Analysis of xx-top500-197-base.sdk
Contents
Original Sudoku
level: medium
position: ..7.4.........1.........2.....3..9...1....4..65.......2..79.......8...5...9.....1 initial
Autosolve
position: 32754.19.4.8..15..1.5...2..8723.491.913...4..6541.98..2317956..7468123595894..721 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D2: 6,9 => CTR => D2: 2 * PRF # D2: 2 => SOL * PRF # F5: 6,8 => SOL * DIS # F5: 7 => CTR => F5: 6,8 * DIS # D2: 6,9 => CTR => D2: 2 * PRF # D2: 2 => SOL * DIS # I3: 4,8 => CTR => I3: 3,7 * PRF # I3: 3,7 => SOL * DIS # E5: 5,6 => CTR => E5: 2,7,8 * PRF # E5: 2,7,8 => SOL * PRF # E5: 2,6 => SOL * DIS # I5: 2,6 => CTR => I5: 5,7 * PRF # I5: 5,7 => SOL * DIS # D2: 9 => CTR => D2: 2,6 * PRF # E5: 2,7 => SOL * DIS # I6: 3 => CTR => I6: 2,7 * PRF # E2: 3,6 => SOL * PRF # I5: 5,6 => SOL * DIS # I5: 2,7 => CTR => I5: 5,6 * DIS # I5: 6,7 => CTR => I5: 2,5 * DIS # E5: 6,7 => CTR => E5: 2,5,8 * DIS # F5: 6,7 => CTR => F5: 8 * PRF # F5: 8 => SOL * DIS # H2: 3 => CTR => H2: 6,7 * DIS # I6: 3,7 => CTR => I6: 2 * PRF # I6: 2 => SOL * DIS # H2: 3,7 => CTR => H2: 6 * PRF # H2: 6 => SOL * PRF # E2: 3,6 => SOL * DIS # I3: 4,8 => CTR => I3: 3,7 * PRF # I3: 3,7 => SOL * CNT 31 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 # D2: 6,9 => CTR => D2: 2 * PRF D2: 2 => SOL * STA D2: 2 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..7.4.........1.........2.....3..9...1....4..65.......2..79.......8...5...9.....1 | initial |
| 32754.19.4.8..15..1.5...2..8723.491.913...4..6541.98..2317956..7468123595894..721 | autosolve |
| 327546198498231567165987243872354916913628475654179832231795684746812359589463721 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) B2: 6,9 B3: 6,9 F1: 6,8 D3: 6,9 I1: 6,8 H3: 4,8 E4: 5,6 D5: 2,6 E6: 2,7 I4: 5,6 H5: 6,7 H6: 3,7 E9: 3,6 F9: 3,6 H7: 4,8 I7: 4,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D2,E2: 2.. / D2 = 2 => 0 pairs (*) / E2 = 2 => 0 pairs (X) I5,I6: 2.. / I5 = 2 => 0 pairs (X) / I6 = 2 => 0 pairs (_) E6,I6: 2.. / E6 = 2 => 0 pairs (X) / I6 = 2 => 0 pairs (_) D2,D5: 2.. / D2 = 2 => 0 pairs (*) / D5 = 2 => 0 pairs (X) H6,I6: 3.. / H6 = 3 => 17 pairs (_) / I6 = 3 => 0 pairs (X) E9,F9: 3.. / E9 = 3 => 0 pairs (X) / F9 = 3 => 0 pairs (_) F3,F9: 3.. / F3 = 3 => 0 pairs (X) / F9 = 3 => 0 pairs (_) H2,H6: 3.. / H2 = 3 => 0 pairs (X) / H6 = 3 => 17 pairs (_) H3,I3: 4.. / H3 = 4 => 13 pairs (_) / I3 = 4 => 0 pairs (X) H7,I7: 4.. / H7 = 4 => 0 pairs (X) / I7 = 4 => 13 pairs (_) H3,H7: 4.. / H3 = 4 => 13 pairs (_) / H7 = 4 => 0 pairs (X) I3,I7: 4.. / I3 = 4 => 0 pairs (X) / I7 = 4 => 13 pairs (_) E4,E5: 5.. / E4 = 5 => 0 pairs (*) / E5 = 5 => 0 pairs (X) I4,I5: 5.. / I4 = 5 => 0 pairs (X) / I5 = 5 => 0 pairs (_) E4,I4: 5.. / E4 = 5 => 0 pairs (*) / I4 = 5 => 0 pairs (X) E5,I5: 5.. / E5 = 5 => 0 pairs (X) / I5 = 5 => 0 pairs (_) B2,B3: 6.. / B2 = 6 => 0 pairs (X) / B3 = 6 => 14 pairs (_) E9,F9: 6.. / E9 = 6 => 0 pairs (*) / F9 = 6 => 0 pairs (X) F1,I1: 6.. / F1 = 6 => 0 pairs (*) / I1 = 6 => 0 pairs (X) B3,D3: 6.. / B3 = 6 => 14 pairs (_) / D3 = 6 => 0 pairs (X) E4,I4: 6.. / E4 = 6 => 0 pairs (X) / I4 = 6 => 0 pairs (_) H2,H5: 6.. / H2 = 6 => 0 pairs (*) / H5 = 6 => 0 pairs (X) F3,F5: 7.. / F3 = 7 => 0 pairs (*) / F5 = 7 => 0 pairs (X) E5,F5: 8.. / E5 = 8 => 0 pairs (X) / F5 = 8 => 0 pairs (_) H7,I7: 8.. / H7 = 8 => 13 pairs (_) / I7 = 8 => 0 pairs (X) F1,I1: 8.. / F1 = 8 => 0 pairs (X) / I1 = 8 => 0 pairs (_) E3,E5: 8.. / E3 = 8 => 0 pairs (*) / E5 = 8 => 0 pairs (X) H3,H7: 8.. / H3 = 8 => 0 pairs (X) / H7 = 8 => 13 pairs (_) B2,B3: 9.. / B2 = 9 => 14 pairs (_) / B3 = 9 => 0 pairs (X) D2,D3: 9.. / D2 = 9 => 0 pairs (X) / D3 = 9 => 14 pairs (_) B2,D2: 9.. / B2 = 9 => 14 pairs (_) / D2 = 9 => 0 pairs (X) B3,D3: 9.. / B3 = 9 => 0 pairs (X) / D3 = 9 => 14 pairs (_) * DURATION: 0:00:54.922588 START: 09:28:02.156834 END: 09:28:57.079422 2017-05-04 * CP COUNT: (32) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B3,D3,D5,E4,E6,E9,F1,F9,H3,H5,H6,H7,I1,I4,I7) * 32754.19.4.8..15..1.5...2..8723.491.913...4..6541.98..2317956..7468123595894..721 * PAIR B2: 6,9 ROW 2 D2: 6,9,2 # reduction candidate for 6,9 D2: 6,9 => CTR * 32754.19.4.8.215731.5.372..8723.49159132..4.76541798322317956..7468123595894.3721 D2: 2 => SOLVED * 327546198498231567165987243872354916913628475654179832231795684746812359589463721 * PAIR F1: 6,8 COL F F5: 6,8,7 # reduction candidate for 6,8 F5: 6,8 => SOLVED * 327546198498231567165987243872354916913628475654179832231795684746812359589463721 F5: 7 => CTR * 32754.19.4.8..15..1.5...2..8723.491.913.874656541.98..2317956..7468123595894..721 * PAIR D3: 6,9 BLK 2 D2: 6,9,2 # reduction candidate for 6,9 D2: 6,9 => CTR * 32754.19.4.8.215731.5.372..8723.49159132..4.76541798322317956..7468123595894.3721 D2: 2 => SOLVED * 327546198498231567165987243872354916913628475654179832231795684746812359589463721 * PAIR H3: 4,8 BLK 3 I3: 4,8,3,7 # reduction candidate for 4,8 I3: 4,8 => CTR * 3275481964.8..15..1.5...2..8723649159132..4..6541.98..2317956..7468123595894..721 I3: 3,7 => SOLVED * 327546198498231567165987243872354916913628475654179832231795684746812359589463721 * PAIR E4: 5,6 BLK 5 E5: 5,6,2,7,8 # reduction candidate for 5,6 E5: 5,6 => CTR * 3275461984.8.215.31.598.24.8723.491.913..84..6541798322317956847468123595894..721 E5: 2,7,8 => SOLVED * 327546198498231567165987243872354916913628475654179832231795684746812359589463721 * PAIR D5: 2,6 BLK 5 E5: 2,6,5,7,8 # reduction candidate for 2,6 E5: 2,6 => SOLVED * 327546198498231567165987243872354916913628475654179832231795684746812359589463721 E5: 5,7,8 # 16 pairs * PAIR D5: 2,6 ROW 5 I5: 2,6,5,7 # reduction candidate for 2,6 I5: 2,6 => CTR * 3275461984.8.2156.1.5...2..8723.4915913.584766541798322317956..7468123595894..721 I5: 5,7 => SOLVED * 327546198498231567165987243872354916913628475654179832231795684746812359589463721 * PAIR D5: 2,6 COL D D2: 2,6,9 # reduction candidate for 2,6 D2: 9 => CTR * 3275481964689215731956372..87236491.9132..4..6541798322317956..7468123595894..721 D2: 2,6 # 14 pairs * PAIR E6: 2,7 BLK 5 E5: 2,7,5,6,8 # reduction candidate for 2,7 E5: 2,7 => SOLVED * 327546198498231567165987243872354916913628475654179832231795684746812359589463721 E5: 5,6,8 # 16 pairs * PAIR E6: 2,7 ROW 6 I6: 2,7,3 # reduction candidate for 2,7 I6: 3 => CTR * 32754.19.4.8..15..1.5...2..8723.491.913...4.26541298732317956..7468123595894..721 I6: 2,7 # 17 pairs * PAIR E6: 2,7 COL E E2: 2,7,3,6 # reduction candidate for 2,7 E2: 3,6 => SOLVED * 327546198498231567165987243872354916913628475654179832231795684746812359589463721 E2: 2,7 # 18 pairs * PAIR I4: 5,6 BLK 6 I5: 5,6,2,7 # reduction candidate for 5,6 I5: 5,6 => SOLVED * 327546198498231567165987243872354916913628475654179832231795684746812359589463721 I5: 2,7 => CTR * 3275461984.8.2157.1.5...2..8723.4915913.584676541798322317956..7468123595894..721 * PAIR H5: 6,7 BLK 6 I5: 6,7,2,5 # reduction candidate for 6,7 I5: 6,7 => CTR * 3275461984.8.215.31659..2..8723.4915913.584..6541798322317956..7468123595894..721 I5: 2,5 # 17 pairs * PAIR H5: 6,7 ROW 5 E5: 6,7,2,5,8 # reduction candidate for 6,7 E5: 6,7 => CTR * 3275461984.8.2156.1.5.8.24.872354916913..84756541798322317956847468123595894..721 E5: 2,5,8 # 16 pairs F5: 6,7,8 # reduction candidate for 6,7 F5: 6,7 => CTR * 32754.19.4.8.215..1.5...2..8723549169132864756541798322317956..746812359589463721 F5: 8 => SOLVED * 327546198498231567165987243872354916913628475654179832231795684746812359589463721 * PAIR H5: 6,7 COL H H2: 6,7,3 # reduction candidate for 6,7 H2: 3 => CTR * 32754.19.4.8..153.1.5...2..8723.491.913...46.6541.98732317956..7468123595894..721 H2: 6,7 # 17 pairs * PAIR H6: 3,7 BLK 6 I6: 3,7,2 # reduction candidate for 3,7 I6: 3,7 => CTR * 32754.19.4.82.15..1.59..2..8723.49159136..4.26541298..2317956..7468123595894..721 I6: 2 => SOLVED * 327546198498231567165987243872354916913628475654179832231795684746812359589463721 * PAIR H6: 3,7 COL H H2: 3,7,6 # reduction candidate for 3,7 H2: 3,7 => CTR * 32754.19.4.8..15..1.5...2..8723649159132584676541798322317956..746812359589436721 H2: 6 => SOLVED * 327546198498231567165987243872354916913628475654179832231795684746812359589463721 * PAIR E9: 3,6 COL E E2: 3,6,2,7 # reduction candidate for 3,6 E2: 3,6 => SOLVED * 327546198498231567165987243872354916913628475654179832231795684746812359589463721 E2: 2,7 # 18 pairs * PAIR I7: 4,8 COL I I3: 4,8,3,7 # reduction candidate for 4,8 I3: 4,8 => CTR * 3275481964.8..15..1.5...2..8723649159132..4..6541.98..2317956..7468123595894..721 I3: 3,7 => SOLVED * 327546198498231567165987243872354916913628475654179832231795684746812359589463721 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-197-base-pr-000.dot * REASONING * DIS # D2: 6,9 => CTR => D2: 2 * PRF # D2: 2 => SOL * PRF # F5: 6,8 => SOL * DIS # F5: 7 => CTR => F5: 6,8 * DIS # D2: 6,9 => CTR => D2: 2 * PRF # D2: 2 => SOL * DIS # I3: 4,8 => CTR => I3: 3,7 * PRF # I3: 3,7 => SOL * DIS # E5: 5,6 => CTR => E5: 2,7,8 * PRF # E5: 2,7,8 => SOL * PRF # E5: 2,6 => SOL * DIS # I5: 2,6 => CTR => I5: 5,7 * PRF # I5: 5,7 => SOL * DIS # D2: 9 => CTR => D2: 2,6 * PRF # E5: 2,7 => SOL * DIS # I6: 3 => CTR => I6: 2,7 * PRF # E2: 3,6 => SOL * PRF # I5: 5,6 => SOL * DIS # I5: 2,7 => CTR => I5: 5,6 * DIS # I5: 6,7 => CTR => I5: 2,5 * DIS # E5: 6,7 => CTR => E5: 2,5,8 * DIS # F5: 6,7 => CTR => F5: 8 * PRF # F5: 8 => SOL * DIS # H2: 3 => CTR => H2: 6,7 * DIS # I6: 3,7 => CTR => I6: 2 * PRF # I6: 2 => SOL * DIS # H2: 3,7 => CTR => H2: 6 * PRF # H2: 6 => SOL * PRF # E2: 3,6 => SOL * DIS # I3: 4,8 => CTR => I3: 3,7 * PRF # I3: 3,7 => SOL * CNT 31 HDP CHAINS / 40 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B3,D3,D5,E4,E6,E9,F1,F9,H3,H5,H6,H7,I1,I4,I7) * 32754.19.4.8..15..1.5...2..8723.491.913...4..6541.98..2317956..7468123595894..721 * PAIR B2: 6,9 ROW 2 D2: 6,9,2 # reduction candidate for 6,9 D2: 6,9 => CTR * 32754.19.4.8.215731.5.372..8723.49159132..4.76541798322317956..7468123595894.3721 D2: 2 => SOLVED * 327546198498231567165987243872354916913628475654179832231795684746812359589463721 * DURATION: 0:00:02.982495 START: 09:29:41.656044 END: 09:29:44.638539 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-197-base-pr-001.dot * REASONING * DIS # D2: 6,9 => CTR => D2: 2 * PRF D2: 2 => SOL * STA D2: 2 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 197 solution: 327546198498231567165987243872354916913628475654179832231795684746812359589463721 info: 1880 FNTHWY S8.f 45534 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 327546198498231567165987243872354916913628475654179832231795684746812359589463721 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 # D2: 6,9 => CTR => D2: 2 * PRF # D2: 2 => SOL * PRF # F5: 6,8 => SOL * DIS # F5: 7 => CTR => F5: 6,8 * DIS # D2: 6,9 => CTR => D2: 2 * PRF # D2: 2 => SOL * DIS # I3: 4,8 => CTR => I3: 3,7 * PRF # I3: 3,7 => SOL * DIS # E5: 5,6 => CTR => E5: 2,7,8 * PRF # E5: 2,7,8 => SOL * PRF # E5: 2,6 => SOL * INC # E5: 5,7,8 => UNS * DIS # I5: 2,6 => CTR => I5: 5,7 * PRF # I5: 5,7 => SOL * INC # D2: 2,6 => UNS * DIS # D2: 9 => CTR => D2: 2,6 * PRF # E5: 2,7 => SOL * INC # E5: 5,6,8 => UNS * INC # I6: 2,7 => UNS * DIS # I6: 3 => CTR => I6: 2,7 * INC # E2: 2,7 => UNS * PRF # E2: 3,6 => SOL * PRF # I5: 5,6 => SOL * DIS # I5: 2,7 => CTR => I5: 5,6 * DIS # I5: 6,7 => CTR => I5: 2,5 * INC # I5: 2,5 => UNS * DIS # E5: 6,7 => CTR => E5: 2,5,8 * INC # E5: 2,5,8 => UNS * DIS # F5: 6,7 => CTR => F5: 8 * PRF # F5: 8 => SOL * INC # H2: 6,7 => UNS * DIS # H2: 3 => CTR => H2: 6,7 * DIS # I6: 3,7 => CTR => I6: 2 * PRF # I6: 2 => SOL * DIS # H2: 3,7 => CTR => H2: 6 * PRF # H2: 6 => SOL * PRF # E2: 3,6 => SOL * INC # E2: 2,7 => UNS * DIS # I3: 4,8 => CTR => I3: 3,7 * PRF # I3: 3,7 => SOL * CNT 40 HDP CHAINS / 40 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # D2: 6,9 => CTR => D2: 2 * PRF D2: 2 => SOL * STA D2: 2 * CNT 2 HDP CHAINS / 1 HYP OPENED