,9,6 # reduction candidate for 7,9 D7: 7,9 # 8 pairs * PAIR H4: 1,9 BLK 6 H5: 1,9,7 # reduction candidate for 1,9 H5: 1,9 # 10 pairs I6: 1,9,7 # reduction candidate for 1,9 I6: 1,9 # 7 pairs * PAIR H4: 1,9 ROW 4 C4: 1,9,3,8 # reduction candidate for 1,9 C4: 1,9 # 15 pairs E4: 1,9,3,6 # reduction candidate for 1,9 E4: 1,9 => CTR * 284..5.63...32.48..3.48..5272.6..5.44..8.23.6.6.5.482...2.63.4834.2586..8.614.235 E4: 3,6 # 5 pairs F4: 1,9,3 # reduction candidate for 1,9 F4: 1,9 # 8 pairs * PAIR H4: 1,9 COL H H8: 1,9,7 # reduction candidate for 1,9 H8: 7 # 10 pairs H8: 1,9 # 7 pairs * PAIR B9: 7,9 BLK 7 B7: 7,9,1,5 # reduction candidate for 7,9 B7: 7,9 => CTR * 284.15.63...32.48113.486.5272...159441...2376.6...482.5.2...1483412586..8.614.235 B7: 1,5 # 5 pairs C8: 7,9,1 # reduction candidate for 7,9 C8: 7,9 # 9 pairs * PAIR B9: 7,9 COL B B2: 7,9,1,5 # reduction candidate for 7,9 B2: 1,5 # 8 pairs B2: 7,9 # 7 pairs * PAIR F9: 7,9 BLK 8 D7: 7,9,6 # reduction candidate for 7,9 D7: 7,9 # 8 pairs E7: 7,9,3,6 # reduction candidate for 7,9 E7: 7,9 # 6 pairs F7: 7,9,3 # reduction candidate for 7,9 F7: 7,9 # 15 pairs * PAIR F9: 7,9 COL F F2: 7,9,1,6 # reduction candidate for 7,9 F2: 7,9 # 13 pairs F3: 7,9,1,6 # reduction candidate for 7,9 F3: 7,9 # 12 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-382-base-pr-000.dot * REASONING * DIS # E4: 1,9 => CTR => E4: 3,6 * DIS # B7: 7,9 => CTR => B7: 1,5 * CNT 2 HDP CHAINS / 26 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B9,D1,F9,H4) * 284..5.63...32.48..3.48..5272....5.44....23.6.6...482...2....4834.2586..8.614.235 * PAIR D1: 7,9 BLK 2 E1: 7,9,1 # reduction candidate for 7,9 E1: 7,9 # 15 pairs F2: 7,9,1,6 # reduction candidate for 7,9 F2: 7,9 # 13 pairs F3: 7,9,1,6 # reduction candidate for 7,9 F3: 7,9 # 12 pairs * PAIR D1: 7,9 ROW 1 G1: 7,9,1 # reduction candidate for 7,9 G1: 1 # 15 pairs G1: 7,9 # 11 pairs * PAIR D1: 7,9 COL D D5: 7,9,5,8 # reduction candidate for 7,9 D5: 7,9 # 6 pairs D6: 7,9,5 # reduction candidate for 7,9 D6: 7,9 # 6 pairs D7: 7,9,6 # reduction candidate for 7,9 D7: 7,9 # 8 pairs * PAIR H4: 1,9 BLK 6 H5: 1,9,7 # reduction candidate for 1,9 H5: 1,9 # 10 pairs I6: 1,9,7 # reduction candidate for 1,9 I6: 1,9 # 7 pairs * PAIR H4: 1,9 ROW 4 C4: 1,9,3,8 # reduction candidate for 1,9 C4: 1,9 # 15 pairs E4: 1,9,3,6 # reduction candidate for 1,9 E4: 1,9 => CTR * 284..5.63...32.48..3.48..5272.6..5.44..8.23.6.6.5.482...2.63.4834.2586..8.614.235 F4: 1,9,3 # reduction candidate for 1,9 F4: 1,9 # 8 pairs * PAIR H4: 1,9 COL H H8: 1,9,7 # reduction candidate for 1,9 H8: 7 # 11 pairs H8: 1,9 # 8 pairs * PAIR RESTART * PAIR H4: 1,9 BLK 6 H5: 1,9,7 # reduction candidate for 1,9 H5: 1,9 # 11 pairs I6: 1,9,7 # reduction candidate for 1,9 I6: 1,9 # 8 pairs * PAIR H4: 1,9 ROW 4 C4: 1,9,3,8 # reduction candidate for 1,9 C4: 1,9 # 15 pairs F4: 1,9,3 # reduction candidate for 1,9 F4: 1,9 # 8 pairs * PAIR H4: 1,9 COL H H8: 1,9,7 # reduction candidate for 1,9 H8: 7 # 11 pairs H8: 1,9 # 8 pairs * PAIR B9: 7,9 BLK 7 B7: 7,9,1,5 # reduction candidate for 7,9 B7: 7,9 => CTR * 284.15.63...32.48113.486.5272...159441...2376.6...482.5.2...1483412586..8.614.235 C8: 7,9,1 # reduction candidate for 7,9 C8: 7,9 # 10 pairs * RESTART * PAIR B9: 7,9 BLK 7 C8: 7,9,1 # reduction candidate for 7,9 C8: 1 => CTR * 284.15.63...32.48113.486.5272...159441...2376.6...482.952...1483412586..876149235 * PAIR B9: 7,9 COL B B2: 7,9,1,5 # reduction candidate for 7,9 B2: 1,5 # 21 pairs B2: 7,9 # 14 pairs * PAIR F9: 7,9 BLK 8 D7: 7,9,6 # reduction candidate for 7,9 D7: 7,9 # 13 pairs E7: 7,9,3,6 # reduction candidate for 7,9 E7: 7,9 # 11 pairs F7: 7,9,3 # reduction candidate for 7,9 F7: 7,9 # 15 pairs * PAIR F9: 7,9 COL F F2: 7,9,1,6 # reduction candidate for 7,9 F2: 7,9 => SOLVED * 284915763651327489937486152728631594495872316163594827512763948349258671876149235 * DURATION: 0:00:28.623098 START: 15:55:59.144694 END: 15:56:27.767792 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-382-base-pr-001.dot * REASONING * DIS # E4: 1,9 => CTR => E4: 3,6 * DIS E4: 3,6 # B7: 7,9 => CTR => B7: 1,5 * DIS E4: 3,6 + B7: 1,5 # C8: 1 => CTR => C8: 7,9 * PRF E4: 3,6 + B7: 1,5 + C8: 7,9 # F2: 7,9 => SOL * STA E4: 3,6 + B7: 1,5 + C8: 7,9 + F2: 7,9 * CNT 4 HDP CHAINS / 31 HYP OPENED
Header Info
Top 500 Minimum 17 382 solution: 284915763651327489937486152728631594495872316163594827512763948349258671876149235 info: 33318 FNBTXYO S8.f 42956 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 284915763651327489937486152728631594495872316163594827512763948349258671876149235 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 # E1: 7,9 => UNS * INC # F2: 7,9 => UNS * INC # F3: 7,9 => UNS * INC # G1: 7,9 => UNS * INC # G1: 1 => UNS * INC # D5: 7,9 => UNS * INC # D6: 7,9 => UNS * INC # D7: 7,9 => UNS * INC # H5: 1,9 => UNS * INC # I6: 1,9 => UNS * INC # C4: 1,9 => UNS * DIS # E4: 1,9 => CTR => E4: 3,6 * INC # E4: 3,6 => UNS * INC # F4: 1,9 => UNS * INC # H8: 1,9 => UNS * INC # H8: 7 => UNS * DIS # B7: 7,9 => CTR => B7: 1,5 * INC # B7: 1,5 => UNS * INC # C8: 7,9 => UNS * INC # B2: 7,9 => UNS * INC # B2: 1,5 => UNS * INC # D7: 7,9 => UNS * INC # E7: 7,9 => UNS * INC # F7: 7,9 => UNS * INC # F2: 7,9 => UNS * INC # F3: 7,9 => UNS * CNT 26 HDP CHAINS / 26 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # E1: 7,9 => UNS * INC # F2: 7,9 => UNS * INC # F3: 7,9 => UNS * INC # G1: 7,9 => UNS * INC # G1: 1 => UNS * INC # D5: 7,9 => UNS * INC # D6: 7,9 => UNS * INC # D7: 7,9 => UNS * INC # H5: 1,9 => UNS * INC # I6: 1,9 => UNS * INC # C4: 1,9 => UNS * DIS # E4: 1,9 => CTR => E4: 3,6 * INC E4: 3,6 # F4: 1,9 => UNS * INC E4: 3,6 # H8: 1,9 => UNS * INC E4: 3,6 # H8: 7 => UNS * INC E4: 3,6 # H5: 1,9 => UNS * INC E4: 3,6 # I6: 1,9 => UNS * INC E4: 3,6 # C4: 1,9 => UNS * INC E4: 3,6 # F4: 1,9 => UNS * INC E4: 3,6 # H8: 1,9 => UNS * INC E4: 3,6 # H8: 7 => UNS * DIS E4: 3,6 # B7: 7,9 => CTR => B7: 1,5 * INC E4: 3,6 + B7: 1,5 # C8: 7,9 => UNS * INC E4: 3,6 + B7: 1,5 # C8: 7,9 => UNS * DIS E4: 3,6 + B7: 1,5 # C8: 1 => CTR => C8: 7,9 * INC E4: 3,6 + B7: 1,5 + C8: 7,9 # B2: 7,9 => UNS * INC E4: 3,6 + B7: 1,5 + C8: 7,9 # B2: 1,5 => UNS * INC E4: 3,6 + B7: 1,5 + C8: 7,9 # D7: 7,9 => UNS * INC E4: 3,6 + B7: 1,5 + C8: 7,9 # E7: 7,9 => UNS * INC E4: 3,6 + B7: 1,5 + C8: 7,9 # F7: 7,9 => UNS * PRF E4: 3,6 + B7: 1,5 + C8: 7,9 # F2: 7,9 => SOL * STA E4: 3,6 + B7: 1,5 + C8: 7,9 + F2: 7,9 * CNT 31 HDP CHAINS / 31 HYP OPENED